Using Simulink

Using Simulink
SIMULINK
®
Dynamic System Simulation for MATLAB®
Modeling
Simulation
Implementation
Using Simulink
Version 3
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Using Simulink
 COPYRIGHT 1990 - 1999 by The MathWorks, Inc.
The software described in this document is furnished under a license agreement. The software may be used
or copied only under the terms of the license agreement. No part of this manual may be photocopied or reproduced in any form without prior written consent from The MathWorks, Inc.
U.S. GOVERNMENT: If Licensee is acquiring the Programs on behalf of any unit or agency of the U.S.
Government, the following shall apply: (a) For units of the Department of Defense: the Government shall
have only the rights specified in the license under which the commercial computer software or commercial
software documentation was obtained, as set forth in subparagraph (a) of the Rights in Commercial
Computer Software or Commercial Software Documentation Clause at DFARS 227.7202-3, therefore the
rights set forth herein shall apply; and (b) For any other unit or agency: NOTICE: Notwithstanding any
other lease or license agreement that may pertain to, or accompany the delivery of, the computer software
and accompanying documentation, the rights of the Government regarding its use, reproduction, and disclosure are as set forth in Clause 52.227-19 (c)(2) of the FAR.
MATLAB, Simulink, Stateflow, Handle Graphics, and Real-Time Workshop are registered trademarks and
the Target Language Compiler is a trademark of The MathWorks, Inc.
Other product or brand names are trademarks or registered trademarks of their respective holders.
Printing History: 1990
December 1996
May 1997
January 1998
January 1999
First printing
Revised for Simulink 2
Revised for Simulink 2.1 (online version)
Revised for Simulink 2.2 (online version)
Revised for Simulink 3 (Release 11)
Contents
Getting Started
1
To the Reader . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2
What Is Simulink? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2
How to Use This Manual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
Application Toolboxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
The Simulink Real-Time Workshop . . . . . . . . . . . . . . . . . . . . 1-10
Key Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-10
The Real-Time Workshop Ada Extension . . . . . . . . . . . . . . . 1-12
Key Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-12
Blocksets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The DSP Blockset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Fixed-Point Blockset . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Nonlinear Control Design Blockset . . . . . . . . . . . . . . . . . .
The Power System Blockset . . . . . . . . . . . . . . . . . . . . . . . . . . .
1-14
1-14
1-14
1-16
1-16
Quick Start
2
Running a Demo Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Description of the Demo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Some Things to Try . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
What This Demo Illustrates . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Other Useful Demos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-2
2-3
2-4
2-5
2-5
i
Building a Simple Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6
Creating a Model
3
Starting Simulink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Creating a New Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Editing an Existing Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Entering Simulink Commands . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulink Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Zooming Block Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-2
3-3
3-3
3-3
3-5
3-6
Selecting Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-7
Selecting One Object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-7
Selecting More than One Object . . . . . . . . . . . . . . . . . . . . . . . . . 3-7
Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9
Block Data Tips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9
Virtual Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9
Copying and Moving Blocks from One Window to Another . . 3-10
Moving Blocks in a Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-12
Duplicating Blocks in a Model . . . . . . . . . . . . . . . . . . . . . . . . . . 3-12
Specifying Block Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-12
Block Properties Dialog Box . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-13
Deleting Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-14
Changing the Orientation of Blocks . . . . . . . . . . . . . . . . . . . . . 3-15
Resizing Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-15
Manipulating Block Names . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-16
Displaying Parameters Beneath a Block’s Icon . . . . . . . . . . . . 3-17
Disconnecting Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-18
Vector Input and Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-18
Scalar Expansion of Inputs and Parameters . . . . . . . . . . . . . . 3-18
Assigning Block Priorities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-19
Using Drop Shadows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-20
Libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-21
Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-21
ii
Creating a Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Modifying a Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Copying a Library Block into a Model . . . . . . . . . . . . . . . . . . .
Updating a Linked Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Breaking a Link to a Library Block . . . . . . . . . . . . . . . . . . . . .
Finding the Library Block for a Reference Block . . . . . . . . . . .
Getting Information About Library Blocks . . . . . . . . . . . . . . .
Browsing Block Libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-21
3-22
3-22
3-23
3-23
3-24
3-24
3-25
Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Drawing a Line Between Blocks . . . . . . . . . . . . . . . . . . . . . . . .
Drawing a Branch Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Drawing a Line Segment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Displaying Line Widths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Inserting Blocks in a Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Signal Labels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Setting Signal Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Signal Properties Dialog Box . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-27
3-27
3-28
3-28
3-31
3-31
3-32
3-34
3-35
Annotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-37
Working with Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Data Types Supported by Simulink . . . . . . . . . . . . . . . . . . . . .
Block Support for Data and Numeric Signal Types . . . . . . . . .
Specifying Block Parameter Data Types . . . . . . . . . . . . . . . . .
Creating Signals of a Specific Data Type . . . . . . . . . . . . . . . . .
Displaying Port Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . .
Data Type Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Data Typing Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Enabling Strict Boolean Type Checking . . . . . . . . . . . . . . . . . .
Typecasting Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Typecasting Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-38
3-38
3-39
3-43
3-43
3-43
3-43
3-44
3-45
3-45
3-45
Working with Complex Signals . . . . . . . . . . . . . . . . . . . . . . . . 3-47
Summary of Mouse and Keyboard Actions . . . . . . . . . . . . . . 3-48
Creating Subsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-51
Creating a Subsystem by Adding the Subsystem Block . . . . . 3-51
iii
Creating a Subsystem by Grouping Existing Blocks . . . . . . . . 3-52
Labeling Subsystem Ports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-53
Using Callback Routines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-53
Tips for Building Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-57
Modeling Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-58
Converting Celsius to Fahrenheit . . . . . . . . . . . . . . . . . . . . . . . 3-58
Modeling a Simple Continuous System . . . . . . . . . . . . . . . . . . 3-59
Saving a Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-61
Printing a Block Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Print Dialog Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Print Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Specifying Paper Size and Orientation . . . . . . . . . . . . . . . . . . .
Positioning and Sizing a Diagram . . . . . . . . . . . . . . . . . . . . . . .
3-62
3-62
3-63
3-64
3-64
The Model Browser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-66
Using the Model Browser on Windows . . . . . . . . . . . . . . . . . . . 3-66
Using the Model Browser on UNIX . . . . . . . . . . . . . . . . . . . . . 3-67
Tracking Model Versions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Specifying the Current User . . . . . . . . . . . . . . . . . . . . . . . . . . .
Model Properties Dialog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Creating a Model Change History . . . . . . . . . . . . . . . . . . . . . . .
Version Control Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-70
3-70
3-72
3-76
3-77
Ending a Simulink Session . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-79
Running a Simulation
4
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2
Using Menu Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2
Running a Simulation from the Command Line . . . . . . . . . . . . 4-3
iv
Running a Simulation Using Menu Commands . . . . . . . . . . .
Setting Simulation Parameters and Choosing the Solver . . . . .
Applying the Simulation Parameters . . . . . . . . . . . . . . . . . . . . .
Starting the Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulation Diagnostics Dialog Box . . . . . . . . . . . . . . . . . . . . . . .
4-4
4-4
4-4
4-4
4-6
The Simulation Parameters Dialog Box . . . . . . . . . . . . . . . . . 4-8
The Solver Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8
The Workspace I/O Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-17
The Diagnostics Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-24
Improving Simulation Performance and Accuracy . . . . . . 4-27
Speeding Up the Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-27
Improving Simulation Accuracy . . . . . . . . . . . . . . . . . . . . . . . . 4-28
Running a Simulation from the Command Line . . . . . . . . .
Using the sim Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Using the set_param Command . . . . . . . . . . . . . . . . . . . . . . . .
sim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
simset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
simget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-29
4-29
4-29
4-30
4-32
4-36
Analyzing Simulation Results
5
Viewing Output Trajectories . . . . . . . . . . . . . . . . . . . . . . . . . . .
Using the Scope Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Using Return Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Using the To Workspace Block . . . . . . . . . . . . . . . . . . . . . . . . . .
5-2
5-2
5-2
5-3
Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4
Equilibrium Point Determination . . . . . . . . . . . . . . . . . . . . . . 5-7
linfun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-9
trim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-13
v
Using Masks to Customize Blocks
6
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-2
A Sample Masked Subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . .
Creating Mask Dialog Box Prompts . . . . . . . . . . . . . . . . . . . . . .
Creating the Block Description and Help Text . . . . . . . . . . . . .
Creating the Block Icon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6-3
6-4
6-6
6-6
6-8
The Mask Editor: An Overview . . . . . . . . . . . . . . . . . . . . . . . . . 6-9
The Initialization Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Prompts and Associated Variables . . . . . . . . . . . . . . . . . . . . . .
Control Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Default Values for Masked Block Parameters . . . . . . . . . . . . .
Tunable Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Initialization Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6-10
6-10
6-12
6-14
6-14
6-15
The Icon Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Displaying Text on the Block Icon . . . . . . . . . . . . . . . . . . . . . .
Displaying Graphics on the Block Icon . . . . . . . . . . . . . . . . . . .
Displaying Images on Masks . . . . . . . . . . . . . . . . . . . . . . . . . . .
Displaying a Transfer Function on the Block Icon . . . . . . . . . .
Controlling Icon Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6-18
6-18
6-20
6-21
6-22
6-23
The Documentation Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Mask Type Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Block Description Field . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Mask Help Text Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6-26
6-26
6-26
6-27
Creating Dynamic Dialogs for Masked Blocks . . . . . . . . . . 6-28
Setting Masked Block Dialog Parameters . . . . . . . . . . . . . . . . 6-28
Predefined Masked Dialog Parameters . . . . . . . . . . . . . . . . . . 6-29
vi
Conditionally Executed Subsystems
7
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-2
Enabled Subsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-3
Creating an Enabled Subsystem . . . . . . . . . . . . . . . . . . . . . . . . . 7-3
Blocks an Enabled Subsystem Can Contain . . . . . . . . . . . . . . . 7-5
Triggered Subsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-8
Creating a Triggered Subsystem . . . . . . . . . . . . . . . . . . . . . . . . . 7-9
Function-Call Subsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-10
Blocks That a Triggered Subsystem Can Contain . . . . . . . . . . 7-10
Triggered and Enabled Subsystems . . . . . . . . . . . . . . . . . . . .
Creating a Triggered and Enabled Subsystem . . . . . . . . . . . . .
A Sample Triggered and Enabled Subsystem . . . . . . . . . . . . .
Creating Alternately Executing Subsystems . . . . . . . . . . . . . .
7-11
7-11
7-12
7-12
Block Reference
8
What Each Block Reference Page Contains . . . . . . . . . . . . . . 8-2
Simulink Block Libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-3
Abs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-11
Algebraic Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-12
Backlash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-14
Band-Limited White Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-18
Bus Selector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-20
Chirp Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-22
Clock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-24
Combinatorial Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-25
Complex to Magnitude-Angle . . . . . . . . . . . . . . . . . . . . . . . . . . 8-28
Complex to Real-Imag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-29
Configurable Subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-30
Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-34
vii
Coulomb and Viscous Friction . . . . . . . . . . . . . . . . . . . . . . . . . . 8-35
Data Store Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-36
Data Store Read . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-38
Data Store Write . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-39
Data Type Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-41
Dead Zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-43
Demux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-45
Derivative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-49
Digital Clock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-51
Discrete Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-52
Discrete Pulse Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-54
Discrete State-Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-56
Discrete-Time Integrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-58
Discrete Transfer Fcn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-65
Discrete Zero-Pole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-67
Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-69
Dot Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-72
Enable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-74
Fcn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-76
First-Order Hold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-78
From . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-80
From File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-82
From Workspace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-85
Function-Call Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-88
Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-89
Goto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-91
Goto Tag Visibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-94
Ground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-95
Hit Crossing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-96
IC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-98
Inport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-99
Integrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-103
Logical Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-108
Look-Up Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-110
Look-Up Table (2-D) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-113
Magnitude-Angle to Complex . . . . . . . . . . . . . . . . . . . . . . . . . 8-116
Manual Switch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-118
Math Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-119
MATLAB Fcn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-121
Matrix Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-123
viii
Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Merge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
MinMax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Model Info . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Multiport Switch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Outport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pulse Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Quantizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ramp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Random Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rate Limiter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Real-Imag to Complex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Relational Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Relay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Repeating Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rounding Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Saturation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Selector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S-Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Signal Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sine Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Slider Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
State-Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Stop Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Switch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Terminator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
To File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
To Workspace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Transfer Fcn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Transport Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Trigonometric Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8-124
8-126
8-129
8-131
8-134
8-136
8-139
8-143
8-145
8-146
8-148
8-149
8-150
8-152
8-154
8-156
8-158
8-160
8-161
8-162
8-163
8-173
8-175
8-177
8-178
8-180
8-183
8-185
8-187
8-189
8-190
8-191
8-194
8-196
8-197
8-199
8-203
8-206
8-208
8-210
ix
Uniform Random Number . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Unit Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Variable Transport Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
XY Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Zero-Order Hold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Zero-Pole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8-212
8-214
8-216
8-218
8-219
8-221
8-222
Additional Topics
9
How Simulink Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-2
Zero Crossings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-3
Algebraic Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-7
Invariant Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-11
Discrete-Time Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Discrete Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sample Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Purely Discrete Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Multirate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sample Time Colors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mixed Continuous and Discrete Systems . . . . . . . . . . . . . . . . .
9-13
9-13
9-13
9-13
9-14
9-15
9-17
Model Construction Commands
10
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
How to Specify Parameters for the Commands . . . . . . . . . . . .
How to Specify a Path for a Simulink Object . . . . . . . . . . . . . .
add_block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
add_line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
bdclose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
bdroot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
x
Contents
10-2
10-3
10-3
10-4
10-5
10-6
10-7
close_system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-8
delete_block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-10
delete_line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-11
find_system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-12
gcb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-14
gcbh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-15
gcs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-16
get_param . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-17
new_system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-19
open_system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-20
replace_block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-21
save_system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-23
set_param . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-24
simulink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-26
Simulink Debugger
11
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-2
Using the Debugger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Starting the Debugger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Getting Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Entering Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
About Block Indexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Accessing the MATLAB Workspace . . . . . . . . . . . . . . . . . . . . .
11-3
11-3
11-4
11-4
11-4
11-4
Running a Simulation Incrementally . . . . . . . . . . . . . . . . . .
Stepping by Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Stepping by Time Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Stepping by Breakpoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Running a Simulation Nonstop . . . . . . . . . . . . . . . . . . . . . . . . .
11-6
11-6
11-7
11-8
11-8
Setting Breakpoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-9
Breaking at Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-9
Breaking at Time Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-11
Breaking on Nonfinite Values . . . . . . . . . . . . . . . . . . . . . . . . . 11-11
xi
Breaking on Step-Size Limiting Steps . . . . . . . . . . . . . . . . . . 11-12
Breaking at Zero-Crossings . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-12
xii
Contents
Displaying Information About the Simulation . . . . . . . . .
Displaying Block I/O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Displaying Algebraic Loop Information . . . . . . . . . . . . . . . . .
Displaying System States . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Displaying Integration Information . . . . . . . . . . . . . . . . . . . .
11-13
11-13
11-14
11-15
11-15
Displaying Information About the Model . . . . . . . . . . . . . .
Displaying a Model’s Block Execution Order . . . . . . . . . . . . .
Displaying a Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Displaying a Model’s Nonvirtual Systems . . . . . . . . . . . . . . .
Displaying a Model’s Nonvirtual Blocks . . . . . . . . . . . . . . . . .
Displaying Blocks with Potential Zero-Crossings . . . . . . . . .
Displaying Algebraic Loops . . . . . . . . . . . . . . . . . . . . . . . . . . .
Displaying Debug Settings . . . . . . . . . . . . . . . . . . . . . . . . . . .
11-17
11-17
11-17
11-18
11-18
11-20
11-20
11-21
Debugger Command Reference . . . . . . . . . . . . . . . . . . . . . . .
ashow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
atrace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
bafter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
break . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
bshow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
clear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
continue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
disp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ishow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
minor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
nanbreak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
next . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
quit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
slist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11-22
11-24
11-25
11-26
11-27
11-28
11-29
11-30
11-31
11-32
11-33
11-34
11-35
11-36
11-37
11-38
11-39
11-40
11-41
11-42
11-43
11-44
stop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
tbreak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
trace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
undisp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
untrace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xbreak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
zcbreak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
zclist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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11-46
11-47
11-48
11-49
11-50
11-51
11-52
Model and Block Parameters
A
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2
Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3
Common Block Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-7
Block-Specific Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-10
Mask Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-24
Model File Format
B
Model File Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Model Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
BlockDefaults Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
AnnotationDefaults Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
System Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B-2
B-3
B-3
B-3
B-3
A Sample Model File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-4
xiii
xiv Contents
1
Getting Started
To the Reader . . . . . . . . . . . . . . . . . . . 1-2
What Is Simulink? . . . . . . . . . . . . . . . . . . 1-2
How to Use This Manual . . . . . . . . . . . . . . . 1-3
Application Toolboxes
. . . . . . . . . . . . . . . 1-5
The Simulink Real-Time Workshop . . . . . . . . . 1-10
Key Features . . . . . . . . . . . . . . . . . . . . 1-10
The Real-Time Workshop Ada Extension . . . . . . . 1-12
Key Features . . . . . . . . . . . . . . . . . . . . 1-12
Blocksets . . . . . . . . . . . .
The DSP Blockset . . . . . . . . .
The Fixed-Point Blockset . . . . . .
The Nonlinear Control Design Blockset
The Power System Blockset . . . . .
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. 1-16
1
Getting Started
To the Reader
Welcome to Simulink®! In the last few years, Simulink has become the most
widely used software package in academia and industry for modeling and
simulating dynamical systems.
Simulink encourages you to try things out. You can easily build models from
scratch, or take an existing model and add to it. Simulations are interactive, so
you can change parameters “on the fly” and immediately see what happens.
You have instant access to all of the analysis tools in MATLAB®, so you can
take the results and analyze and visualize them. We hope that you will get a
sense of the fun of modeling and simulation, through an environment that
encourages you to pose a question, model it, and see what happens.
With Simulink, you can move beyond idealized linear models to explore more
realistic nonlinear models, factoring in friction, air resistance, gear slippage,
hard stops, and the other things that describe real-world phenomena. It turns
your computer into a lab for modeling and analyzing systems that simply
wouldn’t be possible or practical otherwise, whether the behavior of an
automotive clutch system, the flutter of an airplane wing, the dynamics of a
predator-prey model, or the effect of the monetary supply on the economy.
Simulink is also practical. With thousands of engineers around the world using
it to model and solve real problems, knowledge of this tool will serve you well
throughout your professional career.
We hope you enjoy exploring the software.
What Is Simulink?
Simulink is a software package for modeling, simulating, and analyzing
dynamical systems. It supports linear and nonlinear systems, modeled in
continuous time, sampled time, or a hybrid of the two. Systems can also be
multirate, i.e., have different parts that are sampled or updated at different
rates.
For modeling, Simulink provides a graphical user interface (GUI) for building
models as block diagrams, using click-and-drag mouse operations. With this
interface, you can draw the models just as you would with pencil and paper (or
as most textbooks depict them). This is a far cry from previous simulation
packages that require you to formulate differential equations and difference
equations in a language or program. Simulink includes a comprehensive block
1-2
library of sinks, sources, linear and nonlinear components, and connectors. You
can also customize and create your own blocks. For information on creating
your own blocks, see the separate Writing S-Functions guide.
Models are hierarchical, so you can build models using both top-down and
bottom-up approaches. You can view the system at a high level, then
double-click on blocks to go down through the levels to see increasing levels of
model detail. This approach provides insight into how a model is organized and
how its parts interact.
After you define a model, you can simulate it, using a choice of integration
methods, either from the Simulink menus or by entering commands in
MATLAB’s command window. The menus are particularly convenient for
interactive work, while the command-line approach is very useful for running
a batch of simulations (for example, if you are doing Monte Carlo simulations
or want to sweep a parameter across a range of values). Using scopes and other
display blocks, you can see the simulation results while the simulation is
running. In addition, you can change parameters and immediately see what
happens, for “what if” exploration. The simulation results can be put in the
MATLAB workspace for postprocessing and visualization.
Model analysis tools include linearization and trimming tools, which can be
accessed from the MATLAB command line, plus the many tools in MATLAB
and its application toolboxes. And because MATLAB and Simulink are
integrated, you can simulate, analyze, and revise your models in either
environment at any point.
How to Use This Manual
Because Simulink is graphical and interactive, we encourage you to jump right
in and try it.
For a useful introduction that will help you start using Simulink quickly, take
a look at “Running a Demo Model” in Chapter 2. Browse around the model,
double-click on blocks that look interesting, and you will quickly get a sense of
how Simulink works. If you want a quick lesson in building a model, see
“Building a Simple Model” in Chapter 2.
Chapter 3 describes in detail how to build and edit a model. It also discusses
how to save and print a model and provides some useful tips.
Chapter 4 describes how Simulink performs a simulation. It covers simulation
parameters and the integration solvers used for simulation, including some of
1-3
1
Getting Started
the strengths and weaknesses of each solver that should help you choose the
appropriate solver for your problem. It also discusses multirate and hybrid
systems.
Chapter 5 discusses Simulink and MATLAB features useful for viewing and
analyzing simulation results.
Chapter 6 discusses methods for creating your own blocks and using masks to
customize their appearance and use.
Chapter 7 describes subsystems whose execution depends on triggering
signals.
Chapter 8 provides reference information for all Simulink blocks.
Chapter 9 provides information about how Simulink works, including
information about zero crossings, algebraic loops, and discrete and hybrid
systems.
Chapter 10 provides reference information for commands you can use to create
and modify a model from the MATLAB command window or from an M-file.
Chapter 11 explains how to use the Simulink debugger to debug Simulink
models. It also documents debugger commands.
Appendix A lists model and block parameters. This information is useful with
the get_param and set_param commands, described in Chapter 10.
Appendix B describes the format of the file that stores model information.
Although we have tried to provide the most complete and up-to-date
information in this manual, some information may have changed after it was
completed. Please check the Known Software and Documentation Problems
delivered with your Simulink system, for the latest release notes.
1-4
Application Toolboxes
Application Toolboxes
One of the key features of Simulink is that it is built on top of MATLAB. As a
result, Simulink users have direct access to the wide range of MATLAB-based
tools for generating, analyzing, and optimizing systems implemented in
Simulink. These tools include MATLAB Application Toolboxes, specialized
collections of M-files for working on particular classes of problems.
Toolboxes are more than just collections of useful functions; they represent the
efforts of some of the world’s top researchers in fields such as controls, signal
processing, and system identification. MATLAB Application Toolboxes
therefore let you “stand on the shoulders” of world class scientists.
All toolboxes are built using MATLAB. This has some very important
implications for you:
• Every toolbox builds on the robust numerics, rock-solid accuracy, and years
of experience in MATLAB.
• You get seamless and immediate integration with Simulink and any other
toolboxes you may own.
• Because all toolboxes are written in MATLAB code, you can take advantage
of MATLAB’s open-system approach. You can inspect M-files, add to them,
or use them for templates when creating your own functions.
• Every toolbox is available on any computer platform that runs MATLAB.
Here is a list of professional toolboxes currently available from The
MathWorks. This list is by no means static— more are being created every
year.
The Communications Toolbox. The Communications Toolbox provides an
integrated set of tools for accelerating the design, analysis, and simulation of
modern communications systems. It combines MATLAB's high-level language
with the ease of use of Simulink's block diagram interface, and provides
communications engineers with comprehensive communications system
design and analysis capabilities. The toolbox is useful in such diverse
industries as telecommunications, telephony, aerospace, and computer
peripherals.
1-5
1
Getting Started
The Control System Toolbox. The Control System Toolbox, the foundation of the
MATLAB control design toolbox family, contains functions for modeling,
analyzing, and designing automatic control systems. The application of
automatic control grows each year as sensors and computers become less
expensive. As a result, automatic controllers are used not only in highly
technical settings for automotive and aerospace systems, computer
peripherals, and process control, but also in less obvious applications such as
washing machines and cameras.
The Financial Toolbox. The Financial Toolbox operates with MATLAB to provide
a robust set of financial functions essential to financial and quantitative
analysis. Applications include pricing securities, calculating interest and yield,
analyzing derivatives, and optimizing portfolios. The Financial Toolbox
requires the Statistics and Optimization Toolboxes. The Simulink graphical
interface is recommended for Monte Carlo and non-stochastic simulations for
pricing fixed-income securities, derivatives, and other instruments.
The Frequency-Domain System Identification Toolbox. The Frequency-Domain System
Identification Toolbox by István Kollár, in cooperation with Johan Schoukens
and researchers at the Vrije Universiteit in Brussels, is a set of M-files for
modeling linear systems based on measurements of the system’s frequency
response.
The Fuzzy Logic Toolbox. The Fuzzy Logic Toolbox provides a complete set of
GUI-based tools for designing, simulating, and analyzing fuzzy inference
systems. Fuzzy logic provides an easily understandable, yet powerful way to
map an input space to an output space with arbitrary complexity, with rules
and relationships specified in natural language. Systems can be simulated in
MATLAB or incorporated into a Simulink block diagram, with the ability to
generate code for stand-alone execution.
The Higher-Order Spectral Analysis Toolbox. The Higher-Order Spectral Analysis
Toolbox, by Jerry Mendel, C. L. (Max) Nikias, and Ananthram Swami, provides
tools for signal processing using higher-order spectra. These methods are
particularly useful for analyzing signals originating from a nonlinear process
or corrupted by non-Gaussian noise.
The Image Processing Toolbox. The Image Processing Toolbox contains tools for
image processing and algorithm development. It includes tools for filter design
1-6
Application Toolboxes
and image restoration; image enhancement; analysis and statistics; color,
geometric, and morphological operations; and 2-D transforms.
The LMI Control Toolbox. The LMI Control Toolbox, authored by leading
researchers: Pascal Gahinet, Arkadi Nemirovski, and Alan Laub, allows one to
efficiently solve Linear Matrix Inequalities (LMIs). LMIs are special convex
optimization problems that arise in many disciplines, including control,
identification, filtering, structural design, graph theory, and linear algebra.
The LMI Control Toolbox also features a variety of LMI-based tools for control
systems design and covers applications such as robust stability and
performance analysis, robust gain scheduling, and multi-objective controller
synthesis with a mix of H-infinity, LQG, and pole placement objectives.
The Model Predictive Control Toolbox. The Model Predictive Control Toolbox was
written by Manfred Morari and N. Lawrence Ricker. Model predictive control
is especially useful for control applications with many input and output
variables, many of which have constraints. As a result, it has become
particularly popular in chemical engineering and other process control
applications.
The Mu-Analysis and Synthesis Toolbox. The Mu-Analysis and Synthesis Toolbox, by
Gary Balas, Andy Packard, John Doyle, Keith Glover, and Roy Smith, contains
specialized tools for H∞ optimal control, and µ-analysis and synthesis, an
approach to advanced robust control design of multivariable linear systems.
The NAG Foundation Toolbox. The NAG Foundation Toolbox includes more than
200 numeric computation functions from the well-regarded NAG Fortran
subroutine libraries. It provides specialized tools for boundary-value problems,
optimization, adaptive quadrature, surface and curve-fitting, and other
applications.
The Neural Network Toolbox. The Neural Network Toolbox by Howard Demuth
and Mark Beale is a collection of MATLAB functions for designing and
simulating neural networks. Neural networks are computing architectures,
inspired by biological nervous systems, that are useful in applications where
formal analysis is extremely difficult or impossible, such as pattern recognition
and nonlinear system identification and control.
The Optimization Toolbox. The Optimization Toolbox contains commands for the
optimization of general linear and nonlinear functions, including those with
1-7
1
Getting Started
constraints. An optimization problem can be visualized as trying to find the
lowest (or highest) point in a complex, highly contoured landscape. An
optimization algorithm can thus be likened to an explorer wandering through
valleys and across plains in search of the topographical extremes.
The Partial Differential Equation Toolbox. The Partial Differential Equation Toolbox
extends the MATLAB Technical Computing Environment for the study and
solution of PDEs in two space dimensions (2-D) and time. The PDE Toolbox
provides a set of command line functions and an intuitive graphical user
interface for preprocessing, solving, and postprocessing generic 2-D PDEs
using the Finite Element Method (FEM). The toolbox also provides automatic
and adaptive meshing capabilities and a suite of eight application modes for
common PDE application areas such as heat transfer, structural mechanics,
electrostatics, magnetostatics, and diffusion. These application areas are
common in the fields of engineering and physics.
The QFT Control Design Toolbox. The Quantitative Feedback Theory Toolbox by
Yossi Chait, Craig Borghesani, and Oded Yaniv implements QFT, a
frequency-domain approach to controller design for uncertain systems that
provides direct insight into the trade-offs between controller complexity (hence
the ability to implement it) and specifications.
The Robust Control Toolbox. The Robust Control Toolbox provides a specialized set
of tools for the analysis and synthesis of control systems that are “robust” with
respect to uncertainties that can arise in the real world. The Robust Control
Toolbox was created by controls theorists Richard Y. Chiang and Michael G.
Safonov.
The Signal Processing Toolbox. The Signal Processing Toolbox contains tools for
signal processing. Applications include audio (e.g., compact disc and digital
audio tape), video (digital HDTV, image processing, and compression),
telecommunications (fax and voice telephone), medicine (CAT scan, magnetic
resonance imaging), geophysics, and econometrics.
The Spline Toolbox. The Spline Toolbox by Carl de Boor, a pioneer in the field of
splines, provides a set of M-files for constructing and using splines, which are
piecewise polynomial approximations. Splines are useful because they can
approximate other functions without the unwelcome side effects that result
from other kinds of approximations, such as piecewise linear curves.
1-8
Application Toolboxes
The Statistics Toolbox. The Statistics Toolbox provides a set of M-files for
statistical data analysis, modeling, and Monte Carlo simulation, with
GUI-based tools for exploring fundamental concepts in statistics and
probability.
The Symbolic Math Toolbox. The Symbolic Math Toolbox gives MATLAB an
integrated set of tools for symbolic computation and variable-precision
arithmetic, based on Maple V. The Extended Symbolic Math Toolbox adds
support for Maple programming plus additional specialized functions.
The System Identification Toolbox. The System Identification Toolbox, written by
Lennart Ljung, is a collection of tools for estimation and identification. System
identification is a way to find a mathematical model for a physical system (like
an electric motor, or even a financial market) based only on a record of the
system’s inputs and outputs.
The Wavelet Toolbox. The Wavelet Toolbox provides a comprehensive collection of
routines for examining local, multiscale, or nonstationary phenomena. Wavelet
methods offer additional insight and performance in any application where
Fourier techniques have been used. The toolbox is useful in many signal and
image processing applications, including speech and audio processing,
communications, geophysics, finance, and medicine.
1-9
1
Getting Started
The Simulink Real-Time Workshop
The Simulink Real-Time Workshop® automatically generates C code directly
from Simulink block diagrams. This allows the execution of continuous,
discrete-time, and hybrid system models on a wide range of computer
platforms, including real-time hardware. Simulink is required.
The Real-Time Workshop can be used for:
• Rapid Prototyping. As a rapid prototyping tool, the Real-Time Workshop
enables you to implement your designs quickly without lengthy hand coding
and debugging. Control, signal processing, and dynamic system algorithms
can be implemented by developing graphical Simulink block diagrams and
automatically generating C code.
• Embedded Real-Time Control. Once a system has been designed with
Simulink, code for real-time controllers or digital signal processors can be
generated, cross-compiled, linked, and downloaded onto your selected target
processor. The Real-Time Workshop supports DSP boards, embedded
controllers, and a wide variety of custom and commercially available
hardware.
• Real-Time Simulation. You can create and execute code for an entire system
or specified subsystems for hardware-in-the-loop simulations. Typical
applications include training simulators (pilot-in-the-loop), real-time model
validation, and testing.
• Stand-Alone Simulation. Stand-alone simulations can be run directly on
your host machine or transferred to other systems for remote execution.
Because time histories are saved in MATLAB as binary or ASCII files, they
can be easily loaded into MATLAB for additional analysis or graphic display.
Key Features
Real-Time Workshop provides a comprehensive set of features and capabilities
that provide the flexibility to address a broad range of applications:
• Automatic code generation handles continuous-time, discrete-time, and
hybrid systems.
• Optimized code guarantees fast execution.
1-10
The Simulink Real-Time Workshop
• Control framework Application Program Interface (API) uses customizable
makefiles to build and download object files to target hardware
automatically.
• Portable code facilitates usage in a wide variety of environments.
• Concise, readable, and well-commented code provides ease of maintenance.
• Interactive parameter downloading from Simulink to external hardware
allows system tuning on the fly.
• A menu-driven, graphical user interface makes the software easy to use.
The Real-Time Workshop supports the following target environments:
• dSPACE DS1102, DS1002, DS1003 using TI C30/C31/C40 DSPs
• VxWorks, VME/68040
• 486 PC-based systems with Xycom, Matrix, Data Translation, or Computer
Boards I/O devices and Quanser Multiq board
1-11
1
Getting Started
The Real-Time Workshop Ada Extension
The Simulink Real-Time Workshop (RTW) Ada Extension automatically
generates Ada code directly from Simulink block diagrams. This allows the
execution of continuous, discrete-time, and hybrid system models on a wide
range of computer platforms, including real-time hardware. Simulink is
required.
RTW Ada Extension can be used for:
• Rapid Prototyping. As a rapid prototyping tool, the RTW Ada Extension
enables you to implement your designs quickly without lengthy hand coding
and debugging. Control and dynamic system algorithms can be implemented
by developing graphical Simulink block diagrams and automatically
generating Ada code.
• Embedded Real-Time Control. Once a system has been designed with
Simulink, code for real-time controllers can be generated, cross-compiled,
linked, and downloaded onto your selected target processor. The RTW Ada
Extension generates Ada code, which can be run on a wide variety of custom
and commercially available hardware.
• Real-Time Simulation. You can create and execute code for an entire system
or specified subsystems for hardware-in-the-loop simulations. Typical
applications include training simulators (pilot-in-the-loop), real-time model
validation, and testing.
• Stand-Alone Simulation. Stand-alone simulations can be run directly on
your host machine or transferred to other systems for remote execution.
Because time histories are saved in MATLAB as binary or ASCII files, they
can be easily loaded into MATLAB for additional analysis or graphic display.
Key Features
RTW Ada Extension provides a comprehensive set of features and capabilities
that provide the flexibility to address a broad range of applications:
• Automatic code generation handles continuous-time, discrete-time, and
hybrid systems.
• Optimized code guarantees fast execution.
1-12
The Real-Time Workshop Ada Extension
• Control framework Application Program Interface (API) uses customizable
makefiles to build and download object files to target hardware
automatically.
• Portable code facilitates usage in a wide variety of environments.
• Concise, readable, and well-commented code provides ease of maintenance.
• A menu-driven, graphical user interface makes it easy to use.
The RTW Ada Extension provides turnkey solutions for the following Ada 83
compilers:
• Rational VADS for UNIX platforms
• Thomson ActivAda for Microsoft Windows Professional Edition
• Thomson ActivAda for Windows NT
1-13
1
Getting Started
Blocksets
Similar to MATLAB and its application toolboxes, The MathWorks offers
blocksets for use with Simulink. Blocksets are collections of Simulink blocks
that are grouped in a separate library from the main Simulink library.
The DSP Blockset
The DSP Blockset extends Simulink for use in the rapid design and simulation
of DSP-based devices and systems. With the DSP Blockset, Simulink provides
an intuitive tool for interactive block-diagram simulation and evaluation of
signal processing algorithms. Its graphical programming environment makes
it easier for engineers to create, modify, and prototype DSP designs. Simulink
is required.
Applications for the DSP Blockset include design and analysis of
communications systems, computer peripherals, speech and audio processing,
automotive and aerospace controls, and medical electronics. It is ideal for both
time and frequency domain algorithms, including problems such as adaptive
noise cancellation.
The Fixed-Point Blockset requires Simulink 3.0 and MATLAB 5.3 and is
shipping on Microsoft Windows and UNIX.
The Fixed-Point Blockset
The Fixed-Point Blockset includes a collection of block diagram components
that extend the standard Simulink block library. With this new set of blocks,
you can create discrete-time dynamic systems that utilize fixed-point
arithmetic. As a result, Simulink can simulate effects commonly encountered
in fixed-point systems for applications such as control systems and
time-domain filtering. Simulink is required.
The Fixed-Point Blockset allows you to simulate fixed-point effects in a
convenient and productive environment. The new blocks provided by the
Fixed-Point Blockset include blocks for:
• Addition and subtraction
• Multiplication and division
• Summation
• Gains and constants
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Blocksets
• Conversion between floating-point and fixed-point signals
• One- and two-dimensional lookup tables
• Logical operators
• Relational operators
• Conversion/saturation of fixed-point signals
• Switch between two values
• Delay
• Delta-inverse operator
• Monitoring signals
Signal conversion blocks let you convert between floating-point and fixed-point
signals. Using the conversion blocks, you can create Simulink block diagrams,
which consist of both standard Simulink block library components and
fixed-point blocks.
For example, you can create plant models using the standard Simulink blocks
and model the controller with fixed-point blocks. Data range blocks provide
maximum and minimum values encountered during simulation from any point
in the block diagram.
The Fixed-Point Blockset lets you build models using unsigned or two’s
complement 8-, 16-, or 32-bit word lengths. A combination of blocks with
differing word lengths may be used in the same block diagram. Scaling of
fixed-point values is achieved by specifying the location of the binary-point
within the fixed-point blocks. During simulation, data types can be changed
allowing you to immediately see the effects of different word sizes, binary-point
locations, rounding versus truncation, and overflow checking.
Another powerful feature of this blockset is automatic location of the
binary-point to give maximum precision without overflow.
By using the data range blocks, you can fix binary point locations to
appropriate values.
The Fixed-Point Blockset requires Simulink 3.0 and MATLAB 5.3 and is
shipping on Microsoft Windows and UNIX.
1-15
1
Getting Started
The Nonlinear Control Design Blockset
The Nonlinear Control Design (NCD) Blockset offers time domain-based,
robust, nonlinear control design. Controller designs are developed as block
diagrams in Simulink. You select a set of tunable model parameters and
graphically place time response constraints on selected output signals.
Successive simulation and optimization methods are applied automatically,
thereby tuning the selected model parameters.
Simulink is required with the NCD Blockset.
The Power System Blockset
The Power System Blockset allows scientists and engineers to build models
that simulate power systems. The blockset uses the Simulink environment,
allowing a model to be built using click and drag procedures. Not only can the
circuit topology be drawn rapidly, but the analysis of the circuit can include its
interactions with mechanical, thermal, control, and other disciplines. This is
possible because all the electrical parts of the simulation interact with
Simulink’s extensive modeling library. Because Simulink uses MATLAB as the
computational engine, MATLAB’s toolboxes can also be used by the designer.
The blockset libraries contain models of typical power equipment such as
transformers, lines, machines, and power electronics. These models are proven
ones coming from textbooks, and their validity is based on the experience of the
Power Systems Testing and Simulation Laboratory of Hydro-Quebec, a large
North American utility located in Canada. The capabilities of the blockset for
modeling a typical electrical grid are illustrated in demonstration files. For
users who want to refresh their knowledge of power system theory, there are
also case studies available.
1-16
2
Quick Start
Running a Demo Model .
Description of the Demo . .
Some Things to Try . . . .
What This Demo Illustrates
Other Useful Demos . . .
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2-5
Building a Simple Model
. . . . . . . . . . . . . . 2-6
2
Quick Start
Running a Demo Model
An interesting demo program provided with Simulink models the
thermodynamics of a house. To run this demo, follow these steps:
1 Start MATLAB. See your MATLAB documentation if you’re not sure how to
do this.
2 Run the demo model by typing thermo in the MATLAB command window.
This command starts up Simulink and creates a model window that contains
this model.
When you open the model, Simulink opens a Scope block containing two plots
labeled Indoor vs. Outdoor Temp and Heat Cost ($), respectively.
3 To start the simulation, pull down the Simulation menu and choose the
Start command (or, on Microsoft Windows, press the Start button on the
Simulink toolbar). As the simulation runs, the indoor and outdoor
temperatures appear in the Indoor vs. Outdoor Temp plot and the
cumulative heating cost appears in the Heat Cost ($) plot.
2-2
4 To stop the simulation, choose the Stop command from the Simulation
menu (or press the Pause button on the toolbar). If you want to explore other
parts of the model, look over the suggestions in “Some Things to Try” on page
2-4.
5 When you’re finished running the simulation, close the model by choosing
Close from the File menu.
Description of the Demo
The demo models the thermodynamics of a house using a simple model. The
thermostat is set to 70 degrees Fahrenheit and is affected by the outside
temperature, which varies by applying a sine wave with amplitude of 15
degrees to a base temperature of 50 degrees. This simulates daily temperature
fluctuations.
The model uses subsystems to simplify the model diagram and create reusable
systems. A subsystem is a group of blocks that is represented by a Subsystem
block. This model contains five subsystems: one named Thermostat, one named
House, and three Temp Convert subsystems (two convert Fahrenheit to
Celsius, one converts Celsius to Fahrenheit).
The internal and external temperatures are fed into the House subsystem,
which updates the internal temperature. Double-click on the House block to
see the underlying blocks in that subsystem.
House subsystem
2-3
2
Quick Start
The Thermostat subsystem models the operation of a thermostat, determining
when the heating system is turned on and off. Double-click on the block to see
the underlying blocks in that subsystem.
Thermostat subsystem
Both the outside and inside temperatures are converted from Fahrenheit to
Celsius by identical subsystems
Fahrenheit to Celsius conversion (F2C)
When the heat is on, the heating costs are computed and displayed on the Heat
Cost ($) plot on the Thermo Plots Scope. The internal temperature is displayed
on the Indoor Temp Scope.
Some Things to Try
Here are several things to try to see how the model responds to different
parameters:
• Each Scope block contains one or more signal display areas and controls that
enable you to select the range of the signal displayed, zoom in on a portion of
the signal, and perform other useful tasks. The horizontal axis represents
time and the vertical axis represents the signal value. For more information
about the Scope block, see Chapter 8.
• The Constant block labeled Set Point (at the top left of the model) sets the
desired internal temperature. Open this block and reset the value to 80
degrees while the simulation is running. See how the indoor temperature
and heating costs change. Also, adjust the outside temperature (the Avg
Outdoor Temp block) and see how it affects the simulation.
• Adjust the daily temperature variation by opening the Sine Wave block
labeled Daily Temp Variation and changing the Amplitude parameter.
2-4
What This Demo Illustrates
This demo illustrates several tasks commonly used when building models:
• Running the simulation involves specifying parameters and starting the
simulation with the Start command, described in detail in Chapter 4.
• You can encapsulate complex groups of related blocks in a single block, called
a subsystem. Creating subsystems is described in detail in Chapter 3.
• You can create a customized icon and design a dialog box for a block by using
the masking feature, described in detail in Chapter 6. In the thermo model,
all Subsystem blocks have customized icons created using the masking
feature.
• Scope blocks display graphic output much as an actual oscilloscope does.
Scope blocks are described in detail in Chapter 8.
Other Useful Demos
Other demos illustrate useful modeling concepts. You can access these demos
from the Simulink block library window:
1 Type simulink3 in the MATLAB command window. The Simulink block
library window appears.
The Demos icon
2 Double-click on the Demos icon. The MATLAB Demos window appears. This
window contains several interesting sample models that illustrate useful
Simulink features.
2-5
2
Quick Start
Building a Simple Model
This example shows you how to build a model using many of the model building
commands and actions you will use to build your own models. The instructions
for building this model in this section are brief. All of the tasks are described
in more detail in the next chapter.
The model integrates a sine wave and displays the result, along with the sine
wave. The block diagram of the model looks like this.
To create the model, first type simulink in the MATLAB command window. On
Microsoft Windows, the Simulink Library Browser appears.
On UNIX, the Simulink library window appears.
2-6
Building a Simple Model
To create a new model on UNIX, select Model from the New submenu of the
Simulink library window’s File menu. To create a new model on Windows,
select the New Model button on the Library Browser’s toolbar.
New Model button
Simulink opens a new model window.
You might want to move the new model window to the right side of your screen
so you can see its contents and the contents of block libraries at the same time.
To create this model, you will need to copy blocks into the model from the
following Simulink block libraries:
• Sources library (the Sine Wave block)
• Sinks library (the Scope block)
• Continuous library (the Integrator block)
• Signals & Systems library (the Mux block)
You can copy a Sine Wave block from the Sources library, using the Library
Browser (Windows only) or the Sources library window (UNIX or Windows).
2-7
2
Quick Start
To copy the Sine Wave block from the Library Browser, first expand the
Library Browser tree to display the blocks in the Sources library. Do this by
clicking first on the Simulink node to display the Sources node, then on the
Sources node to display the Sources library blocks. Finally click on the Sine
Wave node to select the Sine Wave block. Here is how the Library Browser
should look after you have done this.
Simulink library
Sources library
Sine Wave block
Now drag the Sine Wave node from the browser and drop it in the model
window. Simulink creates a copy of the Sine Wave block at the point where you
dropped the node icon.
To copy the Sine Wave block from the Sources library window, open the Sources
window by double-clicking on the Sources icon in the Simulink library window.
(On Windows, you can open the Simulink library window by right-clicking the
2-8
Building a Simple Model
Simulink node in the Library Browser and then clicking the resulting Open
Library button.) Simulink displays the Sources library window.
The Sine Wave block
Now drag the Sine Wave block from the Sources window to your model window.
Copy the rest of the blocks in a similar manner from their respective libraries
into the model window. You can move a block from one place in the model
window to another by dragging the block. You can move a block a short distance
by selecting the block, then pressing the arrow keys.
2-9
2
Quick Start
With all the blocks copied into the model window, the model should look
something like this.
If you examine the block icons, you see an angle bracket on the right of the Sine
Wave block and two on the left of the Mux block. The > symbol pointing out of
a block is an output port; if the symbol points to a block, it is an input port. A
signal travels out of an output port and into an input port of another block
through a connecting line. When the blocks are connected, the port symbols
disappear.
Input port
Output port
Now it’s time to connect the blocks. Connect the Sine Wave block to the top
input port of the Mux block. Position the pointer over the output port on the
right side of the Sine Wave block. Notice that the cursor shape changes to cross
hairs.
Hold down the mouse button and move the cursor to the top input port of the
Mux block. Notice that the line is dashed while the mouse button is down and
that the cursor shape changes to double-lined cross hairs as it approaches the
Mux block.
2-10
Building a Simple Model
Now release the mouse button. The blocks are connected. You can also connect
the line to the block by releasing the mouse button while the pointer is inside
the icon. If you do, the line is connected to the input port closest to the cursor’s
position.
If you look again at the model at the beginning of this section (see “Building a
Simple Model” on page 2-6), you’ll notice that most of the lines connect output
ports of blocks to input ports of other blocks. However, one line connects a line
to the input port of another block. This line, called a branch line, connects the
Sine Wave output to the Integrator block, and carries the same signal that
passes from the Sine Wave block to the Mux block.
Drawing a branch line is slightly different from drawing the line you just drew.
To weld a connection to an existing line, follow these steps:
1 First, position the pointer on the line between the Sine Wave and the Mux
block.
2 Press and hold down the Ctrl key. Press the mouse button, then drag the
pointer to the Integrator block’s input port or over the Integrator block itself.
2-11
2
Quick Start
3 Release the mouse button. Simulink draws a line between the starting point
and the Integrator block’s input port.
Finish making block connections. When you’re done, your model should look
something like this.
Now, open the Scope block to view the simulation output. Keeping the Scope
window open, set up Simulink to run the simulation for 10 seconds. First, set
the simulation parameters by choosing Parameters from the Simulation
menu. On the dialog box that appears, notice that the Stop time is set to 10.0
(its default value).
Stop time parameter
2-12
Building a Simple Model
Close the Simulation Parameters dialog box by clicking on the Ok button.
Simulink applies the parameters and closes the dialog box.
Choose Start from the Simulation menu and watch the traces of the Scope
block’s input.
The simulation stops when it reaches the stop time specified in the Simulation
Parameters dialog box or when you choose Stop from the Simulation menu.
To save this model, choose Save from the File menu and enter a filename and
location. That file contains the description of the model.
To terminate Simulink and MATLAB, choose Exit MATLAB (on a Microsoft
Windows system) or Quit MATLAB (on a UNIX system). You can also type
quit in the MATLAB command window. If you want to leave Simulink but not
terminate MATLAB, just close all Simulink windows.
This exercise shows you how to perform some commonly used model-building
tasks. These and other tasks are described in more detail in Chapter 3.
2-13
2
Quick Start
2-14
3
Creating a Model
Starting Simulink . . . . . . . . . . . . . . . . . . 3-2
Selecting Objects . . . . . . . . . . . . . . . . . . 3-7
Blocks . . . . . . . . . . . . . . . . . . . . . . . 3-9
Libraries . . . . . . . . . . . . . . . . . . . . . . 3-21
Lines
. . . . . . . . . . . . . . . . . . . . . . . 3-27
Annotations . . . . . . . . . . . . . . . . . . . . 3-37
Working with Data Types . . . . . . . . . . . . . . 3-38
Working with Complex Signals . . . . . . . . . . . . 3-47
Summary of Mouse and Keyboard Actions
. . . . . . 3-48
Creating Subsystems . . . . . . . . . . . . . . . . 3-51
Tips for Building Models
. . . . . . . . . . . . . . 3-57
Modeling Equations . . . . . . . . . . . . . . . . . 3-58
Saving a Model . . . . . . . . . . . . . . . . . . . 3-61
Printing a Block Diagram . . . . . . . . . . . . . . 3-62
The Model Browser . . . . . . . . . . . . . . . . . 3-66
Tracking Model Versions . . . . . . . . . . . . . . 3-70
Ending a Simulink Session. . . . . . . . . . . . . . 3-79
3
Creating a Model
Starting Simulink
To start Simulink, you must first start MATLAB. Consult your MATLAB
documentation for more information. You can then start Simulink in two ways:
• Click on the Simulink icon
on the MATLAB toolbar.
• Enter the simulink command at the MATLAB prompt.
On Microsoft Windows platforms, starting Simulink displays the Simulink
Library Browser.
The Library Browser displays a tree-structured view of the Simulink block
libraries installed on your system. You can build models by copying blocks from
the Library Browser into a model window (this procedure is described later in
this chapter).
On UNIX platforms, starting Simulink displays the Simulink block library
window.
The Simulink library window displays icons representing the block libraries
that come with Simulink. You can create models by copying blocks from the
library into a model window.
3-2
Note On Windows, you can display the Simulink library window by
right-clicking the Simulink node in the Library Browser window.
Creating a New Model
To create a new model, click the New button on the Library Browser’s toolbar
(Windows only) or choose New from the library window’s File menu and select
Model. You can move the window as you do other windows. Chapter 2 describes
how to build a simple model. “Modeling Equations” on page 3–58 describes how
to build systems that model equations.
Editing an Existing Model
To edit an existing model diagram, either:
• Choose the Open button on the Library Browser’s toolbar (Windows only) or
the Open command from the Simulink library window’s File menu and then
choose or enter the model filename for the model you want to edit.
• Enter the name of the model (without the .mdl extension) in the MATLAB
command window. The model must be in the current directory or on the path.
Entering Simulink Commands
You run Simulink and work with your model by entering commands. You can
enter commands by:
• Selecting items from the Simulink menu bar
• Selecting items from a context-sensitive Simulink menu (Windows only)
• Clicking buttons on the Simulink toolbar (Windows only)
• Entering commands in the MATLAB command window
Using the Simulink Menu Bar to Enter Commands
The Simulink menu bar appears near the top of each model window. The menu
commands apply to the contents of that window.
3-3
3
Creating a Model
Using Context-Sensitive Menus to Enter Commands
The Windows version of Simulink displays a context-sensitive menu when you
click the right mouse button over a model or block library window. The contents
of the menu depend on whether a block is selected. If a block is selected, the
menu displays commands that apply only to the selected block. If no block is
selected, the menu displays commands that apply to a model or library as a
whole.
Using the Simulink Toolbar to Enter Commands
Model windows in the Windows version of Simulink optionally display a
toolbar beneath the Simulink menu bar. To display the toolbar, check the
Toolbar option on the Simulink View menu.
Toolbar
The toolbar contains buttons corresponding to frequently used Simulink
commands, such as those for opening, running, and closing models. You can
run such commands by clicking on the corresponding button. For example, to
open a Simulink model, click on the button containing an open folder icon. You
can determine which command a button executes by moving the mouse pointer
over the button. A small window appears containing text that describes the
button. The window is called a tooltip. Each button on the toolbar displays a
tooltip when the mouse pointer hovers over it. You can hide the toolbar by
unchecking the Toolbar option on the Simulink View menu.
Using the MATLAB Window to Enter Commands
When you run a simulation and analyze its results, you can enter MATLAB
commands in the MATLAB command window. Running a simulation is
discussed in Chapter 4, and analyzing simulation results is discussed in
Chapter 5.
3-4
Undoing a Command
You can cancel the effects of up to 101 consecutive operations by choosing Undo
from the Edit menu. You can undo these operations:
• Adding or deleting a block
• Adding or deleting a line
• Adding or deleting a model annotation
• Editing a block name
You can reverse the effects of an Undo command by choosing Redo from the
Edit menu.
Simulink Windows
Simulink uses separate windows to display a block library browser, a block
library, a model, and graphical (scope) simulation output. These windows are
not MATLAB figure windows and cannot be manipulated using Handle
Graphics® commands.
Simulink windows are sized to accommodate the most common screen
resolutions available. If you have a monitor with exceptionally high or low
resolution, you may find the window sizes too small or too large. If this is the
case, resize the window and save the model to preserve the new window
dimensions.
Status Bar
The Windows version of Simulink displays a status bar at the bottom of each
model and library window.
Status Bar
3-5
3
Creating a Model
When a simulation is running, the status bar displays the status of the
simulation, including the current simulation time and the name of the current
solver. You can display or hide the status bar by checking or unchecking the
Status Bar item on the Simulink View menu.
Zooming Block Diagrams
Simulink allows you to enlarge or shrink the view of the block diagram in the
current Simulink window. To zoom a view:
• Select Zoom In from the View menu (or type r) to enlarge the view.
• Select Zoom Out from the View menu (or type v) to shrink the view.
• Select Fit System to View from the View menu (or press the space bar) to
fit the diagram to the view.
• Select Normal from the View menu to view the diagram at actual size.
By default, Simulink fits a block diagram to view when you open the diagram
either in the model browser’s content pane or in a separate window. If you
change a diagram’s zoom setting, Simulink saves the setting when you close
the diagram and restores the setting the next time you open the diagram. If you
want to restore the default behavior, choose Fit System to View from the View
menu the next time you open the diagram.
3-6
Selecting Objects
Selecting Objects
Many model building actions, such as copying a block or deleting a line, require
that you first select one or more blocks and lines (objects).
Selecting One Object
To select an object, click on it. Small black square “handles” appear at the
corners of a selected block and near the end points of a selected line. For
example, the figure below shows a selected Sine Wave block and a selected line:
When you select an object by clicking on it, any other selected objects become
deselected.
Selecting More than One Object
You can select more than one object either by selecting objects one at a time, by
selecting objects located near each other using a bounding box, or by selecting
the entire model.
Selecting Multiple Objects One at a Time
To select more than one object by selecting each object individually, hold down
the Shift key and click on each object to be selected. To deselect a selected
object, click on the object again while holding down the Shift key.
Selecting Multiple Objects Using a Bounding Box
An easy way to select more than one object in the same area of the window is
to draw a bounding box around the objects.
3-7
3
Creating a Model
1 Define the starting corner of a bounding box by positioning the pointer at
one corner of the box, then pressing and holding down the mouse button.
Notice the shape of the cursor.
2 Drag the pointer to the opposite corner of the box. A dotted rectangle
encloses the selected blocks and lines.
3 Release the mouse button. All blocks and lines at least partially enclosed by
the bounding box are selected.
Selecting the Entire Model
To select all objects in the active window, choose Select All from the Edit
menu. You cannot create a subsystem by selecting blocks and lines in this way;
for more information, see “Creating Subsystems” on page 3–51.
3-8
Blocks
Blocks
Blocks are the elements from which Simulink models are built. You can model
virtually any dynamic system by creating and interconnecting blocks in
appropriate ways. This section discusses how to use blocks to build models of
dynamic systems.
Block Data Tips
On Microsoft Windows, Simulink displays information about a block in a
pop-up window when you allow the pointer to hover over the block in the
diagram view. To disable this feature or control what information a data tip
includes, select Block Data Tips from the Simulink View menu.
Virtual Blocks
When creating models, you need to be aware that Simulink blocks fall into two
basic categories: nonvirtual and virtual blocks. Nonvirtual blocks play an
active role in the simulation of a system. If you add or remove a nonvirtual
block, you change the model’s behavior. Virtual blocks, by contrast, play no
active role in the simulation. They simply help to organize a model graphically.
Some Simulink blocks can be virtual in some circumstances and nonvirtual in
others. Such blocks are called conditionally virtual blocks. The following table
lists Simulink’s virtual and conditionally virtual blocks.
Table 3-1: Virtual Blocks
Block Name
Condition Under Which Block Will Be Virtual
Bus Selector
Always virtual.
Data Store Memory
Always virtual.
Demux
Always virtual.
Enable Port
Always virtual.
From
Always virtual.
Goto
Always virtual.
Goto Tag Visibility
Always virtual.
3-9
3
Creating a Model
Table 3-1: Virtual Blocks (Continued)
Block Name
Condition Under Which Block Will Be Virtual
Ground
Always virtual.
Inport
Always virtual unless the block resides in a
conditionally executed subsystem and has a direct
connection to an outport block.
Mux
Always virtual.
Outport
Virtual if the block resides within any subsystem
block (conditional or not), and does not reside in the
root (top-level) Simulink window.
Selector
Always virtual.
Subsystem
Virtual if the block is not conditionally executed.
Terminator
Always virtual.
Test Point
Always virtual.
Trigger Port
Virtual if the outport port is not present.
Copying and Moving Blocks from One Window to
Another
As you build your model, you often copy blocks from Simulink block libraries or
other libraries or models into your model window. To do this, follow these steps:
1 Open the appropriate block library or model window.
2 Drag the block you want to copy into the target model window. To drag a
block, position the cursor over the block icon, then press and hold down the
mouse button. Move the cursor into the target window, then release the
mouse button.
You can also drag blocks from the Simulink Library Browser into a model
window. See “Browsing Block Libraries” on page 3-25 for more information.
3-10
Blocks
Note Simulink hides the names of Sum, Mux, Demux, and Bus Selector
blocks when you copy them from the Simulink block library to a model.This is
done to avoid unnecessarily cluttering the model diagram. (The shapes of
these blocks clearly indicates their respective functions.)
You can also copy blocks by using the Copy and Paste commands from the Edit
menu:
1 Select the block you want to copy.
2 Choose Copy from the Edit menu.
3 Make the target model window the active window.
4 Choose Paste from the Edit menu.
Simulink assigns a name to each copied block. If it is the first block of its type
in the model, its name is the same as its name in the source window. For
example, if you copy the Gain block from the Math library into your model
window, the name of the new block is Gain. If your model already contains a
block named Gain, Simulink adds a sequence number to the block name (for
example, Gain1, Gain2). You can rename blocks; see “Manipulating Block
Names” on page 3–16.
When you copy a block, the new block inherits all the original block’s parameter
values.
Simulink uses an invisible five-pixel grid to simplify the alignment of blocks.
All blocks within a model snap to a line on the grid. You can move a block
slightly up, down, left, or right by selecting the block and pressing the arrow
keys.
You can display the grid in the model window by typing the following command
in the MATLAB window:
set_param('<model name>','showgrid','on')
To change the grid spacing, type:
set_param('<model name>','gridspacing',<number of pixels>)
3-11
3
Creating a Model
For example, to change the grid spacing to 20 pixels, type:
set_param('<model name>','gridspacing',20)
For either of the above commands, you can also select the model, and then type
gcs instead of <model name>.
You can copy or move blocks to compatible applications (such as word
processing programs) using the Copy, Cut, and Paste commands. These
commands copy only the graphic representation of the blocks, not their
parameters.
Moving blocks from one window to another is similar to copying blocks, except
that you hold down the Shift key while you select the blocks.
You can use the Undo command from the Edit menu to remove an added block.
Moving Blocks in a Model
To move a single block from one place to another in a model window, drag the
block to a new location. Simulink automatically repositions lines connected to
the moved block.
To move more than one block, including connecting lines:
1 Select the blocks and lines. If you need information about how to select more
than one block, see “Selecting More than One Object” on page 3–7.
2 Drag the objects to their new location and release the mouse button.
Duplicating Blocks in a Model
You can duplicate blocks in a model as follows. While holding down the Ctrl
key, select the block with the left mouse button, then drag it to a new location.
You can also do this by dragging the block using the right mouse button.
Duplicated blocks have the same parameter values as the original blocks.
Sequence numbers are added to the new block names.
Specifying Block Parameters
The Simulink user interface lets you assign values to block parameters. Some
block parameters are common to all blocks. Use the Block Properties dialog
box to set these parameters. To display the dialog box, select the block whose
3-12
Blocks
properties you want to set. Then select Block Properties... from Simulink’s
Edit menu. See “Block Properties Dialog Box” on page 3-13 for more
information.
Other block parameters are specific to particular blocks. Use a block’s
block-specific parameter dialog to set these parameters. Double-click on the
block to open its dialog box. You can accept the displayed values or change
them. You can also use the set_param command to change block parameters.
See set_param on page 10-24 for details.
Some block dialogs allow you to specify a data type for some or all of their
parameters.The reference material that describes each block (in Chapter 8)
shows the dialog box and describes the block parameters.
Block Properties Dialog Box
The Block Properties dialog box lets you set some common block parameters.
The dialog box contains the following fields:
Description
Brief description of the block’s purpose.
3-13
3
Creating a Model
Priority
Execution priority of this block relative to other blocks in the model. See
“Assigning Block Priorities” on page 3-19 for more information.
Tag
A general text field that is saved with the block.
Open function
MATLAB (m-) function to be called when a user opens this block.
Attributes format string
Current value of the block’s AttributesFormatString parameter. This
parameter specifies which parameters to display beneath a block’s icon. The
attributes format string can be any text string with embedded parameter
names. An embedded parameter name is a parameter name preceded by %< and
followed by >, for example, %<priority>. Simulink displays the attributes
format string beneath the block’s icon, replacing each parameter name with the
corresponding parameter value. You can use line feed characters (\n) to display
each parameter on a separate line. For example, specifying the attributes
format string
pri=%<priority>\ngain=%<Gain>
for a Gain block displays
If a parameter’s value is not a string or an integer, Simulink displays N/S (not
supported) for the parameter’s value. If the parameter name is invalid,
Simulink displays “???”.
Deleting Blocks
To delete one or more blocks, select the blocks to be deleted and press the
Delete or Backspace key. You can also choose Clear or Cut from the Edit
menu. The Cut command writes the blocks into the clipboard, which enables
3-14
Blocks
you to paste them into a model. Using the Delete or Backspace key or the
Clear command does not enable you to paste the block later.
You can use the Undo command from the Edit menu to replace a deleted block.
Changing the Orientation of Blocks
By default, signals flow through a block from left to right. Input ports are on
the left, and output ports are on the right. You can change the orientation of a
block by choosing one of these commands from the Format menu:
• The Flip Block command rotates the block 180 degrees.
• The Rotate Block command rotates a block clockwise 90 degrees.
The figure below shows how Simulink orders ports after changing the
orientation of a block using the Rotate Block and Flip Block menu items. The
text in the blocks shows their orientation.
1 2 3
Rotate
1
2
3
Left
to
Right
Down
Flip
Rotate
Up
Rotate
Right
to
Left
1
2
3
Rotate
1 2 3
Resizing Blocks
To change the size of a block, select it, then drag any of its selection handles.
While you hold down the mouse button, a dotted rectangle shows the new block
size. When you release the mouse button, the block is resized.
For example, the figure below shows a Signal Generator block being resized.
The lower-right handle was selected and dragged to the cursor position. When
3-15
3
Creating a Model
the mouse button is released, the block takes its new size. This figure shows a
block being resized.
Manipulating Block Names
All block names in a model must be unique and must contain at least one
character. By default, block names appear below blocks whose ports are on the
sides, and to the left of blocks whose ports are on the top and bottom, as this
figure shows.
Changing Block Names
You can edit a block name in one of these ways:
• To replace the block name on a Microsoft Windows or UNIX system, click on
the block name, then double-click or drag the cursor to select the entire
name. Then, enter the new name.
• To insert characters, click between two characters to position the insertion
point, then insert text.
• To replace characters, drag the mouse to select a range of text to replace,
then enter the new text.
When you click the pointer someplace else in the model or take any other
action, the name is accepted or rejected. If you try to change the name of a block
to a name that already exists or to a name with no characters, Simulink
displays an error message.
You can modify the font used in a block name by selecting the block, then
choosing the Font menu item from the Format menu. Select a font from the
Set Font dialog box. This procedure also changes the font of text on the block
icon.
You can cancel edits to a block name by choosing Undo from the Edit menu.
3-16
Blocks
Note If you change the name of a library block, all links to that block will
become unresolved.
Changing the Location of a Block Name
You can change the location of the name of a selected block in two ways:
• By dragging the block name to the opposite side of the block
• By choosing the Flip Name command from the Format menu. This
command changes the location of the block name to the opposite side of the
block.
For more information about block orientation, see “Changing the Orientation
of Blocks” on page 3–15.
Changing Whether a Block Name Appears
To change whether the name of a selected block is displayed, choose a menu
item from the Format menu:
• The Hide Name menu item hides a visible block name. When you select Hide
Name, it changes to Show Name when that block is selected.
• The Show Name menu item shows a hidden block name.
Displaying Parameters Beneath a Block’s Icon
You can cause Simulink to display one or more of a block’s parameters beneath
the block’s icon in a block diagram. You specify the parameters to be displayed
in the following ways:
• By entering an attributes format string in the Attributes format string field
of the block’s Block Properties dialog box (see “Block Properties Dialog Box”
on page 3-13)
• By setting the value of the block’s AttributesFormatString property to the
format string, using set_param (see set_param on page 10-24)
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Creating a Model
Disconnecting Blocks
To disconnect a block from its connecting lines, hold down the Shift key, then
drag the block to a new location.
Vector Input and Output
Almost all Simulink blocks accept scalar or vector inputs, generate scalar or
vector outputs, and allow you to provide scalar or vector parameters. These
blocks are referred to in this manual as being vectorized.
You can determine which lines in a model carry vector signals by choosing
Wide Vector Lines from the Format menu. When this option is selected, lines
that carry vectors are drawn thicker than lines that carry scalars. The figures
in the next section show scalar and vector lines.
If you change your model after choosing Wide Vector Lines, you must
explicitly update the display by choosing Update Diagram from the Edit
menu. Starting the simulation also updates the block diagram display.
Block descriptions in Chapter 8 discuss the characteristics of block inputs,
outputs, and parameters.
Scalar Expansion of Inputs and Parameters
Scalar expansion is the conversion of a scalar value into a vector of identical
elements. Simulink applies scalar expansion to inputs and/or parameters for
most blocks. Block descriptions in Chapter 8 indicate whether Simulink
applies scalar expansion to a block’s inputs and parameters.
Scalar Expansion of Inputs
When using blocks with more than one input port (such as the Sum or
Relational Operator block), you can mix vector and scalar inputs. When you do
this, the scalar inputs are expanded into vectors of identical elements whose
widths are equal to the width of the vector inputs. (If more than one block input
is a vector, they must have the same number of elements.)
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Blocks
This model adds scalar and vector inputs. The input from block Constant1 is
scalar expanded to match the size of the vector input from the Constant block.
The input is expanded to the vector [3 3 3].
Scalar Expansion of Parameters
You can specify the parameters for vectorized blocks as either vectors or
scalars. When you specify vector parameters, each parameter element is
associated with the corresponding element in the input vector(s). When you
specify scalar parameters, Simulink applies scalar expansion to convert them
automatically into appropriately sized vectors.
This example shows that a scalar parameter (the Gain) is expanded to a vector
of identically valued elements to match the size of the block input, a
three-element vector.
Assigning Block Priorities
You can assign evaluation priorities to nonvirtual blocks in a model. Higher
priority blocks evaluate before lower priority blocks, though not necessarily
before blocks that have no assigned priority.
You can assign block priorities interactively or programmatically. To set
priorities programmatically, use the command
set_param(b,'Priority','n')
where b is a block path and n is any valid integer. (Negative numbers and 0 are
valid priority values.) The lower the number, the higher the priority; that is, 2
is higher priority than 3. To set a block’s priority interactively, enter the
priority in the Priority field of the block’s Block Properties dialog box (see
“Block Properties Dialog Box” on page 3-13).
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Creating a Model
Using Drop Shadows
You can add a drop shadow to a block by selecting the block, then choosing
Show Drop Shadow from the Format menu. When you select a block with a
drop shadow, the menu item changes to Hide Drop Shadow. The figure below
shows a Subsystem block with a drop shadow.
3-20
Libraries
Libraries
Libraries enable users to copy blocks into their models from external libraries
and automatically update the copied blocks when the source blocks change.
Using libraries allows users who develop their own block libraries, or who use
those provided by others (such as blocksets), to ensure that their models
automatically include the most recent versions of these blocks.
Terminology
It is important to understand the terminology used with this feature.
Library – A collection of library blocks. A library must be explicitly created
using New Library from the File menu.
Library block – A block in a library.
Reference block – A copy of a library block.
Link – The connection between the reference block and its library block that
allows Simulink to update the reference block when the library block changes.
Copy – The operation that creates a reference block from either a library block
or another reference block.
This figure illustrates this terminology.
link
library
block
Library (Source)
copy
reference
block
Model or Library (Destination)
Creating a Library
To create a library, select Library from the New submenu of the File menu.
Simulink displays a new window, labeled Library: untitled. If an untitled
window already appears, a sequence number is appended.
You can create a library from the command line using this command.
new_system('newlib', 'Library')
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Creating a Model
This command creates a new library named 'newlib'. To display the library,
use the open_system command. These commands are described in Chapter 10.
The library must be named (saved) before you can copy blocks from it.
Modifying a Library
When you open a library, it is automatically locked and you cannot modify its
contents. To unlock the library, select Unlock Library from the Edit menu.
Closing the library window locks the library.
Copying a Library Block into a Model
You can copy a block from a library into a model by copying and pasting or
dragging the block from the library window to the model window (see “Copying
and Moving Blocks from One Window to Another” on page 3-10) or by dragging
the block from the Library Browser (see “Browsing Block Libraries” on page
3-25) into the model window.
When you copy a library block into a model or another library, Simulink creates
a link to the library block. The reference block is a copy of the library block. You
can modify block parameters in the reference block but you cannot mask the
block or, if it is masked, edit the mask. Also, you cannot set callback
parameters for a reference block. If you look under the mask of a reference
block, Simulink displays the underlying system for the library block.
The library and reference blocks are linked by name; that is, the reference block
is linked to the specific block and library whose names are in effect at the time
the copy is made.
If Simulink is unable to find either the library block or the source library on
your MATLAB path when it attempts to update the reference block, the link
becomes unresolved. Simulink issues an error message and displays these
blocks using red dashed lines. The error message is
Failed to find block "source-block-name"
in library "source-library-name"
referenced by block
"reference-block-path".
3-22
Libraries
The unresolved reference block is displayed like this (colored red).
To fix a bad link, you must either:
• Delete the unlinked reference block and copy the library block back into your
model.
• Add the directory that contains the required library to the MATLAB path
and select Update Diagram from the Edit menu.
• Double-click on the reference block. On the dialog box that appears, correct
the pathname and click on Apply or Close.
All blocks have a LinkStatus parameter that indicates whether the block is a
reference block. The parameter can have these values:
• 'none' indicates that the block is not a reference block.
• 'resolved' indicates that the block is a reference block and that the link is
resolved.
• 'unresolved' indicates that the block is a reference block but that the link
is unresolved.
Updating a Linked Block
Simulink updates out-of-date reference blocks in a model or library at these
times:
• When the model or library is loaded
• When you select Update Diagram from the Edit menu or run the simulation
• When you query the LinkStatus parameter of a block using the get_param
command (see “Getting Information About Library Blocks” on page 3-24)
• When you use the find_system command
Breaking a Link to a Library Block
You can break the link between a reference block and its library block to cause
the reference block to become a simple copy of the library block, unlinked to the
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Creating a Model
library block. Changes to the library block no longer affect the block. Breaking
links to library blocks enables you to transport a model as a stand-alone model,
without the libraries.
To break the link between a reference block and its library block, select the
block, then choose Break Library Link from the Edit menu. You can also
break the link between a reference block and its library block from the
command line by changing the value of the LinkStatus parameter to 'none'
using this command.
set_param('refblock', 'LinkStatus', 'none')
You can save a system and break all links between reference blocks and library
blocks using this command.
save_system('sys', 'newname', 'BreakLinks')
Finding the Library Block for a Reference Block
To find the source library and block linked to a reference block, select the
reference block, then choose Go To Library Link from the Edit menu. If the
library is open, Simulink selects the library block (displaying selection handles
on the block) and makes the source library the active window. If the library is
not open, Simulink opens it and selects the library block.
Getting Information About Library Blocks
Use the libinfo command to get information about reference blocks in a
system. The format for the command is
libdata = libinfo(sys)
where sys is the name of the system. The command returns a structure of size
n-by-1, where n is the number of library blocks in sys. Each element of the
structure has four fields:
• Block, the block path
• Library, the library name
• ReferenceBlock, the reference block path
• LinkStatus, the link status, either 'resolved' or 'unresolved'
3-24
Libraries
Browsing Block Libraries
The Library Browser lets you quickly locate and copy library blocks into a
model.
Note The Library Browser is available only on Microsoft Windows platforms.
You can locate blocks either by navigating the Library Browser’s library tree
or by using the Library Browser’s search facility.
Navigating the Library Tree
The library tree displays a list of all the block libraries installed on the system.
You can view or hide the contents of libraries by expanding or collapsing the
tree using the mouse or keyboard. To expand/collapse the tree, click the +/buttons next to library entries or select an entry and press the +/- or right/left
arrow key on your keyboard. Use the up/down arrow keys to move up or down
the tree.
Searching Libraries
To find a particular block, enter the block’s name in the edit field next to the
Library Browser’s Find button and then click the Find button.
Opening a Library
To open a library, right-click the library’s entry in the browser. Simulink
displays an Open Library button. Select the Open Library button to open the
library.
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Creating a Model
Creating and Opening Models
To create a model, select the New button on the Library Browser’s toolbar. To
open an existing model, select the Open button on the toolbar.
Copying Blocks
To copy a block from the Library Browser into a model, select the block in the
browser, drag the selected block into the model window, and drop it where you
want to create the copy.
Displaying Help on a Block
To display help on a block, right-click the block in the Library Browser and
select the button that subsequently pops up.
Pinning the Library Browser
To keep the Library Browser above all other windows on your desktop, select
the PushPin button on the browser’s toolbar.
3-26
Lines
Lines
Lines carry signals. Each line can carry a scalar or vector signal. A line can
connect the output port of one block with the input port of another block. A line
can also connect the output port of one block with input ports of many blocks
by using branch lines.
Drawing a Line Between Blocks
To connect the output port of one block to the input port of another block:
1 Position the cursor over the first block’s output port. It is not necessary to
position the cursor precisely on the port. The cursor shape changes to a cross
hair.
2 Press and hold down the mouse button.
3 Drag the pointer to the second block’s input port. You can position the cursor
on or near the port, or in the block. If you position the cursor in the block,
the line is connected to the closest input port. The cursor shape changes to a
double cross hair.
4 Release the mouse button. Simulink replaces the port symbols by a
connecting line with an arrow showing the direction of the signal flow. You
can create lines either from output to input, or from input to output. The
arrow is drawn at the appropriate input port, and the signal is the same.
Simulink draws connecting lines using horizontal and vertical line segments.
To draw a diagonal line, hold down the Shift key while drawing the line.
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Creating a Model
Drawing a Branch Line
A branch line is a line that starts from an existing line and carries its signal to
the input port of a block. Both the existing line and the branch line carry the
same signal. Using branch lines enables you to cause one signal to be carried
to more than one block.
In this example, the output of the Product block goes to both the Scope block
and the To Workspace block.
To add a branch line, follow these steps:
1 Position the pointer on the line where you want the branch line to start.
2 While holding down the Ctrl key, press and hold down the left mouse button.
3 Drag the pointer to the input port of the target block, then release the mouse
button and the Ctrl key.
You can also use the right mouse button instead of holding down the left mouse
button and the Ctrl key.
Drawing a Line Segment
You may want to draw a line with segments exactly where you want them
instead of where Simulink draws them. Or, you might want to draw a line
before you copy the block to which the line is connected. You can do either by
drawing line segments.
To draw a line segment, you draw a line that ends in an unoccupied area of the
diagram. An arrow appears on the unconnected end of the line. To add another
line segment, position the cursor over the end of the segment and draw another
segment. Simulink draws the segments as horizontal and vertical lines. To
draw diagonal line segments, hold down the Shift key while you draw the lines.
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Lines
Moving a Line Segment
To move a line segment, follow these steps:
1 Position the pointer on the segment you want to move.
2 Press and hold down the left mouse button.
3 Drag the pointer to the desired location.
4 Release the mouse button.
You cannot move the segments that are connected directly to block ports.
Dividing a Line into Segments
You can divide a line segment into two segments, leaving the ends of the line
in their original locations. Simulink creates line segments and a vertex that
joins them. To divide a line into segments, follow these steps:
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Creating a Model
1 Select the line.
2 Position the pointer on the line where you want the vertex.
3 While holding down the Shift key, press and hold down the mouse button.
The cursor shape changes to a circle that encloses the new vertex.
4 Drag the pointer to the desired location.
5 Release the mouse button and the Shift key.
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Lines
Moving a Line Vertex
To move a vertex of a line, follow these steps:
1 Position the pointer on the vertex, then press and hold down the mouse
button. The cursor changes to a circle that encloses the vertex.
2 Drag the pointer to the desired location.
3 Release the mouse button.
Displaying Line Widths
You can display the widths of vector lines in a model by turning on Vector Line
Widths from the Format menu. Simulink indicates the width of each signal at
the block that originates the signal and the block that receives it. You can cause
Simulink to use a thick line to display vector lines by selecting Wide Vector
Lines from the Format menu.
When you start a simulation or update the diagram and Simulink detects a
mismatch of input and output ports, it displays an error message and shows
line widths in the model.
Inserting Blocks in a Line
You can insert a block in a line by dropping the block on the line. Simulink
inserts the block for you at the point where you drop the block. The block that
you insert can have only one input and one output.
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Creating a Model
To insert a block in a line:
1 Position the pointer over the block and press the left mouse button.
2 Drag the block over the line in which you want to insert the block.
3 Release the mouse button to drop the block on the line. Simulink inserts the
block where you dropped it.
Signal Labels
You can label signals to annotate your model. Labels can appear above or below
horizontal lines or line segments, and left or right of vertical lines or line
segments. Labels can appear at either end, at the center, or in any combination
of these locations.
3-32
Lines
Using Signal Labels
To create a signal label, double-click on the line segment and type the label at
the insertion point. When you click on another part of the model, the label fixes
its location.
Note When you create a signal label, take care to double-click on the line. If
you click in an unoccupied area close to the line, you will create a model
annotation instead.
To move a signal label, drag the label to a new location on the line. When you
release the mouse button, the label fixes its position near the line.
To copy a signal label, hold down the Ctrl key while dragging the label to
another location on the line. When you release the mouse button, the label
appears in both the original and the new locations.
To edit a signal label, select it:
• To replace the label, click on the label, then double-click or drag the cursor
to select the entire label. Then, enter the new label.
• To insert characters, click between two characters to position the insertion
point, then insert text.
• To replace characters, drag the mouse to select a range of text to replace,
then enter the new text.
To delete all occurrences of a signal label, delete all the characters in the label.
When you click outside the label, the labels are deleted. To delete a single
occurrence of the label, hold down the Shift key while you select the label, then
press the Delete or Backspace key.
To change the font of a signal label, select the signal, choose Font from the
Format menu, then select a font from the Set Font dialog box.
Signal Label Propagation
Signal label propagation is the automatic labeling of a line emitting from a
connection block. Blocks that support signal label propagation are the Demux,
Enable, From, Inport, Mux, Selector, and Subsystem blocks. The labeled signal
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Creating a Model
must be on a line feeding a connecting block and the propagated signal must be
on a line coming from the same connecting block or one associated with it.
To propagate a signal label, create a signal label starting with the “<” character
on the output of one of the listed connection blocks. When you run the
simulation or update the diagram, the actual signal label appears, enclosed
within angle brackets. The actual signal label is obtained by tracing back
through the connection blocks until a signal label is encountered.
This example shows a model with a signal label and the propagated label both
before and after updating the block diagram. In the first figure, the signal
entering the Goto block is labeled label and the signal leaving the associated
From block is labeled with a single <. The second figure shows the same model
after choosing Update Diagram from the Edit menu.
1
The signal label and propagated label before updating the diagram.
2
The same signal labels after updating the diagram.
In the next example, the propagated signal label shows the contents of a vector
signal. This figure shows the label only after updating the diagram.
Setting Signal Properties
Signals have properties. Use Simulink’s Signal Properties dialog box to view
or set a signal’s properties. To display the dialog box, select the line that carries
the signal and choose Signal Properties from the Simulink Edit menu.
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Lines
Signal Properties Dialog Box
The Signal Properties dialog box allows you to view and edit signal properties.
The dialog box includes the following controls.
Signal Name
Name of signal.
Description
Enter a description of the signal in this field.
Document Link
Enter a MATLAB expression in the field that displays documentation for the
signal. To display the documentation, click the field’s label (that is, “Document
Link”). For example, entering the expression
web(['file:///' which('foo_signal.html')])
in the field causes MATLAB’s default Web browser to display
foo_signal.html when you click the field’s label.
Displayable (Test Point)
Check this option to indicate that the signal can be displayed during
simulation.
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Note The next two controls are used to set properties used by the Real-Time
Workshop to generate code from the model. You can ignore them if you do not
plan to generate code from the model.
RTW storage class
Select the storage class of this signal from the list. See the Real-Time Workshop
User’s Guide for an explanation of the listed options.
RTW storage type qualifier
Select the storage type of this signal from the list. See the Real-Time Workshop
User’s Guide for more information.
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Annotations
Annotations
Annotations provide textual information about a model. You can add an
annotation to any unoccupied area of your block diagram.
Annotations
To create a model annotation, double-click on an unoccupied area of the block
diagram. A small rectangle appears and the cursor changes to an insertion
point. Start typing the annotation contents. Each line is centered within the
rectangle that surrounds the annotation.
To move an annotation, drag it to a new location.
To edit an annotation, select it:
• To replace the annotation on a Microsoft Windows or UNIX system, click on
the annotation, then double-click or drag the cursor to select it. Then, enter
the new annotation.
• To insert characters, click between two characters to position the insertion
point, then insert text.
• To replace characters, drag the mouse to select a range of text to replace,
then enter the new text.
To delete an annotation, hold down the Shift key while you select the
annotation, then press the Delete or Backspace key.
To change the font of all or part of an annotation, select the text in the
annotation you want to change, then choose Font from the Format menu.
Select a font and size from the dialog box.
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Working with Data Types
The term data type refers to the way in which a computer represents numbers
in memory. A data type determines the amount of storage allocated to a
number, the method used to encode the number’s value as a pattern of binary
digits, and the operations available for manipulating the type. Most computers
provide a choice of data types for representing numbers, each with specific
advantages in the areas of precision, dynamic range, performance, and memory
usage. To enable you to take advantage of data typing to optimize the
performance of MATLAB programs, MATLAB allows you to specify the data
type of MATLAB variables. Simulink builds on this capability by allowing you
to specify the data types of Simulink signals and block parameters.
The ability to specify the data types of a model’s signals and block parameters
is particularly useful in real-time control applications. For example, it allows a
Simulink model to specify the optimal data types to use to represent signals
and block parameters in code generated from a model by automatic
code-generation tools, such as the Real-Time Workshop available from The
MathWorks. By choosing the most appropriate data types for your model’s
signals and parameters, you can dramatically increase the performance and
decrease the size of the code generated from the model.
Simulink performs extensive checking before and during a simulation to
ensure that your model is typesafe, that is, that code generated from the model
will not overflow or underflow and thus produce incorrect results. Simulink
models that use Simulink’s default data type (double) are inherently typesafe.
Thus, if you never plan to generate code from your model or use a nondefault
data type in your models, you can skip the remainder of this section.
On the other hand, if you plan to generate code from your models and use
nondefault data types, read the remainder of this section carefully, especially
the section on data type rules (see “Data Typing Rules” on page 3-44). In that
way, you can avoid introducing data type errors that prevent your model from
running to completion or simulating at all.
Data Types Supported by Simulink
Simulink supports all built-in MATLAB data types. The term built-in data type
refers to data types defined by MATLAB itself as opposed to data types defined
by MATLAB users. Unless otherwise specified, the term data type in the
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Working with Data Types
Simulink documentation refers to built-in data types. The following table lists
MATLAB’s built-in data types.
Name
Description
double
Double-precision floating point
single
Single-precision floating point
int8
Signed eight-bit integer
uint8
Unsigned eight-bit integer
int16
Signed 16-bit integer
uint16
Unsigned 16-bit integer
int32
Signed 32-bit integer
uint32
Unsigned 32-bit integer
Besides the built-in types, Simulink defines a boolean (1 or 0) type, instances
of which are represented internally by uint8 values.
Block Support for Data and Numeric Signal Types
All Simulink blocks accept signals of type double by default. Some blocks
prefer boolean input and others support multiple data types on their inputs.
The following table lists Simulink blocks that prefer boolean or support
multiple data types. The table also lists blocks that support complex signals.
Block
Comments
Abs
Inputs a real or complex signal of type double. Outputs
a real signal of type double.
Combinatorial
Logic
Input and output data type is boolean, if Boolean mode
is enabled (see “Enabling Strict Boolean Type
Checking” on page 3-45); otherwise, double.
Constant
Outputs a real or complex signal of any data type.
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Block
Comments
Data Type
Conversion
Inputs and outputs any real or complex data type.
Demux
Accepts mixed-type signal vectors.
Display
Accepts signals of any complex or real data type.
Dot Product
Inputs and outputs real or complex values of type
double.
3-40
Enable
The corresponding subsystem enable port accepts
signals of type boolean or double.
From
Outputs the data type (or types) of the signal connected
to the corresponding Goto block.
From
Workspace
Outputs type of corresponding workspace values.
Gain
Input can be a real- or complex-valued signal or vector
of any data type except boolean.
Goto
Input can be of any type.
Ground
Outputs a 0 signal of the same type as the port to which
it is connected.
Hit Crossing
Inputs a double signal. Outputs boolean, if Boolean
mode is enabled (see “Enabling Strict Boolean Type
Checking” on page 3-45); otherwise, double.
Inport
An inport accepts real- or complex-valued signals of any
data type. The elements of an input signal vector must
be of the same type if the inport is a root-level inport or
the inport is directly connected to an outport of the
same subsystem.
Integrator
An Integrator block accepts and outputs signals of type
double on its data ports. Its external reset port accepts
signals of type double or boolean.
Working with Data Types
Block
Comments
Logical
Operator
Inputs and outputs real signals of type boolean, if
Boolean mode is enabled (see “Enabling Strict Boolean
Type Checking” on page 3-45); otherwise, real signals of
type double.
Manual Switch
Accepts real- or complex-valued signals of any type. All
inputs must have the same signal and data type.
Math Function
Inputs and outputs real or complex values of type
double.
MATLAB
Function
Inputs and outputs real or complex values of type
double.
Memory
Inputs real or complex signals of any data type.
Merge
Inputs and outputs any real or complex data type.
Multiport
Switch
The control input of a Multiport Switch block accepts a
real-valued signal of any type except boolean. The
other inputs accept real- or complex-valued inputs of
any type. All inputs must of the same data and numeric
type. The block outputs the type of signal on its inputs.
Mux
Accepts any supported Simulink data type, including
mixed-type vectors, on each input.
Out
Accepts any Simulink data type as input. Accepts
mixed-type vectors as input, if the outport is in a
subsystem and no initial condition is specified.
Product
Accepts real- or complex-valued signals of any data
type except boolean. All inputs must be of the same
data type.
Relational
Operator
Accepts any supported data type as inputs. Both inputs
must be of the same type. Outputs boolean, if Boolean
mode is enabled (see “Enabling Strict Boolean Type
Checking” on page 3-45); otherwise, double.
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Block
Comments
Rounding
Function
double.
Scope
Accepts real or complex signals of any data type.
Selector
Outputs the data types of the selected input signals.
Sum
Accepts any Simulink data type as input. All inputs
must be of the same type. Outputs the same type as the
input.
Switch
Accepts real- or complex-valued signals of any data
type as switched inputs (inputs 1 and 3). Both switched
inputs must be of the same type. The block output
signal has the data type of the input. The data type of
the threshold input must be boolean or double.
Terminator
Accepts any Simulink type.
To Workspace
Accepts any Simulink data type as input.
Trigger
The corresponding subsystem control port accepts
signals of type boolean or double.
Trigonometric
Function
Inputs and outputs real- or complex-valued signals of
type double.
Unit Delay
Accepts and outputs real- or complex-valued signals of
any data type.
Width
Accepts real- or complex-valued signals of any data
type, including mixed-type signal vectors.
Zero-Order Hold
Accepts any Simulink data type as input.
Accepts and outputs real or complex values of type
See Chapter 8, “Block Reference” for more information on the data types
supported by specific blocks for parameter and input and output values. If the
documentation for a block does not specify a data type, the block inputs or
outputs only data of type double.
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Working with Data Types
Specifying Block Parameter Data Types
When entering block parameters whose data type is user-specifiable, use the
syntax
type(value)
to specify the parameter, where type is the name of the data type and value is
the parameter value. The following examples illustrate this syntax.
single(1.0)
Specifies a single-precision value of 1.0
int8(2)
Specifies an eight-bit integer of value 2
int32(3+2i)
Specifies a complex value whose real and
imaginary parts are 32-bit integers
Creating Signals of a Specific Data Type
You can introduce a signal of a specific data type into a model in any of the
following ways:
• Load signal data of the desired type from the MATLAB workspace into your
model via a root-level inport or a From Workspace block.
• Create a Constant block in your model and set its parameter to the desired
type.
• Use a Data Type Conversion block to convert a signal to the desired data
type.
Displaying Port Data Types
To display the data types of ports in your model, select Port Data Types from
Simulink’s Format menu. Simulink does not update the port data type display
when you change the data type of a diagram element. To refresh the display,
type Ctrl-D.
Data Type Propagation
Whenever you start a simulation, enable display of port data types, or refresh
the port data type display, Simulink performs a processing step called data
type propagation. This step involves determining the types of signals whose
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Creating a Model
type is not otherwise specified and checking the types of signals and input ports
to ensure that they do not conflict. If type conflicts arise, Simulink displays an
error dialog that specifies the signal and port whose data types conflict.
Simulink also highlights the signal path that creates the type conflict.
Note You can insert typecasting (data type conversion) blocks in your model
to resolve type conflicts. See“Typecasting Signals” on page 3-45 for more
information.
Data Typing Rules
Observing the following rules will help you to create models that are typesafe
and therefore execute without error:
• Signal data types generally do not affect parameter data types, and vice
versa.
A significant exception to this rule is the Constant block whose output data
type is determined by the data type of its parameter.
• If the output of a block is a function of an input and a parameter and the
input and parameter differ in type, Simulink converts the parameter to the
input type before computing the output.
See “Typecasting Parameters” on page 3-45 for more information.
• In general, a block outputs the data type that appears at its inputs.
Significant exceptions include constant blocks and data type conversion
blocks whose output data types are determined by block parameters.
• Virtual blocks accept signals of any type on their inputs.
Examples of virtual blocks include Mux and Demux blocks and
unconditionally executed subsystems.
• The elements of a signal vector connected to a port of a nonvirtual block must
be of the same data type.
• The signals connected to the input data ports of a nonvirtual block cannot
differ in type.
• Control ports (for example, Enable and Trigger ports) accept boolean or
double signals.
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Working with Data Types
• Solver blocks accept only double signals.
• Connecting a nondouble signal to a block disables zero-crossing detection for
that block.
Enabling Strict Boolean Type Checking
By default, Simulink detects but does not signal an error when it detects that
double signals are connected to block that prefer boolean input. This ensures
compatibility with models created by earlier versions of Simulink that support
only double data type. You can enable strict boolean type checking by
unchecking the Relax boolean type checking option on the Diagnostics page
of the Simulation Parameters dialog box (see “The Diagnostics Page” on page
4-24).
Typecasting Signals
Simulink signals an error whenever it detects that a signal is connected to a
block that does not accept the signal’s data type. If you want to create such a
connection, you must explicitly typecast (convert) the signal to a type that the
block does accept. You can use Simulink’s Data Type Conversion block to
perform such conversions (see Data Type Conversion on page 8-41).
Typecasting Parameters
In general, during simulation, Simulink silently converts parameter data types
to signal data types (if they differ) when computing block outputs that are a
function of an input signal and a parameter. The following exceptions occur to
this rule:
• If the signal data type cannot represent the parameter value, Simulink halts
the simulation and signals an error.
Consider, for example, the following model.
This model uses a Gain block to amplify a constant input signal. Computing
the output of the Gain block requires computing the product of the input
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Creating a Model
signal and the gain. Such a computation requires that the two values be of
the same data type. However, in this case, the data type of the signal, uint8
(unsigned 8-bit word), differs from the data type of the gain parameter, int32
(signed 32-bit integer). Thus computing the output of the gain block entails
a type conversion.
When making such conversions, Simulink always casts the parameter type
to the signal type. Thus, in this case, Simulink must convert the Gain block’s
gain value to the data type of the input signal. Simulink can make this
conversion only if the input signal’s data type (uint8) can represent the gain.
In this case, Simulink can make the conversion because the gain is 255,
which is within the range of the uint8 data type (0 to 255). Thus, this model
simulates without error. However, if the gain were slightly larger (for
example, 256), Simulink would signal an out-of-range error if you attempted
to simulate the model.
• If the signal data type can represent the parameter value but only at reduced
precision, Simulink issues a warning message and continues the simulation.
Consider, for example, the following model.
In this example, the signal type accommodates only integer values while the
gain value has a fractional component. Simulating this model causes
Simulink to truncate the gain to the nearest integral value (2) and issue a
loss-of-precision warning. On the other hand, if the gain were 2.0, Simulink
would simulate the model without complaint because in this case the
conversion entails no loss of precision.
Note Conversion of an int32 parameter to a float or double can entail a
loss of precision. The loss can be severe if the magnitude of the parameter
value is large. If an int32 parameter conversion does entail a loss of precision,
Simulink issues a warning message.
3-46
Working with Complex Signals
Working with Complex Signals
By default, the values of Simulink signals are real numbers. However, models
can create and manipulates signals that have complex numbers as values.
You can introduce a complex-valued signal into a model in any of the following
ways:
• Load complex-valued signal data from the MATLAB workspace into the
model via a root-level inport.
• Create a Constant block in your model and set its value to a complex number.
• Create real signals corresponding to the real and imaginary parts of a
complex signal and then combine the parts into a complex signal, using
Real-Imag to Complex conversion block.
You can manipulate complex signals via blocks that accept them. Most
Simulink blocks accept complex signals as input. If you are not sure whether a
block accepts complex signals, refer to the documentation for the block in
Chapter 8, “Block Reference.”
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Creating a Model
Summary of Mouse and Keyboard Actions
These tables summarize the use of the mouse and keyboard to manipulate
blocks, lines, and signal labels. LMB means press the left mouse button; CMB,
the center mouse button; and RMB, the right mouse button.
The first table lists mouse and keyboard actions that apply to blocks.
Table 3-2: Manipulating Blocks
Task
Microsoft Windows
UNIX
Select one block
LMB
LMB
Select multiple
blocks
Shift + LMB
Shift + LMB; or CMB
alone
Copy block from
another window
Drag block
Drag block
Move block
Drag block
Drag block
Duplicate block
Ctrl + LMB and drag;
Ctrl + LMB and drag;
or RMB and drag
or RMB and drag
Connect blocks
LMB
LMB
Disconnect block
Shift + drag block
Shift + drag block; or
CMB and drag
The next table lists mouse and keyboard actions that apply to lines.
Table 3-3: Manipulating Lines
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Task
Microsoft Windows
UNIX
Select one line
LMB
LMB
Select multiple lines
Shift + LMB
Shift + LMB; or CMB
alone
Draw branch line
Ctrl + drag line; or
RMB and drag line
Ctrl + drag line; or
RMB + drag line
Summary of Mouse and Keyboard Actions
Table 3-3: Manipulating Lines (Continued)
Task
Microsoft Windows
UNIX
Route lines around
blocks
Shift + draw line
segments
Shift + draw line
segments; or CMB and
draw segments
Move line segment
Drag segment
Drag segment
Move vertex
Drag vertex
Drag vertex
Create line
segments
Shift + drag line
Shift + drag line; or
CMB + drag line
The next table lists mouse and keyboard actions that apply to signal labels.
Table 3-4: Manipulating Signal Labels
Action
Microsoft Windows
UNIX
Create signal label
Double-click on line,
then type label
Double-click on line,
then type label
Copy signal label
Ctrl + drag label
Ctrl + drag label
Move signal label
Drag label
Drag label
Edit signal label
Click in label, then edit
Click in label, then edit
Delete signal label
Shift + click on label,
then press Delete
Shift + click on label,
then press Delete
The next table lists mouse and keyboard actions that apply to annotations.
Table 3-5: Manipulating Annotations
Action
Microsoft Windows
UNIX
Create annotation
Double-click in
diagram, then type text
Double-click in
diagram, then type text
Copy annotation
Ctrl + drag label
Ctrl + drag label
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Creating a Model
Table 3-5: Manipulating Annotations (Continued)
3-50
Action
Microsoft Windows
UNIX
Move annotation
Drag label
Drag label
Edit annotation
Click in text, then edit
Click in text, then edit
Delete annotation
Shift + select
annotation, then press
Delete
Shift + select
annotation, then press
Delete
Creating Subsystems
Creating Subsystems
As your model increases in size and complexity, you can simplify it by grouping
blocks into subsystems. Using subsystems has these advantages:
• It helps reduce the number of blocks displayed in your model window.
• It allows you to keep functionally related blocks together.
• It enables you to establish a hierarchical block diagram, where a Subsystem
block is on one layer and the blocks that make up the subsystem are on
another.
You can create a subsystem in two ways:
• Add a Subsystem block to your model, then open that block and add the
blocks it contains to the subsystem window.
• Add the blocks that make up the subsystem, then group those blocks into a
subsystem.
Creating a Subsystem by Adding the Subsystem
Block
To create a subsystem before adding the blocks it contains, add a Subsystem
block to the model, then add the blocks that make up the subsystem:
1 Copy the Subsystem block from the Signals & Systems library into your
model.
2 Open the Subsystem block by double-clicking on it.
3 In the empty Subsystem window, create the subsystem. Use Inport blocks to
represent input from outside the subsystem and Outport blocks to represent
external output. For example, the subsystem below includes a Sum block
and Inport and Outport blocks to represent input to and output from the
subsystem:
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Creating a Model
Creating a Subsystem by Grouping Existing Blocks
If your model already contains the blocks you want to convert to a subsystem,
you can create the subsystem by grouping those blocks:
1 Enclose the blocks and connecting lines that you want to include in the
subsystem within a bounding box. You cannot specify the blocks to be
grouped by selecting them individually or by using the Select All command.
For more information, see “Selecting Multiple Objects Using a Bounding
Box” on page 3–7.
For example, this figure shows a model that represents a counter. The Sum
and Unit Delay blocks are selected within a bounding box.
When you release the mouse button, the two blocks and all the connecting
lines are selected.
2 Choose Create Subsystem from the Edit menu. Simulink replaces the
selected blocks with a Subsystem block. This figure shows the model after
choosing the Create Subsystem command (and resizing the Subsystem
block so the port labels are readable).
If you open the Subsystem block, Simulink displays the underlying system, as
shown below. Notice that Simulink adds Inport and Outport blocks to
represent input from and output to blocks outside the subsystem.
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Creating Subsystems
As with all blocks, you can change the name of the Subsystem block. Also, you
can customize the icon and dialog box for the block using the masking feature,
described in Chapter 6.
Labeling Subsystem Ports
Simulink labels ports on a Subsystem block. The labels are the names of Inport
and Outport blocks that connect the subsystem to blocks outside the subsystem
through these ports.
You can hide the port labels by selecting the Subsystem block, then choosing
Hide Port Labels from the Format menu. You can also hide one or more port
labels by selecting the appropriate Inport or Outport block in the subsystem
and choosing Hide Name from the Format menu.
This figure shows two models. The subsystem on the left contains two Inport
blocks and one Outport block. The Subsystem block on the right shows the
labeled ports.
Using Callback Routines
You can define MATLAB expressions that execute when the block diagram or
a block is acted upon in a particular way. These expressions, called callback
routines, are associated with block or model parameters. For example, the
callback associated with a block’s OpenFcn parameter is executed when the
model user double-clicks on that block’s name or path changes.
To define callback routines and associate them with parameters, use the
set_param command (see set_param on page 10-24).
For example, this command evaluates the variable testvar when the user
double-clicks on the Test block in mymodel:
set_param('mymodel/Test', 'OpenFcn', testvar)
You can examine the clutch system (clutch.mdl) for routines associated with
many model callbacks.
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Creating a Model
These tables list the parameters for which you can define callback routines,
and indicate when those callback routines are executed. Routines that are
executed before or after actions take place occur immediately before or after the
action.
Table 3-6: Model Callback Parameters
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Parameter
When Executed
CloseFcn
Before the block diagram is closed.
PostLoadFcn
After the model is loaded. Defining a callback
routine for this parameter might be useful for
generating an interface that requires that the
model has already been loaded.
InitFcn
Called at start of model simulation.
PostSaveFcn
After the model is saved.
PreLoadFcn
Before the model is loaded. Defining a callback
routine for this parameter might be useful for
loading variables used by the model.
PreSaveFcn
Before the model is saved.
StartFcn
Before the simulation starts.
StopFcn
After the simulation stops. Output is written to
workspace variables and files before the StopFcn is
executed.
Creating Subsystems
Table 3-7: Block Callback Parameters
Parameter
When Executed
CloseFcn
When the block is closed using the close_system
command.
CopyFcn
After a block is copied. The callback is recursive for
Subsystem blocks (that is, if you copy a Subsystem
block that contains a block for which the CopyFcn
parameter is defined, the routine is also executed).
The routine is also executed if an add_block
command is used to copy the block.
DeleteFcn
Before a block is deleted. This callback is recursive
for Subsystem blocks.
DestroyFcn
When block has been destroyed.
InitFcn
Before the block diagram is compiled and before
block parameters are evaluated.
LoadFcn
After the block diagram is loaded. This callback is
recursive for Subsystem blocks.
ModelCloseFcn
Before the block diagram is closed. This callback is
recursive for Subsystem blocks.
MoveFcn
When block is moved or resized.
NameChangeFcn
After a block’s name and/or path changes. When a
Subsystem block’s path is changed, it recursively
calls this function for all blocks it contains after
calling its own NameChangeFcn routine.
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Creating a Model
Table 3-7: Block Callback Parameters (Continued)
3-56
Parameter
When Executed
OpenFcn
When the block is opened. This parameter is
generally used with Subsystem blocks. The routine
is executed when you double-click on the block or
when an open_system command is called with the
block as an argument. The OpenFcn parameter
overrides the normal behavior associated with
opening a block, which is to display the block’s
dialog box or to open the subsystem.
ParentCloseFcn
Before closing a subsystem containing the block or
when the block is made part of a new subsystem
using the new_system command (see new_system
on page 10-19).
PreSaveFcn
Before the block diagram is saved. This callback is
recursive for Subsystem blocks.
PostSaveFcn
After the block diagram is saved. This callback is
recursive for Subsystem blocks.
StartFcn
After the block diagram is compiled and before the
simulation starts.
StopFcn
At any termination of the simulation.
UndoDeleteFcn
When a block delete is undone.
Tips for Building Models
Tips for Building Models
Here are some model-building hints you might find useful:
• Memory issues
In general, the more memory, the better Simulink performs.
• Using hierarchy
More complex models often benefit from adding the hierarchy of subsystems
to the model. Grouping blocks simplifies the top level of the model and can
make it easier to read and understand the model. For more information, see
“Creating Subsystems” on page 3–51. The Model Browser (see “The Model
Browser” on page 3-66) provides useful information about complex models.
• Cleaning up models
Well organized and documented models are easier to read and understand.
Signal labels and model annotations can help describe what is happening in
a model. For more information, see “Signal Labels” on page 3–32 and
“Annotations” on page 3–37.
• Modeling strategies
If several of your models tend to use the same blocks, you might find it easier
to save these blocks in a model. Then, when you build new models, just open
this model and copy the commonly used blocks from it. You can create a block
library by placing a collection of blocks into a system and saving the system.
You can then access the system by typing its name in the MATLAB command
window.
Generally, when building a model, design it first on paper, then build it using
the computer. Then, when you start putting the blocks together into a model,
add the blocks to the model window before adding the lines that connect
them. This way, you can reduce how often you need to open block libraries.
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Modeling Equations
One of the most confusing issues for new Simulink users is how to model
equations. Here are some examples that may improve your understanding of
how to model equations.
Converting Celsius to Fahrenheit
To model the equation that converts Celsius temperature to Fahrenheit:
TF = 9/5(TC) + 32
First, consider the blocks needed to build the model:
• A Ramp block to input the temperature signal, from the Sources library
• A Constant block, to define a constant of 32, also from the Sources library
• A Gain block, to multiply the input signal by 9/5, from the Math library
• A Sum block, to add the two quantities, also from the Math library
• A Scope block to display the output, from the Sinks library
Next, gather the blocks into your model window.
Assign parameter values to the Gain and Constant blocks by opening
(double-clicking on) each block and entering the appropriate value. Then, click
on the Close button to apply the value and close the dialog box.
Now, connect the blocks.
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Modeling Equations
The Ramp block inputs Celsius temperature. Open that block and change the
Initial output parameter to 0. The Gain block multiplies that temperature by
the constant 9/5. The Sum block adds the value 32 to the result and outputs the
Fahrenheit temperature.
Open the Scope block to view the output. Now, choose Start from the
Simulation menu to run the simulation. The simulation will run for 10
seconds.
Modeling a Simple Continuous System
To model the differential equation
x′ ( t ) = – 2x ( t ) + u ( t )
where u(t) is a square wave with an amplitude of 1 and a frequency of 1
rad/sec. The Integrator block integrates its input, x′, to produce x. Other blocks
needed in this model include a Gain block and a Sum block. To generate a
square wave, use a Signal Generator block and select the Square Wave form
but change the default units to radians/sec. Again, view the output using a
Scope block. Gather the blocks and define the gain.
In this model, to reverse the direction of the Gain block, select the block, then
use the Flip Block command from the Format menu. Also, to create the branch
line from the output of the Integrator block to the Gain block, hold down the
Ctrl key while drawing the line. For more information, see “Drawing a Branch
Line” on page 3–28. Now you can connect all the blocks.
An important concept in this model is the loop that includes the Sum block, the
Integrator block, and the Gain block. In this equation, x is the output of the
Integrator block. It is also the input to the blocks that compute x′, on which it
is based. This relationship is implemented using a loop.
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Creating a Model
The Scope displays x at each time step. For a simulation lasting 10 seconds, the
output looks like this.
The equation you modeled in this example can also be expressed as a transfer
function. The model uses the Transfer Fcn block, which accepts u as input and
outputs x. So, the block implements x/u. If you substitute sx for x′ in the
equation above.
sx = – 2x + u
Solving for x gives
x = u ⁄ (s + 2)
Or,
x ⁄ u = 1 ⁄ (s + 2)
The Transfer Fcn block uses parameters to specify the numerator and
denominator coefficients. In this case, the numerator is 1 and the denominator
is s+2. Specify both terms as vectors of coefficients of successively decreasing
powers of s. In this case the numerator is [1] (or just 1) and the denominator
is [1 2]. The model now becomes quite simple:
The results of this simulation are identical to those of the previous model.
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Saving a Model
Saving a Model
You can save a model by choosing either the Save or Save As command from
the File menu. Simulink saves the model by generating a specially formatted
file called the model file (with the .mdl extension) that contains the block
diagram and block properties. The format of the model file is described in
Appendix B.
If you are saving a model for the first time, use the Save command to provide
a name and location to the model file. Model file names must start with a letter
and can contain no more than 31 letters, numbers, and underscores.
If you are saving a model whose model file was previously saved, use the Save
command to replace the file’s contents or the Save As command to save the
model with a new name or location.
Simulink follows this procedure while saving a model:
1 If the mdl file for the model already exists, it is renamed as a temporary file.
2 Simulink executes all block PreSaveFcn callback routines, then executes the
block diagram’s PreSaveFcn callback routine.
3 Simulink writes the model file to a new file using the same name and an
extension of mdl.
4 Simulink executes all block PostSaveFcn callback routines, then executes
the block diagram’s PostSaveFcn callback routine.
5 Simulink deletes the temporary file.
If an error occurs during this process, Simulink renames the temporary file to
the name of the original model file, writes the current version of the model to a
file with an .err extension, and issues an error message. Simulink performs
steps 2 through 4 even if an error occurs in an earlier step.
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Creating a Model
Printing a Block Diagram
You can print a block diagram by selecting Print from the File menu (on a
Microsoft Windows system) or by using the print command in the MATLAB
command window (on all platforms).
On a Microsoft Windows system, the Print menu item prints the block diagram
in the current window.
Print Dialog Box
When you select the Print menu item, the Print dialog box appears. The Print
dialog box enables you to selectively print systems within your model. Using
the dialog box, you can:
• Print the current system only
• Print the current system and all systems above it in the model hierarchy
• Print the current system and all systems below it in the model hierarchy,
with the option of looking into the contents of masked and library blocks
• Print all systems in the model, with the option of looking into the contents of
masked and library blocks
• Print an overlay frame on each diagram
The portion of the Print dialog box that supports selective printing is similar
on supported platforms. This figure shows how it looks on a Microsoft Windows
system. In this figure, only the current system is to be printed.
3-62
Printing a Block Diagram
When you select either the Current system and below or All systems option,
two check boxes become enabled. In this figure, All systems is selected.
Selecting the Look Under Mask Dialog check box prints the contents of
masked subsystems when encountered at or below the level of the current
block. When printing all systems, the top-level system is considered the current
block so Simulink looks under any masked blocks encountered.
Selecting the Expand Unique Library Links check box prints the contents of
library blocks when those blocks are systems. Only one copy is printed
regardless of how many copies of the block are contained in the model. For more
information about libraries, see “Libraries” on page 3-21.
The print log lists the blocks and systems printed. To print the print log, select
the Include Print Log check box.
Selecting the Frame check box prints a title block frame on each diagram.
Enter the path to the title block frame in the adjacent edit box. You can create
a customized title block frame, using MATLAB’s frame editor. See frameedit
in the online MATLAB reference for information on using the frame editor to
create title block frames.
Print Command
The format of the print command is
print –ssys –device filename
sys is the name of the system to be printed. The system name must be preceded
by the s switch identifier and is the only required argument. sys must be open
or must have been open during the current session. If the system name
contains spaces or takes more than one line, you need to specify the name as a
string. See the examples below.
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Creating a Model
device specifies a device type. For a list and description of device types, see
Using MATLAB Graphics.
filename is the PostScript file to which the output is saved. If filename exists,
it is replaced. If filename does not include an extension, an appropriate one is
appended.
For example, this command prints a system named untitled.
print –suntitled
This command prints the contents of a subsystem named Sub1 in the current
system.
print –sSub1
This command prints the contents of a subsystem named Requisite Friction.
print (['–sRequisite Friction'])
The next example prints a system named Friction Model, a subsystem whose
name appears on two lines. The first command assigns the newline character
to a variable; the second prints the system.
cr = sprintf('\n');
print (['–sFriction' cr 'Model'])
Specifying Paper Size and Orientation
Simulink lets you specify the type and orientation of the paper used to print a
model diagram. You can do this on all platforms by setting the model’s
PaperType and PaperOrientation properties, respectively (see “Model
Parameters” on page A-3), using the set_param command. You can set the
paper orientation alone, using MATLAB’s orient command. On Windows, the
Print dialog box lets you set the page type and orientation properties as well.
Positioning and Sizing a Diagram
You can use a model’s PaperPositionMode and PaperPosition parameters to
position and size the model’s diagram on the printed page. The value of the
PaperPosition parameter is a vector of form [left bottom width height].
The first two elements specify the bottom left corner of a rectangular area on
the page, measured from the page’s bottom left corner. The last two elements
specify the width and height of the rectangle. When the model’s
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Printing a Block Diagram
PaperPositionMode is manual, Simulink positions (and scales, if necessary)
the model’s diagram to fit inside the specified print rectangle. For example, the
following commands
vdp
set_param(‘vdp’,
set_param('vdp',
set_param(‘vdp’,
set_param(‘vdp’,
print -svdp
‘PaperType’, ‘usletter’)
'PaperOrientation', 'landscape')
‘PaperPositionMode’, ‘manual’)
‘PaperPosition’, [0.5 0.5 4 4])
print the block diagram of the vdp sample model in the lower left corner of a
U.S. letter-size page in landscape orientation.
If PaperPositionMode is auto, Simulink centers the model diagram on the
printed page, scaling the diagram, if necessary, to fit the page.
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Creating a Model
The Model Browser
The Model Browser enables you to:
• Navigate a model hierarchically
• Open systems in a model directly
• Determine the blocks contained in a model
The browser operates differently on Microsoft Windows and UNIX platforms.
Using the Model Browser on Windows
To display the Model Browser pane, select Model Browser from the Simulink
View menu. The model window splits into two panes. The left pane displays the
browser, a tree-structured view of the block diagram displayed in the right
pane.
Each entry in the tree view corresponds to a subsystem in the model. You can
expand/collapse the tree by clicking on the +/- boxes beside each subsystem, or
by pressing the left/right arrow or +/- keys on your numeric keypad. You can
move up/down the tree by pressing the up/down arrow on your keypad. Click
on any subsystem to display its contents in the diagram view. To open a new
window on a subsystem, double click the subsystem in the diagram view.
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The Model Browser
Using the Model Browser on UNIX
To open the Model Browser, select Show Browser from the File menu. The
Model Browser window appears, displaying information about the current
model. This figure shows the Model Browser window displaying the contents of
the clutch system.
Current
system and
subsystems
it contains
Blocks in
the selected
system
Contents of the Browser Window
The Model Browser window consists of:
• The systems list. The list on the left contains the current system and the
subsystems it contains, with the current system selected.
• The blocks list. The list on the right contains the names of blocks in the
selected system. Initially, this window displays blocks in the top-level
system.
• The File menu, which contains the Print, Close Model, and Close Browser
menu items.
• The Options menu, which contains these menu items: Open System, Look
Into System, Display Alphabetical/Hierarchical List, Expand All, Look
Under Mask Dialog, and Expand Library Links.
• Options check boxes and buttons: Look Under [M]ask Dialog and Expand
[L]ibrary Links check boxes, and Open System and Look Into System
buttons. By default, Simulink does not display contents of masked blocks and
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Creating a Model
blocks that are library links. These check boxes enable you to override the
default.
• The block type of the selected block.
• Dialog box buttons: Help, Print, and Close.
Interpreting List Contents
Simulink identifies masked blocks, reference blocks, blocks with defined
OpenFcn parameters, and systems that contain subsystems using these
symbols before a block or system name:
• A plus sign (+) before a system name in the systems list indicates that the
system is expandable, which means that it has systems beneath it.
Double-click on the system name to expand the list and display its contents
in the blocks list. When a system is expanded, a minus sign (–) appears
before its name.
• [M] indicates that the block is masked, having either a mask dialog box or a
mask workspace. For more information about masking, see Chapter 6.
• [L] indicates that the block is a reference block. For more information, see
“Libraries” on page 3-21.
• [O] indicates that an open function (OpenFcn) callback is defined for the
block. For more information about block callbacks, see “Using Callback
Routines” on page 3-53.
• [S] indicates that the system is a Stateflow® block.
Opening a System
You can open any block or system whose name appears in the blocks list. To
open a system:
1 In the systems list, select by single-clicking on the name of the parent
system that contains the system you want to open. The parent system’s
contents appear in the blocks list.
2 Depending on whether the system is masked, linked to a library block, or
has an open function callback, you open it as follows:
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The Model Browser
- If the system has no symbol to its left, double-click on its name or select its
name and click on the Open System button.
- If the system has an [M] or [O] before its name, select the system name and
click on the Look Into System button.
Looking into a Masked System or a Linked Block
By default, the Model Browser considers masked systems (identified by [M])
and linked blocks (identified by [L]) as blocks and not subsystems. If you click
on Open System while a masked system or linked block is selected, the Model
Browser displays the system or block’s dialog box (Open System works the
same way as double-clicking on the block in a block diagram). Similarly, if the
block’s OpenFcn callback parameter is defined, clicking on Open System while
that block is selected executes the callback function.
You can direct the Model Browser to look beyond the dialog box or callback
function by selecting the block in the blocks list, then clicking on Look Into
System. The Model Browser displays the underlying system or block.
Displaying List Contents Alphabetically
By default, the systems list indicates the hierarchy of the model. Systems that
contain systems are preceded with a plus sign (+). When those systems are
expanded, the Model Browser displays a minus sign (–) before their names. To
display systems alphabetically, select the Display Alphabetical List menu
item on the Options menu.
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Creating a Model
Tracking Model Versions
A Simulink model can go through many versions during its development.
Simulink helps you to track the various versions by generating and storing
version control information, including the version number, the persons who
created and last updated the model, and optionally a change history. The
following Simulink features allow you to manage and use the version control
information:
• The Simulink Model Parameters dialog box allows you to edit some of the
version control information stored in the model and to select various version
control options.
• The Simulink Model Info block allows you to display version control
information, including that maintained by an external version control
system, as an annotation block in a model diagram.
• Simulink version control parameters allow you to access version control
information from the MATLAB command line or an M-file.
Specifying the Current User
When a user creates or updates a model, Simulink logs the user’s name in the
model for version control purposes. Simulink assumes that the user’s name is
specified by at least one of the following environment variables: USER,
USERNAME, LOGIN, or LOGNAME. If your system does not define any of these
variables, Simulink does not update the user name in the model.
UNIX systems always define the USER environment variable and set its value
to the name you use to log onto your system. Thus, if you are using a UNIX
system, you do not have to do anything to enable Simulink to identify you as
the current user. Windows systems, on the other hand, may define some or
none of the “user name” environment variables that Simulink expects,
depending on the version of Windows installed on your system and whether it
operates stand-alone or connected to a network. You can use the MATLAB
command getenv to determine which if any of the environment variables is
defined. For example, enter
getenv('user')
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Tracking Model Versions
at the MATLAB command line to determine if the USER environment variable
exists on your Windows system. If not, you must set it yourself. On Windows
95 and 98, set the value by entering the following line
set user=yourname
in your system’s autoexec.bat file, where yourname is the name by which you
want to be identified in a model file. Then, reboot your computer.
Note The autoexec.bat file typically is found in the c:\ directory on your
system’s hard disk.
On Windows NT, use the Environment panel of the Windows NT System
Properties dialog box to set the USER environment variable (if it is not already
defined).
To display the System Properties dialog box, select System in your system’s
Control Panel folder, which resides in your system’s My Computer folder,
which resides on your Windows NT desktop. To set the USER variable, enter
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Creating a Model
USER in the Variable field, your login name in the Value field, and select the
Set button. Then select OK to dismiss the dialog box.
Model Properties Dialog
The Model Properties dialog box allows you to edit some version control
parameters and set some related options. To display the dialog box, choose
Model Parameters from the Simulink File menu.
Model Properties Pane
The Model Properties pane lets you edit the following version control
parameters.
Creator. Name of the person who created this model. Simulink sets this
property to the value of the USER environment variable when you create the
model. Edit this field to change the value.
Created. Date and time this model was created.
Model description. Description of the model.
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Tracking Model Versions
Options Pane
The Options pane lets you choose a configuration manager and specify version
control information formats.
Configuration manager. External configuration manager used to manage this
model. Choosing this option allows you to include information from the
configuration manager in a Model Info annotation block. See Model Info on
page 8-131 for more information.
The file cmopts.m in the MATLABROOT/toolbox/local directory specifies the
default configuration manager for models. The default “default” configuration
manager is none. You can edit this file to specify another choice.
Model version format. Format used to display the model version number in the
Model Parameters pane and in Model Info blocks. The value of this parameter
can be any text string. The text string can include occurrences of the tag
%<AutoIncrement:#> where # is an integer. Simulink replaces the tag with #
when displaying the model’s version number. For example, it displays
1.%<AutoIncrement:2>
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Creating a Model
as
1.2
Simulink increments # by 1 when saving the model. For example,
1.%<1.%<AutoIncrement:2>
becomes
1.%<1.%<AutoIncrement:3>
when you save the model.
Modified by format. Format used to display the “Modified By” value in the
History pane, in the history log, and in Model Info blocks. The value of this
field can be any string. The string can include the tag %<Auto>. Simulink
replaces occurrences of this tag with the current value of the USER environment
variable.
Modified date format. Format used to display the “Last modified date” in the
History pane, in the history log, and in Model Info blocks. The value of this
field can be any string. The string can contain the tag %<Auto>. Simulink
replaces occurrences of this tag with the current date and time.
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Tracking Model Versions
History Pane
The History pane allows you enable, view, and edit this model’s change history.
Last modified by. Name of the person who last modified this model. Simulink sets
the value of this parameter to the value of the USER environment variable when
you save a model. You cannot edit this field.
Last modified date. Date that this model was last modified. Simulink sets the
value of this parameter to the system date and time when you save a model.
You cannot edit this field.
Modified history update. Specifies whether to prompt a user for a comment when
this model is saved. If you choose “Prompt for Comments When Save,”
Simulink prompts you for a comment to store in the model. You would typically
use the comment to document any changes you made to the model in the
current session. Simulink stores the previous value of this parameter in the
model’s change history. See “Creating a Model Change History” on page 3–76
for more information.
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Creating a Model
Modified history. History of modifications of this model. Simulink compiles the
history from comments entered by users when they update the model. You can
edit the history at any time by selecting the adjacent Edit button.
Creating a Model Change History
Simulink allows you to create and store a record of changes to a model in the
model itself. Simulink compiles the history automatically from comments that
you or other users enter when they save changes to a model.
Logging Changes
To start a change history, select the “Prompt for Comments When Save” option
from the History pane on the Simulink Model Properties dialog box. The next
time you save the model, Simulink displays a Log Change dialog box.
If you want to add an item to the model’s change history, enter the item in the
Modified Comments edit field and click the Save button. If you do not want to
enter an item for this session, uncheck the Include “Modified Contents” in
“Modified History” option. If you want to discontinue change logging, uncheck
the Show this dialog box next time when save option.
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Tracking Model Versions
Editing the Change History
To edit the change history for a model, click the Edit button on the Simulink
Model Properties dialog box. Simulink displays the model’s history in a
Modification History dialog box.
Edit the history displayed in the dialog and select Apply or OK to save the
changes.
Version Control Properties
Simulink stores version control information in a model as model parameters.
You can access this information from the MATLAB command line or from an
M-file, using the Simulink get_param command. The following table describes
the model parameters used by Simulink to store version control information.
Property
Description
Created
Date created
Creator
Name of the person who created this model
ModifiedBy
Person who last modified this model
ModifiedByFormat
Format of the ModifiedBy parameter. Value
can be an string. The string can include the
tag %<Auto>. Simulink replaces the tag with
the current value of the USER environment
variable.
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Creating a Model
3-78
Property
Description
ModifiedDate
Date modified
ModifiedDateFormat
Format of the ModifiedDate parameter.
Value can be any string. The string can
include the tag %<Auto>. Simulink
replaces the tag with the current date and
time when saving the model.
ModifiedComment
Comment entered by user who last updated
this model
ModifiedHistory
History of changes to this model
ModelVersion
Version number
ModelVersionFormat
Format of model version number. Can be
any string. The string can contain the tag
%<AutoIncrement:#> where # is an integer.
Simulink replaces the tag with # when
displaying the version number. It
increments # when saving the model.
Description
Description of model
LastModificationDate
Date last modified.
Ending a Simulink Session
Ending a Simulink Session
Terminate a Simulink session by closing all Simulink windows.
Terminate a MATLAB session by choosing one of these commands from the
File menu:
• On a Microsoft Windows system: Exit MATLAB
• On a UNIX system: Quit MATLAB
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Creating a Model
3-80
4
Running a Simulation
Introduction . . . . . . . . . . . . . . . . . . . . 4-2
Using Menu Commands . . . . . . . . . . . . . . . . 4-2
Running a Simulation from the Command Line . . . . . . 4-3
Running a Simulation Using Menu Commands . .
Setting Simulation Parameters and Choosing the Solver
Applying the Simulation Parameters . . . . . . . .
Starting the Simulation . . . . . . . . . . . . . .
Simulation Diagnostics Dialog Box . . . . . . . . .
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4-4
4-4
4-4
4-4
4-6
The Simulation Parameters Dialog Box .
The Solver Page . . . . . . . . . . . .
The Workspace I/O Page . . . . . . . . .
The Diagnostics Page . . . . . . . . . .
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4-8
4-8
4-17
4-24
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Improving Simulation Performance and Accuracy . . 4-27
Speeding Up the Simulation . . . . . . . . . . . . . . 4-27
Improving Simulation Accuracy . . . . . . . . . . . . . 4-28
Running a Simulation from the Command Line . . . . 4-29
Using the sim Command . . . . . . . . . . . . . . . 4-29
Using the set_param Command . . . . . . . . . . . . . 4-29
4
Running a Simulation
Introduction
You can run a simulation either by using Simulink menu commands or by
entering commands in the MATLAB command window.
Many users use menu commands while they develop and refine their models,
then enter commands in the MATLAB command window to run the simulation
in “batch” mode.
Using Menu Commands
Running a simulation using menu commands is easy and interactive. These
commands let you select an ordinary differential equation (ODE) solver and
define simulation parameters without having to remember command syntax.
An important advantage is that you can perform certain operations
interactively while a simulation is running:
• You can modify many simulation parameters, including the stop time, the
solver, and the maximum step size.
• You can change the solver.
• You can simulate another system at the same time.
• You can click on a line to see the signal carried on that line on a floating
(unconnected) Scope or Display block.
• You can modify the parameters of a block, as long as you do not cause a
change in:
- The number of states, inputs, or outputs
- The sample time
- The number of zero crossings
- The vector length of any block parameters
- The length of the internal block work vectors
You cannot make changes to the structure of the model, such as adding or
deleting lines or blocks, during a simulation. If you need to make these kinds
of changes, you need to stop the simulation, make the change, then start the
simulation again to see the results of the change.
4-2
Introduction
Running a Simulation from the Command Line
Running a simulation from the command line has these advantages over
running a simulation using menu commands:
• You can simulate M-file and MEX-file models, as well as Simulink block
diagram models.
• You can run a simulation from an M-file, allowing simulation and block
parameters to be changed iteratively.
For more information, see “Running a Simulation from the Command Line” on
page 4-29.
4-3
4
Running a Simulation
Running a Simulation Using Menu Commands
This section discusses how to use Simulink menu commands and the
Simulation Parameters dialog box to run a simulation.
Setting Simulation Parameters and Choosing the
Solver
You set the simulation parameters and select the solver by choosing
Parameters from the Simulation menu. Simulink displays the Simulation
Parameters dialog box, which uses three “pages” to manage simulation
parameters:
• The Solver page allows you to set the start and stop times, choose the solver
and specify solver parameters, and choose some output options.
• The Workspace I/O page manages input from and output to the MATLAB
workspace.
• The Diagnostics page allows you to select the level of warning messages
displayed during a simulation.
Each page of the dialog box, including the parameters you set on the page, is
discussed in detail in “The Simulation Parameters Dialog Box” on page 4-8.
You can specify parameters as valid MATLAB expressions, consisting of
constants, workspace variable names, MATLAB functions, and mathematical
operators.
Applying the Simulation Parameters
After you have set the simulation parameters and selected the solver, you are
ready to apply them to your model. Press the Apply button on the bottom of the
dialog box to apply the parameters to the model. To apply the parameters and
close the dialog box, press the Close button.
Starting the Simulation
After you have applied the solver and simulation parameters to your model,
you are ready to run the simulation. Select Start from the Simulation menu to
run the simulation. You can also use the keyboard shortcut, Ctrl-T. When you
select Start, the menu item changes to Stop.
4-4
Running a Simulation Using Menu Commands
Your computer beeps to signal the completion of the simulation.
Note A common mistake that new Simulink users make is to start a
simulation while the Simulink block library is the active window. Make sure
your model window is the active window before starting a simulation.
To stop a simulation, choose Stop from the Simulation menu. The keyboard
shortcut for stopping a simulation is Ctrl-T, the same as for starting a
simulation.
You can suspend a running simulation by choosing Pause from the Simulation
menu. When you select Pause, the menu item changes to Continue. You
proceed with a suspended simulation by choosing Continue.
If the model includes any blocks that write output to a file or to the workspace,
or if you select output options on the Simulation Parameters dialog box,
Simulink writes the data when the simulation is terminated or suspended.
4-5
4
Running a Simulation
Simulation Diagnostics Dialog Box
If errors occur during a simulation, Simulink halts the simulation and displays
the errors in the Simulation Diagnostics dialog box.
Click to display
error message.
Double-click to
display error
source.
Click to display
error source.
The dialog box has two panes. The upper pane consist of columns that display
the following information for each error.
Message. Message type (for example, block error, warning, log)
Source. Name of the model element (for example, a block) that caused the error.
Fullpath. Path of the element that caused the error.
Summary. Error message abbreviated to fit in the column.
Reported by. Component that reported the error (for example, Simulink,
Stateflow, Real-Time Workshop, etc).
4-6
Running a Simulation Using Menu Commands
The lower pane initially contains the full content of the first error message
listed in the top pane. You can display the content of other messages by
single-clicking on their entries in the upper pane.
In addition to displaying the Simulation Diagnostics dialog box, Simulink
also opens (if necessary) the diagram that contains the error source and
highlights the source.
You can similarly display other error sources by double-clicking on the
corresponding error message in the top pane, by double-clicking on the name of
the error source in the error message (highlighted in blue), or by selecting the
Open button on the dialog box.
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4
Running a Simulation
The Simulation Parameters Dialog Box
This section discusses the simulation parameters, which you specify either on
the Simulation Parameters dialog box or using the sim (see sim on page 4-30)
and simset (see simset on page 4-32) commands. Parameters are described as
they appear on the dialog box pages.
This table summarizes the actions performed by the dialog box buttons, which
appear on the bottom of each dialog box page.
Table 4-1: Simulation Parameters Dialog Box Buttons
Button
Action
Ok
Applies the parameter values and closes the dialog box. During
a simulation, the parameter values are applied immediately.
Cancel
Changes the parameter values back to the values they had
when the dialog box was most recently opened and closes the
dialog box.
Help
Displays help text for the dialog box page.
Apply
Applies the current parameter values and keeps the dialog box
open. During a simulation, the parameter values are applied
immediately.
The Solver Page
The Solver page appears when you first choose Parameters from the
Simulation menu or when you select the Solver tab.
The Solver page allows you to:
• Set the simulation start and stop times
• Choose the solver and specify its parameters
• Select output options
4-8
The Simulation Parameters Dialog Box
Simulation Time
You can change the start time and stop time for the simulation by entering new
values in the Start time and Stop time fields. The default start time is 0.0
seconds and the default stop time is 10.0 seconds.
Simulation time and actual clock time are not the same. For example, running
a simulation for 10 seconds will usually not take 10 seconds. The amount of
time it takes to run a simulation depends on many factors, including the
model’s complexity, the solver’s step sizes, and the computer’s clock speed.
Solvers
Simulation of Simulink models involves the numerical integration of sets of
ordinary differential equations (ODEs). Simulink provides a number of solvers
for the simulation of such equations. Because of the diversity of dynamic
system behavior, some solvers may be more efficient than others at solving a
particular problem. To obtain accurate and fast results, take care when
choosing the solver and setting parameters.
You can choose between variable-step and fixed-step solvers. Variable-step
solvers can modify their step sizes during the simulation. They provide error
control and zero crossing detection. Fixed-step solvers take the same step size
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4
Running a Simulation
during the simulation. They provide no error control and do not locate zero
crossings. For a thorough discussion of solvers, see Using MATLAB.
Default solvers. If you do not choose a solver, Simulink chooses one based on
whether your model has states:
• If the model has continuous states, ode45 is used. ode45 is an excellent
general purpose solver. However, if you know that your system is stiff and if
ode45 is not providing acceptable results, try ode15s. For a definition of stiff,
see the note at the end of the section “Variable-step solvers” on page 4-11.
• If the model has no continuous states, Simulink uses the variable-step solver
called discrete and displays a message indicating that it is not using ode45.
Simulink also provides a fixed-step solver called discrete. This model shows
the difference between the two discrete solvers.
With sample times of 0.5 and 0.75, the fundamental sample time for the
model is 0.25 seconds. The difference between the variable-step and the
fixed-step discrete solvers is the time vector that each generates.
The fixed-step discrete solver generates this time vector:
[0.0 0.25 0.5 0.75 1.0 1.25 ...]
The variable-step discrete solver generates this time vector:
[0.0 0.5 0.75 1.0 1.5 2.0 2.25 ...]
The step size of the fixed-step discrete solver is the fundamental sample
time. The variable-step discrete solver takes the largest possible steps.
4-10
The Simulation Parameters Dialog Box
Variable-step solvers. You can choose these variable-step solvers: ode45, ode23,
ode113, ode15s, ode23s, and discrete. The default is ode45 for systems with
states, or discrete for systems with no states:
• ode45 is based on an explicit Runge-Kutta (4,5) formula, the
Dormand-Prince pair. It is a one-step solver; that is, in computing y(tn), it
needs only the solution at the immediately preceding time point, y(tn–1). In
general, ode45 is the best solver to apply as a “first try” for most problems.
• ode23 is also based on an explicit Runge-Kutta (2,3) pair of Bogacki and
Shampine. It may be more efficient than ode45 at crude tolerances and in the
presence of mild stiffness. ode23 is a one-step solver.
• ode113 is a variable order Adams-Bashforth-Moulton PECE solver. It may be
more efficient than ode45 at stringent tolerances. ode113 is a multistep
solver; that is, it normally needs the solutions at several preceding time
points to compute the current solution.
• ode15s is a variable order solver based on the numerical differentiation
formulas (NDFs). These are related to but are more efficient than the
backward differentiation formulas, BDFs (also known as Gear’s method).
Like ode113, ode15s is a multistep method solver. If you suspect that a
problem is stiff or if ode45 failed or was very inefficient, try ode15s.
• ode23s is based on a modified Rosenbrock formula of order 2. Because it is a
one-step solver, it may be more efficient than ode15s at crude tolerances. It
can solve some kinds of stiff problems for which ode15s is not effective.
• ode23t is an implementation of the trapezoidal rule using a “free”
interpolant. Use this solver if the problem is only moderately stiff and you
need a solution without numerical damping.
• ode23tb is an implementation of TR-BDF2, an implicit Runge-Kutta formula
with a first stage that is a trapezoidal rule step and a second stage that is a
backward differentiation formula of order two. By construction, the same
iteration matrix is used in evaluating both stages. Like ode23s, this solver
may be more efficient than ode15s at crude tolerances.
• discrete (variable-step) is the solver Simulink chooses when it detects that
your model has no continuous states.
4-11
4
Running a Simulation
Note For a stiff problem, solutions can change on a time scale that is very
short compared to the interval of integration, but the solution of interest
changes on a much longer time scale. Methods not designed for stiff problems
are ineffective on intervals where the solution changes slowly because they
use time steps small enough to resolve the fastest possible change. Jacobian
matrices are generated numerically for ode15s and ode23s. For more
information, see Shampine, L. F., Numerical Solution of Ordinary Differential
Equations, Chapman & Hall, 1994.
Fixed-step solvers. You can choose these fixed-step solvers: ode5, ode4, ode3,
ode2, ode1, and discrete:
• ode5 is the fixed-step version of ode45, the Dormand-Prince formula.
• ode4 is RK4, the fourth-order Runge-Kutta formula.
• ode3 is the fixed-step version of ode23, the Bogacki-Shampine formula.
• ode2 is Heun’s method, also known as the improved Euler formula.
• ode1 is Euler’s method.
• discrete (fixed-step) is a fixed-step solver that performs no integration. It is
suitable for models having no states and for which zero crossing detection
and error control are not important.
If you think your simulation may be providing unsatisfactory results, see
“Improving Simulation Performance and Accuracy” on page 4-27.
Solver Options
The default solver parameters provide accurate and efficient results for most
problems. In some cases, however, tuning the parameters can improve
performance. (For more information about tuning these parameters, see
“Improving Simulation Performance and Accuracy” on page 4-27). You can
tune the selected solver by changing parameter values on the Solver panel.
Step Sizes
For variable-step solvers, you can set the maximum and suggested initial step
size parameters. By default, these parameters are automatically determined,
indicated by the value auto.
4-12
The Simulation Parameters Dialog Box
For fixed-step solvers, you can set the fixed step size. The default is also auto.
Maximum step size. The Max step size parameter controls the largest time step
the solver can take. The default is determined from the start and stop times:
t stop – t start
h max = -------------------------------50
Generally, the default maximum step size is sufficient. If you are concerned
about the solver missing significant behavior, change the parameter to prevent
the solver from taking too large a step. If the time span of the simulation is very
long, the default step size may be too large for the solver to find the solution.
Also, if your model contains periodic or nearly periodic behavior and you know
the period, set the maximum step size to some fraction (such as 1/4) of that
period.
In general, for more output points, change the refine factor, not the maximum
step size. For more information, see “Refine output” on page 4-16.
Initial step size. By default, the solvers select an initial step size by examining
the derivatives of the states at the start time. If the first step size is too large,
the solver may step over important behavior. The initial step size parameter is
a suggested first step size. The solver tries this step size but reduces it if error
criteria are not satisfied.
Error Tolerances
The solvers use standard local error control techniques to monitor the error at
each time step. During each time step, the solvers compute the state values at
the end of the step and also determine the local error, the estimated error of
these state values. They then compare the local error to the acceptable error,
which is a function of the relative tolerance (rtol) and absolute tolerance (atol).
If the error is greater than the acceptable error for any state, the solver reduces
the step size and tries again:
• Relative tolerance measures the error relative to the size of each state. The
relative tolerance represents a percentage of the state’s value. The default,
1e-3, means that the computed state will be accurate to within 0.1%.
• Absolute tolerance is a threshold error value. This tolerance represents the
acceptable error as the value of the measured state approaches zero.
4-13
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Running a Simulation
The error for the ith state, ei, is required to satisfy.
e i ≤ max ( rtol × x i , atol i )
The figure below shows a plot of a state and the regions in which the acceptable
error is determined by the relative tolerance and the absolute tolerance:
rtol*|x|
State
Region in which rtol determines acceptable error
Region in which atol determines acceptable error
atol
Time
If you specify auto (the default), Simulink sets the absolute tolerance for each
state initially to 1e-6. As the simulation progresses, Simulink resets the
absolute tolerance for each state to the maximum value that the state has
assumed thus far times the relative tolerance for that state. Thus, if a state
goes from 0 to 1 and reltol is 1e-3, then by the end of the simulation the
abstol is set to 1e-3 also. If a state goes from 0 to 1000, then the abstol is set
to 1.
If the computed setting is not suitable, you can determine an appropriate
setting yourself. You might have to run a simulation more than once to
determine an appropriate value for the absolute tolerance. If the magnitudes
of the states vary widely, it might be appropriate to specify different absolute
tolerance values for different states. You can do this on the Integrator block’s
dialog box.
The Maximum Order for ode15s
The ode15s solver is based on NDF formulas of order one through five.
Although the higher order formulas are more accurate, they are less stable. If
your model is stiff and requires more stability, reduce the maximum order to 2
(the highest order for which the NDF formula is A-stable). When you choose the
ode15s solver, the dialog box displays this parameter.
As an alternative, you might try using the ode23s solver, which is a fixed-step,
lower order (and A-stable) solver.
4-14
The Simulation Parameters Dialog Box
Multitasking Options
If you select a fixed-step solver, the Solver page of the Simulation Parameters
dialog box displays a Mode options list. The list allows you to select one of the
following simulation modes.
MultiTasking. This mode issues an error if it detects an illegal sample rate
transition between blocks, that is, a direct connection between blocks operating
at different sample rates. In real-time multitasking systems, illegal sample
rate transitions between tasks can result in a task’s output not being available
when needed by another task. By checking for such transitions, multitasking
mode helps you to create valid models of real-world multitasking systems,
where sections of your model represent concurrent tasks.
Use rate transition blocks to eliminate illegal rate transitions from your model.
Simulink provides two such blocks: Unit Delay (see Unit Delay on page 8-214)
and Zero-Order Hold (see Zero-Order Hold on page 8-221). To eliminate an
illegal slow-to-fast transition, insert a Unit Delay block running at the slow
rate between the slow output port and the fast input port. To eliminate an
illegal fast-to-slow transition, insert a Zero-Order Hold block running at the
slow rate between the fast output port and the slow input port. For more
information, see Chapter 7, “Models with Multiple Sample Rates,” in the
Real-Time Workshop Users Guide.
SingleTasking. This mode does not check for sample rate transitions among
blocks. This mode is useful when you are modeling a single-tasking system. In
such systems, task synchronization is not an issue.
Auto. This option causes Simulink to use single-tasking mode if all blocks
operate at the same rate and multitasking mode if the model contains blocks
operating at different rates.
Output Options
The Output options area of the dialog box enables you to control how much
output the simulation generates. You can choose from three popup options:
• Refine output
• Produce additional output
• Produce specified output only
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4
Running a Simulation
Refine output. The Refine output choice provides additional output points when
the simulation output is too coarse. This parameter provides an integer
number of output points between time steps; for example, a refine factor of 2
provides output midway between the time steps, as well as at the steps. The
default refine factor is 1.
To get smoother output, it is much faster to change the refine factor instead of
reducing the step size. When the refine factor is changed, the solvers generate
additional points by evaluating a continuous extension formula at those points.
Changing the refine factor does not change the steps used by the solver.
The refine factor applies to variable-step solvers and is most useful when using
ode45. The ode45 solver is capable of taking large steps; when graphing
simulation output, you may find that output from this solver is not sufficiently
smooth. If this is the case, run the simulation again with a larger refine factor.
A value of 4 should provide much smoother results.
Produce additional output. The Produce additional output choice enables you to
specify directly those additional times at which the solver generates output.
When you select this option, Simulink displays an Ouput Times field on the
Solver page. Enter a MATLAB expression in this field that evaluates to an
additional time or a vector of additional times. The additional output is
produced using a continuous extension formula at the additional times. Unlike
the refine factor, this option changes the simulation step size so that time steps
coincide with the times that you have specified for additional output.
Produce specified output only. The Produce specified output only choice provides
simulation output only at the specified output times. This option changes the
simulation step size so that time steps coincide with the times that you have
specified for producing output. This choice is useful when comparing different
simulations to ensure that the simulations produce output at the same times.
Comparing Output options. A sample simulation generates output at these times:
0, 2.5, 5, 8.5, 10
Choosing Refine output and specifying a refine factor of 2 generates output at
these times:
0, 1.25, 2.5, 3.75, 5, 6.75, 8.5, 9.25, 10
4-16
The Simulation Parameters Dialog Box
Choosing the Produce additional output option and specifying [0:10]
generates output at these times:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
and perhaps at additional times, depending on the step-size chosen by the
variable-step solver.
Choosing the Produce Specified Output Only option and specifying [0:10]
generates output at these times:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
The Workspace I/O Page
You can direct simulation output to workspace variables and get input and
initial states from the workspace. On the Simulation Parameters dialog box,
select the Workspace I/O tab. This page appears:
Loading Input from the Base Workspace
Simulink can apply input from a model’s base workspace to the model’s
top-level inports during a simulation run. To specify this option, check the
Input box in the Load from workspace area of the Workspace I/O page. Then,
enter an external input specification (see below) in the adjacent edit box and
select Apply.
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4
Running a Simulation
The external input can take any of the following forms.
External Input Matrix. The first column of an external input matrix must be a
vector of times in ascending order. The remaining columns specify input
values. In particular, each column represents the input for a different Inport
block signal (in sequential order) and each row is the input value for the
corresponding time point. Simulink linearly interpolates or extrapolates input
values as necessary, if the Interpolate data option is selected for the
corresponding inport (see “Interpolate data” on page 8-102).
The total number of columns of the input matrix must equal n + 1, where n is
the total number of signals entering the model’s inports. If you define t and u
in the base workspace, you do not need to enter an external input specification
for the model. This is because the default external input specification for a
model is [t,u].
For example, suppose that a model has two inports, one of which accepts two
signals and the other, one signal. Also, suppose that the base workspace
defines u and t as follows:
t = (0:0.1:1)';
u = [sin(t), cos(t), 4*cos(t)];
Then, to specify the external input for this model, simply check the model’s
external input box.
Structure with time. Simulink can read data from the workspace in the form of a
structure whose name is specified in the Input text field. The input structure
must have two top-level fields: time and signals. The time field contains a
column vector of the simulation times. The signals field contains an array of
substructures, each of which corresponds to a model input port. Each
substructure has the field: values. The values field contains a column vector
of inputs for the corresponding input port.
For example, consider the following model, which has two inputs.
4-18
The Simulation Parameters Dialog Box
Suppose that the base workspace defines a model input vector, a, as follows:
a.time = (0:0.1:1)';
a.signals(1).values = sin(a.time);
a.signals(2).values = cos(a.time);
Then, to specify a as the external input for this model, check the Input box and
enter a in the adjacent text field.
Note Simulink can read back simulation data saved to the workspace in the
Structure with time output format. See “Structure with time” on page 4-21
for more information.
Structure. The structure format is the same as the Structure with time format
except that time field is empty. For example, in the preceding example, you
could set the time field as follows.
a.time = []
In this case, Simulink reads the input for the first time step from the first
element of an inport’s value array, the value for the second time step from the
second element of the value array, etc.
Note Simulink can read back simulation data saved to the workspace in the
Structure output format. See “Structure” on page 4-21 for more information.
Per-Port Structures. This format consists of a separate structure-with-time or
structure-without-time for each port. Each port’s input data structure has only
one signals field. To specify this option, enter the names of the structures in
the Input text field as a comma-separated list in1, in2, ..., inN, where in1
is the data for your model’s first port, in2 for the second inport, and so on.
External Input Time Expression. The time expression can be any MATLAB
expression that evaluates to a row vector equal in length to the number of
signals entering the model’s inports. For example, suppose that a model has
one vector inport that accepts two signals. Furthermore, suppose that timefcn
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4
Running a Simulation
is a user-defined function that returns a row vector two elements long. The
following are valid input time expressions for such a model:
'[3*sin(t), cos(2*t)]'
'4*timefcn(w*t)+7'
Simulink evaluates the expression at each step of the simulation, applying the
resulting values to the model’s inports. Note that Simulink defines the variable
t when it runs the simulation. Also, you can omit the time variable in
expressions for functions of one variable. For example, Simulink interprets the
expression sin as sin(t).
Saving Output to the Workspace
You can specify return variables by selecting the Time, States, and/or Output
check boxes in the Save to workspace area of this dialog box page. Specifying
return variables causes Simulink to write values for the time, state, and output
trajectories (as many as are selected) into the workspace.
To assign values to different variables, specify those variable names in the field
to the right of the check boxes. To write output to more than one variable,
specify the variable names in a comma-separated list. Simulink saves the
simulation times in a vector have the name specified in the Save to Workspace
area.
Note Simulink saves the output to the workspace at the base sample rate of
the model. Use a To Workspace block if you want to save output at a different
sample rate (see To Workspace on page 8-199).
The Save options area enables you to specify the format and restrict the
amount of output saved.
Format options for model states and outputs are:
Matrix. Simulink saves the model states in a matrix that has the name specified
in the Save to Workspace area (for example, xout). Each column of the state
matrix corresponds to a model state, each row to the states at a specific time.
The model output matrix has the name specified in the Save to Workspace
4-20
The Simulation Parameters Dialog Box
area (for example, yout). Each column corresponds to a model outport, each
row to the outputs at a specific time.
Structure with time. Simulink saves the model’s outputs in a structure having the
name specified in the Save to Workspace area (for example, yout). The
structure has two top-level fields: time and signals. The time field contains a
vector of the simulation times. The signals field contains an array of
substructures, each of which corresponds to a model outport. Each
substructure has three fields: values, label, blockName. The values field
contains a vector of outputs for the corresponding outport. The label field
specifies the label of the signal connected to the outport. The blockName field
specifies the name of the outport. Simulink saves the model’s states in a
structure have the same organization as the model output structure.
Structure. This format is the same as the preceding except that Simulink does
not store simulation times in the time field of the saved structure.
Per-Port Structures. This format consists of a separate structure-with-time or
structure-without-time for each output port. Each output data structure has
only one signals field. To specify this option, enter the names of the structures
in the Output text field as a comma-separated list out1, out2, ..., outN,
where out1 is the data for your model’s first port, out2 for the second inport,
and so on.
To set a limit on the number of rows of data saved, select the check box labeled
Limit rows to last and specify the number of rows to save. To apply a
decimation factor, enter a value in the field to the right of the Decimation
label. For example, a value of 2 saves every other point generated.
Loading and Saving States
Initial conditions, which are applied to the system at the start of the
simulation, are generally set in the blocks. You can override initial conditions
set in the blocks by specifying them in the States area of this page.
You can also save the final states for a simulation and apply them to another
simulation. This feature might be useful when you want to save a steady-state
solution and restart the simulation at that known state. The states are saved
in the format that you select in the Save options area of the Workspace I/O
page. If you select Structure or Structure with Time, the saved format is as
follows:
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Running a Simulation
Structure with time. Simulink saves the model’s states in a structure having the
name specified in the Final State field of the Save to Workspace area (for
example, xFinal). The structure has two top-level fields: time and signals.
The time field contains a vector of the simulation times. The signals field
contains an array of substructures, each of which corresponds to a block that
has states. Each substructure has three fields: values, label, blockName. The
values field contains a vector of states for the corresponding block. The label
field can be either CState (for continuous state) or DState_n where n can be 1,
2, 3 ... to the maximum number of sets of discrete states for the corresponding
block. The blockName field specifies the name of the block represented by this
structure element.
Structure. This format is the same as the preceding except that Simulink does
not store simulation times in the time field of the saved structure
You load states by selecting the Initial State check box and specifying the
name of a variable that contains the initial state values. This variable can be a
matrix or a structure of the same form as is used to save final states. This
allows Simulink to set the initial states for the current session to the final
states saved in previous session, using the Structure or Structure with time
format.
If the check box is not selected or the state vector is empty ([]), Simulink uses
the initial conditions defined in the blocks.
You save the final states (the values of the states at the termination of the
simulation) by selecting the Final State check box and entering a variable in
the adjacent edit field.
When the Model Has Multiple States. If you want to specify the initial conditions for
a model that has multiple states, you need to determine the order of the states.
You can determine a model’s initial conditions and the ordering of its states
with this command
[sizes, x0, xstord] = sys([], [], [], 0)
where sys is the model name. The command returns:
• sizes, a vector that indicates certain model characteristics. Only the first
two elements apply to initial conditions: sizes(1) is the number of
continuous states, and sizes(2) is the number of discrete states. The sizes
4-22
The Simulation Parameters Dialog Box
vector is described in more detail in the companion volume to this guide,
Writing S-Functions.
• x0, the block initial conditions.
• xstord, a string matrix that contains the full path name of all blocks in the
model that have states. The order of the blocks in the xstord and x0 vectors
are the same.
For example, this statement obtains the values of the initial conditions and the
ordering of the states for the vdp model (the example shows only the values for
sizes(1), the number of continuous states, and sizes(2), the number of
discrete states):
[sizes, x0, xstord] = vdp([], [], [], 0)
sizes =
2
0
x0 =
2
0
xstord =
'vdp/Integrator1'
'vdp/Integrator2'
4-23
4
Running a Simulation
The Diagnostics Page
You can indicate the desired action for many types of events or conditions that
can be encountered during a simulation by selecting the Diagnostics tab on the
Simulation Parameters dialog box. This dialog box appears:
For each event type, you can choose whether you want no message, a warning
message, or an error message. A warning message does not terminate a
simulation, but an error message does.
Consistency Checking
Consistency checking is a debugging tool that validates certain assumptions
made by Simulink’s ODE solvers. Its main use is to make sure that S-functions
adhere to the same rules as Simulink built-in blocks. Because consistency
checking results in a significant decrease in performance (up to 40%), it should
generally be set to off. Use consistency checking to validate your S-functions
and to help you determine the cause of unexpected simulation results.
To perform efficient integration, Simulink saves (caches) certain values from
one time step for use in the next time step. For example, the derivatives at the
end of a time step can generally be reused at the start of the next time step. The
solvers take advantage of this to avoid redundant derivative calculations.
Another purpose of consistency checking is to ensure that blocks produce
constant output when called with a given value of t (time). This is important
for the stiff solvers (ode23s and ode15s) because, while calculating the
4-24
The Simulation Parameters Dialog Box
Jacobian, the block’s output functions may be called many times at the same
value of t.
When consistency checking is enabled, Simulink recomputes the appropriate
values and compares them to the cached values. If the values are not the same,
a consistency error occurs. Simulink compares computed values for these
quantities:
• Outputs
• Zero crossings
• Derivatives
• States
Disabling Zero Crossing Detection
You can disable zero crossing detection for a simulation. For a model that has
zero crossings, disabling the detection of zero crossings may speed up the
simulation but might have an adverse effect on the accuracy of simulation
results.
This option disables zero crossing detection for those blocks that have intrinsic
zero crossing detection. It does not disable zero crossing detection for the Hit
Crossing block.
Disable optimized I/O storage
Checking this option causes Simulink to allocate a separate memory buffer for
each block’s I/O values instead of reusing memory buffers. This can
substantially increase the amount of memory required to simulate large
models. So you should select this option only when you need to debug a model.
In particular, you should disable buffer reuse if you need to:
• Debug a C-MEX s-function
• Use a floating scope or display to inspect signals in a model that you are
debugging
Simulink opens an error dialog if buffer reuse is enabled and you attempt to
use a floating scope or display to display a signal whose buffer has been
reused.
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4
Running a Simulation
Relax boolean type checking (2.x compatible)
Checking this option causes blocks that would otherwise require inputs of type
boolean to accept inputs of type double. This ensures compatibility with
models created by versions of Simulink earlier than Simulink 3. For example,
consider the following model.
This model connects signals of type double to a Logical Operator block that
ordinarily requires inputs of type boolean. Consequently, this model runs
without error only if the Relax boolean type checking option is selected.
4-26
Improving Simulation Performance and Accuracy
Improving Simulation Performance and Accuracy
Simulation performance and accuracy can be affected by many things,
including the model design and choice of simulation parameters.
The solvers handle most model simulations accurately and efficiently with
their default parameter values. However, some models will yield better results
if you adjust solver and simulation parameters. Also, if you know information
about your model’s behavior, your simulation results can be improved if you
provide this information to the solver.
Speeding Up the Simulation
Slow simulation speed can have many causes. Here are a few:
• Your model includes a MATLAB Fcn block. When a model includes a
MATLAB Fcn block, the MATLAB interpreter is called at each time step,
drastically slowing down the simulation. Use the built-in Fcn block or
Elementary Math block whenever possible.
• Your model includes an M-file S-function. M-file S-functions also cause the
MATLAB interpreter to be called at each time step. Consider either
converting the S-function to a subsystem or to a C-MEX file S-function.
• Your model includes a Memory block. Using a Memory block causes the
variable-order solvers (ode15s and ode113) to be reset back to order 1 at each
time step.
• The maximum step size is too small. If you changed the maximum step size,
try running the simulation again with the default value (auto).
• Did you ask for too much accuracy? The default relative tolerance (0.1%
accuracy) is usually sufficient. For models with states that go to zero, if the
absolute tolerance parameter is too small, the simulation may take too many
steps around the near-zero state values. See the discussion of error in “Error
Tolerances” on page 4-13.
• The time scale may be too long. Reduce the time interval.
• The problem may be stiff but you’re using a nonstiff solver. Try using ode15s.
• The model uses sample times that are not multiples of each other. Mixing
sample times that are not multiples of each other causes the solver to take
small enough steps to ensure sample time hits for all sample times.
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Running a Simulation
• The model contains an algebraic loop. The solutions to algebraic loops are
iteratively computed at every time step. Therefore, they severely degrade
performance. For more information, see “Algebraic Loops” on page 9-7.
• Your model feeds a Random Number block into an Integrator block. For
continuous systems, use the Band-Limited White Noise block in the Sources
library.
Improving Simulation Accuracy
To check your simulation accuracy, run the simulation over a reasonable time
span. Then, reduce either the relative tolerance to 1e-4 (the default is 1e-3) or
the absolute tolerance and run it again. Compare the results of both
simulations. If the results are not significantly different, you can feel confident
that the solution has converged.
If the simulation misses significant behavior at its start, reduce the initial step
size to ensure that the simulation does not “step over” the significant behavior.
If the simulation results become unstable over time:
• Your system may be unstable.
• If you are using ode15s, you may need to restrict the maximum order to 2
(the maximum order for which the solver is A-stable) or try using the ode23s
solver.
If the simulation results do not appear to be accurate:
• For a model that has states whose values approach zero, if the absolute
tolerance parameter is too large, the simulation will take too few steps
around areas of near-zero state values. Reduce this parameter value or
adjust it for individual states in the Integrator dialog box.
• If reducing the absolute tolerances do not sufficiently improve the accuracy,
reduce the size of the relative tolerance parameter to reduce the acceptable
error and force smaller step sizes and more steps.
4-28
Running a Simulation from the Command Line
Running a Simulation from the Command Line
Entering simulation commands in the MATLAB command window or from an
M-file enables you to run unattended simulations. You can perform Monte
Carlo analysis by changing the parameters randomly and executing
simulations in a loop. You can run a simulation from the command line using
the sim command or the set_param command. Both are described below.
Using the sim Command
The full syntax of the command that runs the simulation is:
[t,x,y] = sim(model, timespan, options, ut);
Only the model parameter is required. Parameters not supplied on the
command are taken from the Simulation Parameters dialog box settings.
For detailed syntax for the sim command, see sim on page 4-30. The options
parameter is a structure that supplies additional simulation parameters,
including the solver name and error tolerances. You define parameters in the
options structure using the simset command (see simset on page 4-32). The
simulation parameters are discussed earlier in this chapter.
Using the set_param Command
You can use the set_param command to start, stop, pause, or continue a
simulation, or update a block diagram. Similarly, you can use the get_param
command to check the status of a simulation. The format of the set_param
command for this use is
set_param('sys', 'SimulationCommand', 'cmd')
where 'sys' is the name of the system and 'cmd' is 'start', 'stop', 'pause',
'continue', or 'update'.
The format of the get_param command for this use is:
get_param('sys', 'SimulationStatus')
Simulink returns 'stopped', 'initializing', 'running', 'paused',
'terminating', and 'external' (used with Real-Time Workshop).
4-29
sim
Purpose
4sim
Simulate a dynamic system.
Syntax
[t,x,y] = sim(model,timespan,options,ut);
[t,x,y1, y2, ..., yn] = sim(model,timespan,options,ut);
Description
The sim command simulates a dynamic system represented by a Simulink
model.
You can supply a null ([]) matrix for any right-side argument except the first
(the model name). The sim command uses default values for arguments
specified as null matrices. You can set optional simulation parameters, using
the sim command’s options argument. Parameters set in this way override
parameters specified by the model.
If you want to simulate a continuous system, you must specify the solver
parameter, using simset (see simset on page 4-32). The solver defaults to
VariableStepDiscrete for purely discrete models.
Arguments
4-30
t
Returns the simulation’s time vector.
x
Returns the simulation’s state matrix consisting of continuous
states followed by discrete states.
y
Returns the simulation’s output matrix. Each column contains
the output of a root-level Outport block, in port number order. If
any Outport block has a vector input, its output takes the
appropriate number of columns.
y1,...,yn
Each yi returns the output of the corresponding root-level
Outport block for a model that has n such blocks.
model
Name of a block diagram.
timespan
Simulation start and stop time. Specify as one of these:
tFinal to specify the stop time. The start time is 0.
[tStart tFinal] to specify the start and stop times.
[tStart OutputTimes tFinal] to specify the start and stop
times and time points to be returned in t. Generally, t will
include more time points. OutputTimes is equivalent to
choosing Produce additional output on the dialog box.
sim
Examples
options
Optional simulation parameters specified as a structure
created by the simset command (see simset on page 4-32).
ut
Optional external inputs to top-level Inport blocks. ut can be a
a MATLAB function (expressed as a string) that specifies the
input u = UT(t) at each simulation time step, a table of input
values versus time for all input ports, or a comma-separated
list of tables, ut1, ut2, ..., each of which corresponds to a
specific port. Tabular input for all ports may be in the form of a
MATLAB matrix or a structure. Tabular input for individual
ports must be in the form of a structure. See “Loading Input
from the Base Workspace” on page 4-17f or a description of the
matrix and structure input formats.
This command simulates the Van der Pol equations, using the vdp model that
comes with Simulink. The command uses all default parameters:
[t,x,y] = sim('vdp')
This command simulates the Van der Pol equations, using the parameter
values associated with the vdp model, but defines a value for the Refine
parameter:
[t,x,y] = sim('vdp', [], simset('Refine',2));
This command simulates the Van der Pol equations for 1,000 seconds, saving
the last 100 rows of the return variables. The simulation outputs values for t
and y only, but saves the final state vector in a variable called xFinal:
[t,x,y] = sim('vdp', 1000, simset('MaxRows', 100,
'OutputVariables', 'ty', 'FinalStateName', 'xFinal'));
See Also
simset, simget
4-31
simset
Purpose
4simset
Create or edit simulation parameters and solver properties for the sim
command.
Syntax
options = simset(property, value, ...);
options = simset(old_opstruct, property, value, ...);
options = simset(old_opstruct, new_opstruct);
simset
Description
The simset command creates a structure called options, in which the named
simulation parameters and solver properties have the specified values. All
unspecified parameters and properties take their default values. It is only
necessary to enter enough leading characters to uniquely identify the
parameter or property. Case is ignored for parameters and properties.
options = simset(property, value, ...) sets the values of the named
properties and stores the structure in options.
options = simset(old_opstruct, property, value, ...) modifies the
named properties in old_opstruct, an existing structure.
options = simset(old_opstruct, new_opstruct) combines two existing
options structures, old_opstruct and new_opstruct, into options. Any
properties defined in new_opstruct overwrite the same properties defined in
old_opstruct.
simset with no input arguments displays all property names and their possible
values.
You cannot obtain or set values of these properties and parameters using the
get_param and set_param commands.
Parameters
AbsTol
positive scalar {1e-6}
Absolute error tolerance. This scalar applies to all elements of the state vector.
AbsTol applies only to the variable-step solvers.
Decimation
positive integer {1}
Decimation for output variables. Decimation factor applied to the return
variables t, x, and y. A decimation factor of 1 returns every data logging time
point, a decimation factor of 2 returns every other data logging time point, etc.
4-32
simset
DstWorkspace
base | {current} | parent
Where to assign variables. This property specifies the workspace in which to
assign any variables defined as return variables or as output variables on the
To Workspace block.
FinalStateName
string {''}
Name of final states variable. This property specifies the name of a variable
into which Simulink saves the model’s states at the end of the simulation.
FixedStep
positive scalar
Fixed step size. This property applies only to the fixed-step solvers. If the model
contains discrete components, the default is the fundamental sample time;
otherwise, the default is one-fiftieth of the simulation interval.
InitialState
vector {[]}
Initial continuous and discrete states. The initial state vector consists of the
continuous states (if any) followed by the discrete states (if any). InitialState
supersedes the initial states specified in the model. The default, an empty
matrix, causes the initial state values specified in the model to be used.
InitialStep
positive scalar {auto}
Suggested initial step size. This property applies only to the variable-step
solvers. The solvers try a step size of InitialStep first. By default, the solvers
determine an initial step size automatically.
MaxOrder
1 | 2 | 3 | 4 | {5}
Maximum order of ode15s. This property applies only to ode15s.
MaxRows
nonnegative integer {0}
Limit number of output rows. This property limits the number of rows returned
in t, x, and y to the last MaxRows data logging time points. If specified as 0, the
default, no limit is imposed.
MaxStep
positive scalar {auto}
Upper bound on the step size. This property applies only to the variable-step
solvers and defaults to one-fiftieth of the simulation interval.
4-33
simset
OutputPoints
{specified} | all
Determine output points. When set to specified, the solver produces outputs
t, x, and y only at the times specified in timespan. When set to all, t, x, and y
also include the time steps taken by the solver.
OutputVariables
{txy} | tx | ty | xy | t | x | y
Set output variables. If 't', 'x', or 'y' is missing from the property string, the
solver produces an empty matrix in the corresponding output t, x, or y.
Refine
positive integer {1}
Output refine factor. This property increases the number of output points by
the specified factor, producing smoother output. Refine applies only to the
variable-step solvers. It is ignored if output times are specified.
RelTol
positive scalar {1e-3}
Relative error tolerance. This property applies to all elements of the state
vector. The estimated error in each integration step satisfies
e(i) <= max(RelTol*abs(x(i)),AbsTol(i))
This property applies only to the variable-step solvers and defaults to 1e-3,
which corresponds to accuracy within 0.1%.
Solver
VariableStepDiscrete |
ode45 | ode23 | ode113 | ode15s | ode23s |
FixedStepDiscrete |
ode5 | ode4 | ode3 | ode2 | ode1
Method to advance time. This property specifies which solver is used to advance
time.
SrcWorkspace
{base} | current | parent
Where to evaluate expressions. This property specifies the workspace in which
to evaluate MATLAB expressions defined in the model.
Trace
'minstep', 'siminfo', 'compile' {''}
Tracing facilities. This property enables simulation tracing facilities (specify
one or more as a comma-separated list):
• The 'minstep' trace flag specifies that simulation will stop when the
solution changes so abruptly that the variable-step solvers cannot take a
4-34
simset
step and satisfy the error tolerances. By default, Simulink issues a warning
message and continues the simulation.
• The 'siminfo' trace flag provides a short summary of the simulation
parameters in effect at the start of simulation.
• The 'compile' trace flag displays the compilation phases of a block diagram
model.
ZeroCross
{on} | off
Enable/disable location of zero crossings. This property applies only to the
variable-step solvers. If set to off, variable-step solvers will not detect zero
crossings for blocks having intrinsic zero crossing detection. The solvers adjust
their step sizes only to satisfy error tolerance.
Examples
This command creates an options structure called myopts that defines values
for the MaxRows and Refine parameters, using default values for other
parameters:
myopts = simset('MaxRows', 100, 'Refine', 2);
This command simulates the vdp model for 10 seconds and uses the parameters
defined in myopts:
[t,x,y] = sim('vdp', 10, myopts);
See Also
sim, simget
4-35
simget
Purpose
4simget
Get options structure properties and parameters.
Syntax
struct = simget(model)
value = simget(model, property)
Description
The simget command gets simulation parameter and solver property values for
the specified Simulink model. If a parameter or property is defined using a
variable name, simget returns the variable’s value, not its name. If the
variable does not exist in the workspace, Simulink issues an error message.
struct = simget(model) returns the current options structure for the
specified Simulink model. The options structure is defined using the sim and
simset commands.
value = simget(model, property) extracts the value of the named simulation
parameter or solver property from the model.
value = simget(OptionStructure, property) extracts the value of the
named simulation parameter or solver property from OptionStructure,
returning an empty matrix if the value is not specified in the structure.
property can be a cell array containing the list of parameter and property
names of interest. If a cell array is used, the output is also a cell array.
You need to enter only as many leading characters of a property name as are
necessary to uniquely identify it. Case is ignored for property names.
Examples
This command retrieves the options structure for the vdp model:
options = simget('vdp');
This command retrieves the value of the Refine property for the vdp model:
refine = simget('vdp', 'Refine');
See Also
4-36
sim, simset
5
Analyzing Simulation
Results
Viewing Output Trajectories
Using the Scope Block . . . . .
Using Return Variables . . . .
Using the To Workspace Block .
Linearization
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5-2
5-2
5-2
5-3
. . . . . . . . . . . . . . . . . . . 5-4
Equilibrium Point Determination . . . . . . . . . . 5-7
linfun . . . . . . . . . . . . . . . . . . . . . . . 5-9
trim . . . . . . . . . . . . . . . . . . . . . . . . 5-13
5
Analyzing Simulation Results
Viewing Output Trajectories
Output trajectories from Simulink can be plotted using one of three methods:
• Feeding a signal into either a Scope or an XY Graph block
• Writing output to return variables and using MATLAB plotting commands
• Writing output to the workspace using To Workspace blocks and plotting the
results using MATLAB plotting commands
Using the Scope Block
You can use display output trajectories on a Scope block during a simulation.
This simple model shows an example of the use of the Scope block.
The display on the Scope shows the output trajectory. The Scope block enables
you to zoom in on an area of interest or save the data to the workspace.
The XY Graph block enables you to plot one signal against another.
These blocks are described in Chapter 8.
Using Return Variables
By returning time and output histories, you can use MATLAB plotting
commands to display and annotate the output trajectories.
The block labeled Out is an Outport block from the Signals & Systems library.
The output trajectory, yout, is returned by the integration solver. For more
information, see Chapter 4.
You can also run this simulation from the Simulation menu by specifying
variables for the time, output, and states on the Workspace I/O page of the
Simulation Parameters dialog box. You can then plot these results using:
plot(tout,yout)
5-2
Viewing Output Trajectories
Using the To Workspace Block
The To Workspace block can be used to return output trajectories to the
MATLAB workspace. The model below illustrates this use.
The variables y and t appear in the workspace when the simulation is
complete. The time vector is stored by feeding a Clock block into a To
Workspace block. The time vector can also be acquired by entering a variable
name for the time on the Workspace I/O page of the Simulation Parameters
dialog box for menu-driven simulations, or by returning it using the sim
command (see Chapter 4 for more information).
The To Workspace block can accept a vector input, with each input element’s
trajectory stored as a column vector in the resulting workspace variable.
5-3
5
Analyzing Simulation Results
Linearization
Simulink provides the linmod and dlinmod functions to extract linear models
in the form of the state-space matrices A, B, C, and D. State-space matrices
describe the linear input-output relationship as
·
x = Ax + Bu
y = Cx + Du
where x, u, and y are state, input, and output vectors, respectively. For
example, the following model is called lmod.
To extract the linear model of this Simulink system, enter this command:
[A,B,C,D] = linmod('lmod')
A =
–2
–1
–1
1
0
0
0
1
–1
B =
1
0
0
C =
0
1
0
0
0
–1
D =
0
1
Inputs and outputs must be defined using Inport and Outport blocks from the
Signals & Systems library. Source and sink blocks do not act as inputs and
5-4
Linearization
outputs. Inport blocks can be used in conjunction with source blocks using a
Sum block. Once the data is in the state-space form or converted to an LTI
object, you can apply functions in the Control System Toolbox for further
analysis:
• Conversion to an LTI object:
sys = ss(A,B,C,D);
• Bode phase and magnitude frequency plot:
bode(A,B,C,D) or bode(sys)
• Linearized time response:
step(A,B,C,D) or step(sys)
impulse(A,B,C,D) or impulse(sys)
lsim(A,B,C,D,u,t) or lsim(sys,u,t)
Other functions in the Control System Toolbox and Robust Control Toolbox can
be used for linear control system design.
When the model is nonlinear, an operating point may be chosen at which to
extract the linearized model. The nonlinear model is also sensitive to the
perturbation sizes at which the model is extracted. These must be selected to
balance the trade-off between truncation and roundoff error. Extra arguments
to linmod specify the operating point and perturbation points:
[A,B,C,D] = linmod('sys', x, u, pert, xpert, upert)
For discrete systems or mixed continuous and discrete systems, use the
function dlinmod for linearization. This has the same calling syntax as linmod
except that the second right-hand argument must contain a sample time at
which to perform the linearization. For more information, see linfun on page
5-9.
Using linmod to linearize a model that contains Derivative or Transport Delay
blocks can be troublesome. Before linearizing, replace these blocks with
specially designed blocks that avoid the problems. These blocks are in the
Simulink Extras library in the Linearization sublibrary. You access the Extras
library by opening the Blocksets & Toolboxes icon.
5-5
5
Analyzing Simulation Results
• For the Derivative block, use the Switched derivative for linearization.
• For the Transport Delay block, use the Switched transport delay for
linearization. (Using this block requires that you have the Control System
Toolbox.)
When using a Derivative block, you can also try to incorporate the derivative
term in other blocks. For example, if you have a Derivative block in series with
a Transfer Fcn block, it is better implemented (although this is not always
possible) with a single Transfer Fcn block of the form
s
-----------s+a
In this example, the blocks on the left of this figure can be replaced by the block
on the right.
5-6
Equilibrium Point Determination
Equilibrium Point Determination
The Simulink trim function determines steady-state equilibrium points.
Consider, for example, this model, called lmod.
You can use the trim function to find the values of the input and the states that
set both outputs to 1. First, make initial guesses for the state variables (x) and
input values (u), then set the desired value for the output (y):
x = [0; 0; 0];
u = 0;
y = [1; 1];
Use index variables to indicate which variables are fixed and which can vary:
ix = [];
iu = [];
iy = [1;2];
% Don't fix any of the states
% Don't fix the input
% Fix both output 1 and output 2
5-7
5
Analyzing Simulation Results
Invoking trim returns the solution. Your results may differ due to roundoff
error.
[x,u,y,dx] = trim('lmod',x,u,y,ix,iu,iy)
x =
0.0000
1.0000
1.0000
u =
2
y =
1.0000
1.0000
dx =
1.0e–015 *
–0.2220
–0.0227
0.3331
Note that there may be no solution to equilibrium point problems. If that is the
case, trim returns a solution that minimizes the maximum deviation from the
desired result after first trying to set the derivatives to zero. For a description
of the trim syntax, see trim on page 5-13.
5-8
linfun
Purpose
5linfun
Extract the linear state-space model of a system around an operating point.
Syntax
[A,B,C,D]
[A,B,C,D]
[A,B,C,D]
[A,B,C,D]
Arguments
linfun
linmod, dlinmod, or linmod2.
sys
The name of the Simulink system from which the linear model
is to be extracted.
x and u
The state and the input vectors. If specified, they set the
operating point at which the linear model is to be extracted.
pert
Optional scalar perturbation factor used for both x and u. If not
specified, a default value of 1e-5 is used.
xpert and
upert
Optional vectors that explicitly set perturbation levels for
individual states and inputs. If specified, the pert argument is
ignored.
The ith state x is perturbed to x(i) + xpert(i)
The jth input u is perturbed to u(j) + upert(j)
Description
=
=
=
=
linfun('sys')
linfun('sys', x, u)
linfun('sys', x, u, pert)
linfun('sys', x, u, pert, xpert, upert)
linmod obtains linear models from systems of ordinary differential equations
described as Simulink models. linmod returns the linear model in state-space
form, A, B, C, D, which describes the linearized input-output relationship:
·
x = Ax + Bu
y = Cx + Du
Inputs and outputs are denoted in Simulink block diagrams using Inport and
Outport blocks.
[A,B,C,D] = linmod('sys') obtains the linearized model of sys around an
operating point with the state variables x and the input u set to zero.
linmod perturbs the states around the operating point to determine the rate of
change in the state derivatives and outputs (Jacobians). This result is used to
calculate the state-space matrices. Each state x(i) is perturbed to
5-9
linfun
x( i ) + ∆(i )
where
∆(i) = δ(1 + x(i) )
Likewise the jth input is perturbed to
u(j) + ∆(j)
where
∆(j) = δ(1 + u(j) )
Discrete-Time System Linearization
The function dlinmod can linearize discrete, multirate, and hybrid continuous
and discrete systems at any given sampling time. Use the same calling syntax
for dlinmod as for linmod, but insert the sample time at which to perform the
linearization as the second argument. For example
[Ad,Bd,Cd,Dd] = dlinmod('sys', Ts, x, u);
produces a discrete state-space model at the sampling time Ts and the
operating point given by the state vector x and input vector u. To obtain a
continuous model approximation of a discrete system, set Ts to 0.
For systems composed of linear, multirate, discrete, and continuous blocks,
dlinmod produces linear models having identical frequency and time responses
(for constant inputs) at the converted sampling time Ts, provided that:
• Ts is an integer multiple of all the sampling times in the system.
• Ts is not less than the slowest sample time in the system.
• The system is stable.
It is possible for valid linear models to be obtained when these conditions are
not met.
Computing the eigenvalues of the linearized matrix Ad provides an indication
of the stability of the system. The system is stable if Ts>0 and the eigenvalues
are within the unit circle, as determined by this statement:
all(abs(eig(Ad))) < 1
5-10
linfun
Likewise, the system is stable if Ts = 0 and the eigenvalues are in the left half
plane, as determined by this statement:
all(real(eig(Ad))) < 0
When the system is unstable and the sample time is not an integer multiple of
the other sampling times, dlinmod produces Ad and Bd matrices, which may be
complex. The eigenvalues of the Ad matrix in this case still, however, provide a
good indication of stability.
You can use dlinmod to convert the sample times of a system to other values or
to convert a linear discrete system to a continuous system or vice versa.
The frequency response of a continuous or discrete system can be found by
using the bode command.
An Advanced Form of Linearization
The linmod2 routine provides an advanced form of linearization. This routine
takes longer to run than linmod, but may produce more accurate results.
The calling syntax for linmod2 is similar to that used for linmod, but functions
differently. For instance, linmod2('sys',x,u) produces a linear model as does
linmod; however, the perturbation levels for each state-space matrix element
are set individually to attempt to minimize roundoff and truncation errors.
linmod2 tries to balance roundoff error (caused by small perturbation levels,
which cause errors associated with finite precision mathematics) and
truncation error (caused by large perturbation levels, which invalidate the
piecewise linear approximation).
With the form [A,B,C,D] = linmod2('sys',x,u,pert), the variable pert
indicates the lowest level of perturbation that can be used; the default is 1e-8.
linmod2 has the advantage that it can detect discontinuities and produce
warning messages, such as the following:
Warning:
discontinuity detected at A(2,3)
When such a warning occurs, try a different operating point at which to obtain
the linear model.
With the form
[A,B,C,D] = linmod2('sys',x,u,pert,Apert,Bpert,Cpert,Dpert)
5-11
linfun
the variables Apert, Bpert, Cpert, and Dpert are matrices used to set the
perturbation levels for each state and input combination; therefore, the ijth
element of Apert is the perturbation level associated with obtaining the ijth
element of the A matrix. Return default perturbation sizes with
[A,B,C,D,Apert,Bpert,Cpert,Dpert] = linmod2('sys', x, u);
Notes
By default, the system time is set to zero. For systems that are dependent on
time, you can set the variable pert to a two-element vector, where the second
element is used to set the value of t at which to obtain the linear model.
When the model being linearized is itself a linear model, the problem of
truncation error no longer exists; therefore, you can set the perturbation levels
to whatever value is desired. A relatively high value is generally preferable,
since this tends to reduce roundoff error. The operating point used does not
affect the linear model obtained.
The ordering of the states from the nonlinear model to the linear model is
maintained. For Simulink systems, a string variable that contains the block
name associated with each state can be obtained using
[sizes,x0,xstring] = sys
where xstring is a vector of strings whose ith row is the block name associated
with the ith state. Inputs and outputs are numbered sequentially on the
diagram.
For single-input multi-output systems, you can convert to transfer function
form using the routine ss2tf or to zero-pole form using ss2zp. You can also
convert the linearized models to LTI objects using ss. This function produces
an LTI object in state-space form that can be further converted to transfer
function or zero-pole-gain form using tf or zpk.
Linearizing a model that contains Derivative or Transport Delay blocks can be
troublesome. For more information, see “Linearization” on page 5–4.
5-12
trim
Purpose
5trim
Find a trim point of a dynamic system.
Syntax
[x,u,y,dx] = trim('sys')
[x,u,y,dx] = trim('sys',x0,u0,y0)
[x,u,y,dx] = trim('sys',x0,u0,y0,ix,iu,iy)
[x,u,y,dx] = trim('sys',x0,u0,y0,ix,iu,iy,dx0,idx)
[x,u,y,dx] = trim('sys',x0,u0,y0,ix,iu,iy,dx0,idx,options)
[x,u,y,dx] = trim('sys',x0,u0,y0,ix,iu,iy,dx0,idx,options,t)
[x,u,y,dx,options] = trim('sys',...)
Description
A trim point, also known as an equilibrium point, is a point in the parameter
space of a dynamic system where the system is in a steady state. For example,
a trim point of an aircraft is a setting of its controls that causes the aircraft to
fly straight and level. Mathematically, a trim point is a point where the
system’s state derivatives equal zero. trim starts from an initial point and
searches, using a sequential quadratic programming algorithm, until it finds
the nearest trim point. You must supply the initial point implicitly or explicitly.
If trim cannot find a trim point, it returns the point encountered in its search
where the state derivatives are closest to zero in a min-max sense; that is, it
returns the point that minimizes the maximum deviation from zero of the
derivatives. trim can find trim points that meet specific input, output, or state
conditions and points where a system is changing in a specified manner, that
is, points where the system’s state derivatives equal specific, nonzero values.
[x,u,y] = trim('sys') finds the equilibrium point nearest to the system’s
initial state x0. Specifically, trim finds the equilibrium point that minimizes
the maximum absolute value of [x–x0,u,y]. If trim cannot find an equilibrium
point near the system’s initial state, it returns the point where the system is
nearest to equilibrium. Specifically, it returns the point that minimizes
abs(dx–0). You can obtain x0 using this command:
[sizes,x0,xstr] = sys([],[],[],0)
[x,u,y] = trim('sys',x0,u0,y0) finds the trim point nearest to x0, u0, y0,
that is, the point that minimizes the maximum value of abs([x–x0; u–u0; y–
y0]).
The command
trim('sys', x0, u0, y0, ix, iu, iy)
5-13
trim
finds the trim point closest to x0, u0, y0 that satisfies a specified set of state,
input, and/or output conditions. The integer vectors ix, iu, and iy select the
values in x0, u0, and y0 that must be satisfied. If trim cannot find an
equilibrium point that satisfies the specified set of conditions exactly, it returns
the nearest point that satisfies the conditions, namely
abs([x(ix)–x0(ix); u(iu)–u0(iu); y(iy)–y0(iy)])
Use the syntax
[x,u,y,dx] = trim('sys', x0, u0, y0, ix, iu, iy, dx0, idx)
to find specific non-equilibrium points, that is, points where the system’s state
derivatives have some specified, nonzero value. Here, dx0 specifies the state
derivative values at the search’s starting point and idx selects the values in
dx0 that the search must satisfy exactly.
The optional options argument is an array of optimization parameters that
trim passes to the optimization function that it uses to find trim points. The
optimization function, in turn, uses this array to control the optimization
process and to return information about the process. trim returns the options
array at the end of the search process. By exposing the underlying optimization
process in this way, trim allows you to monitor and fine-tune the search for
trim points.
Five of the optimization array elements are particularly useful for finding trim
points. The following table describes how each element affects the search for a
trim point.
5-14
No.
Default
Description
1
0
Specifies display options. 0 specifies no display; 1
specifies tabular output; -1 suppresses warning
messages.
2
0.0001
Precision the computed trim point must attain to
terminate the search.
3
0.0001
Precision the trim search goal function must attain to
terminate the search.
trim
No.
Default
Description
4
0.0001
Precision the state derivatives must attain to terminate
the search.
10
N/A
Returns the number of iterations used to find a trim
point.
See the Optimization Toolbox User’s Guide for a detailed description of the
options array.
Examples
Consider a linear state-space model
·
x = Ax + Bu
y = Cx + Du
The A, B, C, and D matrices are as follows in a system called sys:
A
B
C
D
Example 1
=
=
=
=
[–0.09 –0.01;
[ 0
–7;
[ 0
2;
[–3
0;
1
0
1
1
0];
–2];
–5];
0];
To find an equilibrium point, use
[x,u,y,dx,options] = trim('sys')
x =
0
0
u =
0
y =
0
0
dx =
0
0
5-15
trim
The number of iterations taken is
options(10)
ans =
7
Example 2
To find an equilibrium point near x = [1;1], u = [1;1] enter
x0 = [1;1];
u0 = [1;1];
[x,u,y,dx,options] = trim('sys', x0, u0);
x =
1.0e–11 ∗
–0.1167
–0.1167
u =
0.3333
0.0000
y =
–1.0000
0.3333
dx =
1.0e–11 ∗
0.4214
0.0003
The number of iterations taken is
options(10)
ans =
25
5-16
trim
Example 3
To find an equilibrium point with the outputs fixed to 1, use
y = [1;1];
iy = [1;2];
[x,u,y,dx] = trim('sys', [], [], y, [], [], iy)
x =
0.0009
–0.3075
u =
–0.5383
0.0004
y =
1.0000
1.0000
dx =
1.0e–16 ∗
–0.0173
0.2396
Example 4
To find an equilibrium point with the outputs fixed to 1 and the derivatives set
to 0 and 1, use
y = [1;1];
iy = [1;2];
dx = [0;1];
idx = [1;2];
[x,u,y,dx,options] = trim('sys',[],[],y,[],[],iy,dx,idx)
x =
0.9752
–0.0827
u =
–0.3884
–0.0124
y =
1.0000
1.0000
dx =
0.0000
1.0000
5-17
trim
The number of iterations taken is
options(10)
ans =
13
Limitations
The trim point found by trim starting from any given initial point is only a local
value. Other, more suitable trim points may exist. Thus, if you want to find the
most suitable trim point for a particular application, it is important to try a
number of initial guesses for x, u, and y.
Algorithm
trim uses a sequential quadratic programming algorithm to find trim points.
See the Optimization Toolbox User’s Guide for a description of this algorithm.
5-18
6
Using Masks to Customize
Blocks
Introduction . . . . . . . . . . . . . . . . . . . . 6-2
A Sample Masked Subsystem . . . . .
Creating Mask Dialog Box Prompts . . . .
Creating the Block Description and Help Text
Creating the Block Icon . . . . . . . . .
Summary . . . . . . . . . . . . . . .
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6-4
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6-6
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The Mask Editor: An Overview . . . . . . . . . . . . 6-9
The Initialization Page . . . . . . . .
Prompts and Associated Variables . . . . .
Control Types . . . . . . . . . . . . .
Default Values for Masked Block Parameters
Tunable Parameters . . . . . . . . . .
Initialization Commands . . . . . . . .
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6-10
6-12
6-14
6-14
6-15
The Icon Page . . . . . . . . . . . . . .
Displaying Text on the Block Icon . . . . . . .
Displaying Graphics on the Block Icon . . . . .
Displaying Images on Masks . . . . . . . . .
Displaying a Transfer Function on the Block Icon.
Controlling Icon Properties . . . . . . . . . .
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6-18
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The Documentation Page
The Mask Type Field . . .
The Block Description Field
The Mask Help Text Field .
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Creating Dynamic Masked Dialogs . . . . . . . . . . 6-28
Setting Masked Dialog Parameters . . . . . . . . . . . 6-28
Predefined Masked Dialog Parameters . . . . . . . . . . 6-29
6
Using Masks to Customize Blocks
Introduction
Masking is a powerful Simulink feature that enables you to customize the
dialog box and icon for a subsystem. With masking, you can:
• Simplify the use of your model by replacing many dialog boxes in a
subsystem with a single one. Instead of requiring the user of the model to
open each block and enter parameter values, those parameter values can be
entered on the mask dialog box and passed to the blocks in the masked
subsystem.
• Provide a more descriptive and helpful user interface by defining a dialog box
with your own block description, parameter field labels, and help text.
• Define commands that compute variables whose values depend on block
parameters.
• Create a block icon that depicts the subsystem’s purpose.
• Prevent unintended modification of subsystems by hiding their contents
behind a customized interface.
• Create dynamic dialogs.
6-2
A Sample Masked Subsystem
A Sample Masked Subsystem
This simple subsystem models the equation for a line, y = mx + b.
Ordinarily, when you double-click on a Subsystem block, the Subsystem block
opens, displaying its blocks in a separate window. The mx + b subsystem
contains a Gain block, named Slope, whose Gain parameter is specified as m,
and a Constant block, named Intercept, whose Constant value parameter is
specified as b. These parameters represent the slope and intercept of a line.
This example creates a custom dialog box and icon for the subsystem. One
dialog box contains prompts for both the slope and the intercept. After you
create the mask, double-click on the Subsystem block to open the mask dialog
box. The mask dialog box and icon look like this.
The mask dialog box
The block icon
A user enters values for Slope and Intercept into the mask dialog box.
Simulink makes these values available to all the blocks in the underlying
subsystem. Masking this subsystem creates a self-contained functional unit
with its own application-specific parameters, Slope and Intercept. The mask
maps these mask parameters to the generic parameters of the underlying
blocks. The complexity of the subsystem is encapsulated by a new interface
that has the look and feel of a built-in Simulink block.
6-3
6
Using Masks to Customize Blocks
To create a mask for this subsystem, you need to:
• Specify the prompts for the mask dialog box parameters. In this example, the
mask dialog box has prompts for the slope and intercept.
• Specify the variable name used to store the value of each parameter.
• Enter the documentation of the block, consisting of the block description and
the block help text.
• Specify the drawing command that creates the block icon.
• Specify the commands that provide the variables needed by the drawing
command (there are none in this example).
Creating Mask Dialog Box Prompts
To create the mask for this subsystem, select the Subsystem block and choose
Mask Subsystem from the Edit menu.
The mask dialog box shown at the beginning of this section is created largely
on the Initialization page of the Mask Editor. For this sample model, the page
looks like this.
Parameter fields: prompts,
types, and variables that
hold the values entered by the
user.
Where you enter and edit the
parameter field
characteristics.
The commands that define
variables used by the icon
drawing command or by blocks
in the masked subsystem.
6-4
A Sample Masked Subsystem
The Mask Editor enables you to specify these attributes of a mask parameter:
• The prompt – the text label that describes the parameter.
• The control type – the style of user interface control that determines how
parameter values are entered or selected.
• The variable – the name of the variable that will store the parameter value.
Generally, it is convenient to refer to masked parameters by their prompts. In
this example, the parameter associated with slope is referred to as the Slope
parameter, and the parameter associated with intercept is referred to as the
Intercept parameter.
The slope and intercept are defined as edit controls. This means that the user
types values into edit fields in the mask dialog box. These values are stored in
variables in the mask workspace (see “The Mask Workspace” on page 6-15).
Masked blocks can access variables only in the mask workspace. In this
example, the value entered for the slope is assigned to the variable m. The Slope
block in the masked subsystem gets the value for the slope parameter from the
mask workspace. This figure shows how the slope parameter definitions in the
Mask Editor map to the actual mask dialog box parameters.
After you have created the mask parameters for slope and intercept, press the
OK button. Then, double-click on the Subsystem block to open the newly
constructed dialog box. Enter 3 for the Slope and 2 for the Intercept
parameters.
6-5
6
Using Masks to Customize Blocks
Creating the Block Description and Help Text
The mask type, block description, and help text are defined on the
Documentation page. For this sample masked block, the page looks like this.
Creating the Block Icon
So far, we have created a customized dialog box for the mx + b subsystem.
However, the Subsystem block still displays the generic Simulink subsystem
icon. An appropriate icon for this masked block is a plot that indicates the slope
of the line. For a slope of 3, that icon looks like this.
6-6
A Sample Masked Subsystem
The block icon is defined on the Icon page. For this block, the Icon page looks
like this.
Drawing commands
Icon properties
The drawing command plots a line from (0,0) to (0,m). If the slope is negative,
Simulink shifts the line up by 1 to keep it within the visible drawing area of the
block.
The drawing commands have access to all of the variables in the mask
workspace. As you enter different values of slope, the icon updates the slope of
the plotted line.
Select Normalized as the Drawing coordinates parameter, located at the
bottom of the list of icon properties, to specify that the icon be drawn in a frame
whose bottom-left corner is (0,0) and whose top-right corner is (1,1). This
parameter is described later in this chapter.
6-7
6
Using Masks to Customize Blocks
Summary
This discussion of the steps involved in creating a sample mask introduced you
to these tasks:
• Defining dialog box prompts and their characteristics
• Defining the masked block description and help text
• Defining the command that creates the masked block icon
The remainder of this chapter discusses the Mask Editor in more detail.
6-8
The Mask Editor: An Overview
The Mask Editor: An Overview
To mask a subsystem (you can only mask Subsystem blocks), select the
Subsystem block, then choose Mask Subsystem from the Edit menu. The
Mask Editor appears. The Mask Editor consists of three pages, each handling
a different aspect of the mask:
• The Initialization page enables you to define and describe mask dialog box
parameter prompts, name the variables associated with the parameters, and
specify initialization commands.
• The Icon page enables you to define the block icon.
• The Documentation page enables you to define the mask type and specify
the block description and the block help.
Five buttons appear along the bottom of the Mask Editor:
• The Ok button applies the mask settings on all pages and closes the Mask
Editor.
• The Cancel button closes the Mask Editor without applying any changes
made since you last pressed the Apply button.
• The Unmask button deactivates the mask and closes the Mask Editor. The
mask information is retained so that the mask can be reactivated. To
reactivate the mask, select the block and choose Create Mask. The Mask
Editor opens, displaying the previous settings. The inactive mask
information is discarded when the model is closed and cannot be recovered.
• The Help button displays the contents of this chapter.
• The Apply button creates or changes the mask using the information that
appears on all masking pages. The Mask Editor remains open.
To see the system under the mask without unmasking it, select the Subsystem
block, then choose Look Under Mask from the Edit menu. This command
opens the subsystem. The block’s mask is not affected.
6-9
6
Using Masks to Customize Blocks
The Initialization Page
The mask interface enables a user of a masked system to enter parameter
values for blocks within the masked system. You create the mask interface by
defining prompts for parameter values on the Initialization page. The
Initialization page for the mx+b sample masked system looks like this.
List of prompts
Full description of each
parameter prompt
Initialization
commands
Prompts and Associated Variables
A prompt provides information that helps the user enter or select a value for a
block parameter. Prompts appear on the mask dialog box in the order they
appear in the Prompt list.
When you define a prompt, you also specify the variable that is to store the
parameter value, choose the style of control for the prompt, and indicate how
the value is to be stored in the variable.
If the Assignment type is Evaluate, the value entered by the user is evaluated
by MATLAB before it is assigned to the variable. If the type is Literal, the
value entered by the user is not evaluated, but is assigned to the variable as a
string.
6-10
The Initialization Page
For example, if the user enters the string gain in an edit field and the
Assignment type is Evaluate, the string gain is evaluated by MATLAB and
the result is assigned to the variable. If the type is Literal, the string is not
evaluated by MATLAB so the variable contains the string 'gain'.
If you need both the string entered as well as the evaluated value, choose
Literal. Then use the MATLAB eval command in the initialization commands.
For example, if LitVal is the string 'gain', then to obtain the evaluated value,
use the command
value = eval(LitVal)
In general, most parameters use an Assignment type of Evaluate.
Creating the First Prompt
To create the first prompt in the list, enter the prompt in the Prompt field, the
variable that is to contain the parameter value in the Variable field, and
choose a control style and an assignment type.
Inserting a Prompt
To insert a prompt in the list:
1 Select the prompt that appears immediately below where you want to insert
the new prompt and click on the Add button to the left of the prompt list.
2 Enter the text for the prompt in the Prompt field. Enter the variable that is
to hold the parameter value in the Variable field.
Editing a Prompt
To edit an existing prompt:
1 Select the prompt in the list. The prompt, variable name, control style, and
assignment type appear in the fields below the list.
2 Edit the appropriate value. When you click the mouse outside the field or
press the Enter or Return key, Simulink updates the prompt.
6-11
6
Using Masks to Customize Blocks
Deleting a Prompt
To delete a prompt from the list:
1 Select the prompt you want to delete.
2 Click on the Delete button to the left of the prompt list.
Moving a Prompt
To move a prompt in the list:
1 Select the prompt you want to move.
2 To move the prompt up one position in the prompt list, click on the Up
button to the left of the prompt list. To move the prompt down one position,
click on the Down button.
Control Types
Simulink enables you to choose how parameter values are entered or selected.
You can create three styles of controls: edit fields, check boxes, and pop-up
controls. For example, this figure shows the parameter area of a mask dialog
box which uses all three styles of controls (with the pop-up control open):
Edit control
Check box control
Pop-up control
Defining an Edit Control
An edit field enables the user to enter a parameter value by typing it into a
field. This figure shows how the prompt for the sample edit control was defined
6-12
The Initialization Page
The value of the variable associated with the parameter (freq) is determined
by the Assignment type defined for the prompt
Assignment
Value
Evaluate
The result of evaluating the expression entered in the field.
Literal
The actual string entered in the field.
Defining a Check Box Control
A check box enables the user to choose between two alternatives by selecting or
deselecting a check box. This figure shows how the sample check box control is
defined.
The value of the variable associated with the parameter (label) depends on
whether the check box is selected and the Assignment type defined for the
prompt.
Check box
Evaluated Value
Literal Value
Checked
1
'on'
Not checked
0
'off'
Defining a Pop-Up Control
A popup enables the user to choose a parameter value from a list of possible
values. You specify the list in the Popup strings field, separating items with a
vertical line (|). This figure shows how the sample pop-up control is defined.
6-13
6
Using Masks to Customize Blocks
The value of the variable associated with the parameter (color) depends on the
item selected from the pop-up list and the Assignment type defined for the
prompt.
Assignment
Value
Evaluate
The index of the value selected from the list, starting with
1. For example, if the third item is selected, the parameter
value is 3.
Literal
A string that is the value selected. If the third item is
selected, the parameter value is 'green'.
Default Values for Masked Block Parameters
To change default parameter values in a masked library block, follow these
steps:
1 Unlock the library.
2 Open the block to access its dialog box, fill in the desired default values, and
close the dialog box.
3 Save the library.
When the block is copied into a model and opened, the default values appear on
the block’s dialog box.
For more information about libraries, see Chapter 3.
Tunable Parameters
A tunable parameter is a mask parameter that a user can modify at runtime.
When you create a mask, all its parameters are tunable. You can subsequently
disable or re-enable tuning of any of a mask’s parameters via the
MaskTunableValues parameter. The value of this parameter is a cell array of
strings, each of which corresponds to one of a masked block’s parameters. The
first cell corresponds to the first parameter, the second cell to the second
parameter, and so on. If a parameter is tunable, the value of the corresponding
cell is on; otherwise, the value is off. To enable or disable tuning of a
parameter, first get the cell array, using get_param. Then, set the
6-14
The Initialization Page
corresponding cell to on or off and reset the MaskTunableValues parameter
using set_param. For example, the following commands disable tuning of the
first parameter of the currently selected masked block:
ca = get_param(gcb, 'MaskTunableValues');
ca(1) = 'off'
set_param(gcb, 'MaskTunableValues’, ca)
After changing a block’s tunable parameters, make the changes permanent by
saving the block.
Initialization Commands
Initialization commands define variables that reside in the mask workspace.
These variables can be used by all initialization commands defined for the
mask, by blocks in the masked subsystem, and by commands that draw the
block icon (drawing commands).
Simulink executes the initialization commands when:
• The model is loaded.
• The simulation is started or the block diagram is updated.
• The masked block is rotated.
• The block’s icon needs to be redrawn and the plot commands depend on
variables defined in the initialization commands.
Initialization commands are valid MATLAB expressions, consisting of
MATLAB functions, operators, and variables defined in the mask workspace.
Initialization commands cannot access base workspace variables. Terminate
initialization commands with a semicolon to avoid echoing results to the
command window.
The Mask Workspace
Simulink creates a local workspace, called a mask workspace, when either of
the following occurs:
• The mask contains initialization commands.
• The mask defines prompts and associates variables with those prompts.
Masked blocks cannot access the base workspace or other mask workspaces.
6-15
6
Using Masks to Customize Blocks
The contents of a mask workspace include the variables associated with the
mask’s parameters and variables defined by initialization commands. The
variables in the mask workspace can be accessed by the masked block. If the
block is a subsystem, they can also be accessed by all blocks in the subsystem.
Mask workspaces are analogous to the local workspaces used by M-file
functions. You can think of the expressions entered into the dialog boxes of the
underlying blocks and the initialization commands entered on the Mask Editor
as lines of an M-file function. Using this analogy, the local workspace for this
“function” is the mask workspace.
In the mx + b example, described earlier in this chapter, the Mask Editor
explicitly creates m and b in the mask workspace by associating a variable with
a mask parameter. However, variables in the mask workspace are not
explicitly assigned to blocks underneath the mask. Instead, blocks beneath the
mask have access to all variables in the mask workspace. It may be instructive
to think of the underlying blocks as “looking into” the mask workspace.
The figure below shows the mapping of values entered in the mask dialog box
to variables in the mask workspace (indicated by the solid line) and the access
of those variables by the underlying blocks (indicated by the dashed line).
Mask
Workspace
m
b
6-16
The Initialization Page
Debugging Initialization Commands
You can debug initialization commands in these ways:
• Specify an initialization command without a terminating semicolon to echo
its results to the command window.
• Place a keyboard command in the initialization commands to stop execution
and give control to the keyboard. For more information, see the help text for
the keyboard command.
• Enter either of these commands in the MATLAB command window.
dbstop if error
dbstop if warning
If an error occurs in the initialization commands, execution stops and you
can examine the mask workspace. For more information, see the help text for
the dbstop command.
6-17
6
Using Masks to Customize Blocks
The Icon Page
The Icon page enables you to customize the masked block’s icon. You create a
custom icon by specifying commands in the Drawing commands field. You can
create icons that show descriptive text, state equations, images, and graphics.
This figure shows the Icon page.
The mask type
Commands that draw the
block icon
Parameters that control
the icon appearance
Drawing commands have access to all variables in the mask workspace.
Drawing commands can display text, one or more plots, or show a transfer
function. If you enter more than one command, the results of the commands are
drawn on the icon in the order the commands appear.
Displaying Text on the Block Icon
To display text on the icon, enter one of these drawing commands.
disp('text') or disp(variablename)
text(x, y, 'text')
text(x, y, stringvariablename)
6-18
The Icon Page
text(x, y, text, 'horizontalAlignment', halign,
'verticalAlignment', valign)
fprintf('text') or fprintf('format', variablename)
port_label(port_type, port_number, label)
The disp command displays text or the contents of variablename centered on
the icon.
The text command places a character string (text or the contents of
stringvariablename) at a location specified by the point (x,y). The units
depend on the Drawing coordinates parameter. For more information, see
“Controlling Icon Properties” on page 6-23.
You can optionally specify the horizontal and/or vertical alignment of the text
relative to the point (x, y) in the text command. For example, the command
text(0.5, 0.5, 'foobar', 'horizontalAlignment', 'center')
centers foobar in the icon.
The text command offers the following horizontal alignment options.
Option
Aligns
left
The left end of the text at the specified point.
right
The right end of the text at the specified point.
center
The center of the text at the specified point.
The text command offers the following vertical alignment options.
Option
Aligns
base
The baseline of the text at the specified point.
bottom
The bottom line of the text at the specified point.
middle
The midline of the text at the specified point.
6-19
6
Using Masks to Customize Blocks
Option
Aligns
cap
The capitals line of the text at the specified point.
top
The top of the text at the specified point.
The fprintf command displays formatted text centered on the icon and can
display text along with the contents of variablename.
Note While these commands are identical in name to their corresponding
MATLAB functions, they provide only the functionality described above.
To display more than one line of text, use \n to indicate a line break. For
example, the figure below shows two samples of the disp command
The port_label command lets you specify the labels of ports displayed on the
icon. The command’s syntax is
port_label(port_type, port_number, label)
where port_type is either 'input' or 'output', port_number is an integer,
and label is a string specifying the port’s label. For example, the command
port_label('input', 1, 'a')
defines a as the label of input port 1.
Displaying Graphics on the Block Icon
You can display plots on your masked block icon by entering one or more plot
commands. You can use these forms of the plot command.
plot(Y);
plot(X1,Y1,X2,Y2,...);
plot(Y) plots, for a vector Y, each element against its index. If Y is a matrix, it
plots each column of the matrix as though it were a vector.
6-20
The Icon Page
plot(X1,Y1,X2,Y2,...) plots the vectors Y1 against X1, Y2 against X2, and so
on. Vector pairs must be the same length and the list must consist of an even
number of vectors.
For example, this command generates the plot that appears on the icon for the
Ramp block, in the Sources library. The icon appears below the command.
plot([0 1 5], [0 0 4])
Plot commands can include NaN and inf values. When NaNs or infs are
encountered, Simulink stops drawing, then begins redrawing at the next
numbers that are not NaN or inf.
The appearance of the plot on the icon depends on the value of the Drawing
coordinates parameter. For more information, see “Controlling Icon
Properties” on page 6-23.
Simulink displays three question marks (? ? ?) in the block icon and issues
warnings in these situations:
• When the values for the parameters used in the drawing commands are not
yet defined (for example, when the mask is first created and values have not
yet been entered into the mask dialog box).
• When a masked block parameter or drawing command is entered incorrectly.
Displaying Images on Masks
The masked dialog functions, image and patch, enable you to display
bitmapped images and draw patches on masked block icons.
image(a) displays the image a where a is an M by N by 3 array of RGB values.
You can use the MATLAB commands, imread and ind2rgb, to read and convert
bitmap files to the necessary matrix format. For example,
image(imread('icon.tif'))
reads the icon image from a TIFF file named icon.tif in the MATLAB path.
image(a, [x, y, w, h]) creates the image at the specified position relative to
the lower left corner of the mask.
6-21
6
Using Masks to Customize Blocks
image(a, [x, y, w, h], rotation) allows you to specify whether the image
rotates ('on’) or remains stationary ('off') as the icon rotates. The default is
'off’.
patch(x, y) creates a solid patch having the shape specified by the coordinate
vectors x and y. The patch’s color is the current foreground color.
patch(x, y, [r g b]) creates a solid patch of the color specified by the vector
[r g b], where r is the red component, g the green, and b the blue. For
example,
patch([0 .5 1], [0 1 0], [1 0 0])
creates a red triangle on the mask’s icon.
Displaying a Transfer Function on the Block Icon
To display a transfer function equation in the block icon, enter the following
command in the Drawing commands field.
dpoly(num, den)
dpoly(num, den, 'character')
num and den are vectors of transfer function numerator and denominator
coefficients, typically defined using initialization commands. The equation is
expressed in terms of the specified character. The default is s. When the icon
is drawn, the initialization commands are executed and the resulting equation
is drawn on the icon.
• To display a continuous transfer function in descending powers of s, enter
dpoly(num, den)
For example, for num = [0 0 1]; and den = [1 2 1]; the icon looks like this.
• To display a discrete transfer function in descending powers of z, enter
dpoly(num, den, 'z')
For example, for num = [0 0 1]; and den = [1 2 1]; the icon looks like this.
6-22
The Icon Page
• To display a discrete transfer function in ascending powers of 1/z, enter
dpoly(num, den, 'z-')
For example, for num and den as defined above, the icon looks like this.
• To display a zero-pole gain transfer function, enter
droots(z, p, k)
For example, the above command creates this icon for these values.
z = []; p = [-1 -1]; k = 1;
You can add a fourth argument ('z' or 'z-') to express the equation in terms
of z or 1/z.
If the parameters are not defined or have no values when you create the icon,
Simulink displays three question marks (? ? ?) in the icon. When the
parameter values are entered in the mask dialog box, Simulink evaluates the
transfer function and displays the resulting equation in the icon.
Controlling Icon Properties
You can control a masked block’s icon properties by selecting among the choices
below the Drawing commands field.
Icon frame
The icon frame is the rectangle that encloses the block. You can choose to show
or hide the frame by setting the Icon frame parameter to Visible or Invisible.
The default is to make the icon frame visible. For example, this figure shows
visible and invisible icon frames for an AND gate block.
Visible
Invisible
6-23
6
Using Masks to Customize Blocks
Icon transparency
The icon can be set to Opaque or Transparent, either hiding or showing what
is underneath the icon. Opaque, the default, covers information Simulink
draws, such as port labels. This figure shows opaque and transparent icons for
an AND gate block. Notice the text on the transparent icon.
Opaque
Transparent
Icon rotation
When the block is rotated or flipped, you can choose whether to rotate or flip
the icon, or to have it remain fixed in its original orientation. The default is not
to rotate the icon. The icon rotation is consistent with block port rotation. This
figure shows the results of choosing Fixed and Rotates icon rotation when the
AND gate block is rotated.
Fixed
Rotates
Drawing coordinates
This parameter controls the coordinate system used by the drawing commands.
This parameter applies only to plot and text drawing commands. You can
select from among these choices: Autoscale, Normalized, and Pixel.
max(X), max(Y)
min(X), min(Y)
Autoscale
6-24
1,1
0,0
Normalized
block width, block height
0,0
Pixel
The Icon Page
• Autoscale automatically scales the icon within the block frame. When the
block is resized, the icon is also resized. For example, this figure shows the
icon drawn using these vectors.
X = [0 2 3 4 9]; Y = [4 6 3 5 8];
The lower-left corner of the block frame is (0,3) and the upper-right corner is
(9,8). The range of the x-axis is 9 (from 0 to 9), while the range of the y-axis
is 5 (from 3 to 8).
• Normalized draws the icon within a block frame whose bottom-left corner is
(0,0) and whose top right corner is (1,1). Only X and Y values between 0 and
1 appear. When the block is resized, the icon is also resized. For example, this
figure shows the icon drawn using these vectors.
X = [.0 .2 .3 .4 .9]; Y = [.4 .6 .3 .5 .8];
• Pixel draws the icon with X and Y values expressed in pixels. The icon is not
automatically resized when the block is resized. To force the icon to resize
with the block, define the drawing commands in terms of the block size.
This example demonstrates how to create an improved icon for the mx + b
sample masked subsystem discussed earlier in this chapter. These
initialization commands define the data that enables the drawing command
to produce an accurate icon regardless of the shape of the block.
pos = get_param(gcb, 'Position');
width = pos(3) – pos(1); height = pos(4) – pos(2);
x = [0, width];
if (m >= 0), y = [0, (m*width)]; end
if (m < 0), y = [height, (height + (m*width))]; end
The drawing command that generates this icon is plot(x,y).
6-25
6
Using Masks to Customize Blocks
The Documentation Page
The Documentation page enables you to define or modify the type, description,
and help text for a masked block. This figure shows how fields on the
Documentation page correspond to the mx+b sample mask block’s dialog box.
The Mask Type Field
The mask type is a block classification used only for purposes of
documentation. It appears in the block’s dialog box and on all Mask Editor
pages for the block. You can choose any name you want for the mask type.
When Simulink creates the block’s dialog box, it adds “(mask)” after the mask
type to differentiate masked blocks from built-in blocks.
The Block Description Field
The block description is informative text that appears in the block’s dialog box
in the frame under the mask type. If you are designing a system for others to
use, this is a good place to describe the block’s purpose or function.
6-26
The Documentation Page
Simulink automatically wraps long lines of text. You can force line breaks by
using the Enter or Return key.
The Mask Help Text Field
You can provide help text that gets displayed when the Help button is pressed
on the masked block’s dialog box. If you create models for others to use, this is
a good place to explain how the block works and how to enter its parameters.
You can include user-written documentation for a masked block’s help. You can
specify any of the following for the masked block help text:
• URL specification (a string starting with http:, www, file:, ftp:, or
mailto:)
• web command (launches a browser)
• eval command (evaluates a MATLAB string)
• Static text displayed in the Web browser
Simulink examines the first line of the masked block help text. If it detects a
URL specification, web command, or eval command, it accesses the block help
as directed; otherwise, the full contents of the masked block help text are
displayed in the browser.
These examples illustrate several acceptable commands.
web([docroot '/My Blockset Doc/' get_param(gcb,'MaskType')
'.html'])
eval('!Word My_Spec.doc')
http://www.mathworks.com
file:///c:/mydir/helpdoc.html
www.mathworks.com
Simulink automatically wraps long lines of text.
6-27
6
Using Masks to Customize Blocks
Creating Dynamic Dialogs for Masked Blocks
Simulink allows you to create dialogs for masked blocks whose appearance
changes in response to user input. Features of masked dialog features that can
change in this way include:
• Visibility of parameter controls
Changing a parameter can cause the control for another parameter to appear
or disappear. The dialog expands or shrinks when a control appears or
disappears, respectively.
• Enabled state of parameter controls
Changing a parameter can cause the control for another parameter to be
enabled or disabled for input. Simulink grays a disabled control to indicate
visually that it is disabled.
• Parameter values
Changing a parameter can cause related parameters to be set to appropriate
values.
Creating a dynamic masked dialog entails using the mask editor in
combination with the Simulink set_param command. Specifically, you first use
the mask editor to define all the dialog’s parameters both static and dynamic.
Next you use the Simulink set_param command at the MATLAB command line
to specify callback functions that define the dialog’s response to user input.
Finally you save the model or library containing the masked subsystem to
complete the creation of the dynamic masked dialog.
Setting Masked Block Dialog Parameters
Simulink defines a set of masked block parameters that define the current
state of the masked block’s dialog. You can use the mask editor to inspect and
set many of these parameters. The Simulink get_param and set_param
commands also let you inspect and set mask dialog parameters. The
advantage? The set_param command allows you to set parameters and hence
change a dialog’s appearance while the dialog is open. This in turn allows you
to create dynamic masked dialogs.
For example, you can use the set_param command at the MATLAB command
line to specify callback functions to be invoked when a user changes the values
of user-defined parameters. The callback functions in turn can use set_param
6-28
Creating Dynamic Dialogs for Masked Blocks
commands to change the values of the masked dialog’s predefined parameters
and hence its state, for example, to hide, show, enable, or disable a user-defined
parameter control.
Predefined Masked Dialog Parameters
Simulink associates the following predefined parameters with masked dialogs.
MaskCallbacks
The value of this parameter is a cell array of strings that specify callback
expressions for the dialog’s user-defined parameter controls. The first cell
defines the callback for the first parameter’s control, the second for the second
parameter control, etc. The callbacks can be any valid MATLAB expressions,
including expressions that invoke M-file commands. This means that you can
implement complex callbacks as M-files.
The easiest way to set callbacks for a mask dialog is to first select the
corresponding masked dialog in a model or library window and then to issue a
set_param command at the MATLAB command line. For example, the
following code
set_param(gcb,'MaskCallbacks',{'parm1_callback', '',
'parm3_callback'});
defines callbacks for the first and third parameters of the masked dialog for the
currently selected block. To save the callback settings, save the model or
library containing the masked block.
MaskDescription
The value of this parameter is a string specifying the description of this block.
You can change a masked block’s description dynamically by setting this
parameter.
MaskEnables
The value of this parameter is a cell array of strings that define the enabled
state of the user-defined parameter controls for this dialog. The first cell
defines the enabled state of the control for the first parameter, the second for
the second parameter, etc. A value of 'on' indicates that the corresponding
control is enabled for user input; a value of 'off' indicates that the control is
disabled.
6-29
6
Using Masks to Customize Blocks
You can enable or disable user input dynamically by setting this parameter in
a callback. For example, the following command in a callback
set_param(gcb,'MaskEnables',{'on','on','off'});
would disable the third control of the currently open masked block’s dialog.
Simulink colors disabled controls gray to indicate visually that they are
disabled.
MaskPrompts
The value of this parameter is a cell array of strings that specify prompts for
user-defined parameters. The first cell defines the prompt for the first
parameter, the second for the second parameter, etc.
MaskType
The value of this parameter is the mask type of the block associated with this
dialog.
MaskValues
The value of this parameter is a cell array of strings that specify the values of
user-defined parameters for this dialog. The first cell defines the value for the
first parameter, the second for the second parameter, etc.
MaskVisibilities
The value of this parameter is a cell array of strings that specify the visibility
of the user-defined parameter controls for this dialog. The first cell defines the
visibility of the control for the first parameter, the second for the second
parameter, etc. A value of 'on' indicates that the corresponding control is
visible; a value of 'off' indicates that the control is hidden.
You can hide or show user-defined parameter controls dynamically by setting
this parameter in the callback for a control. For example, the following
command in a callback
set_param(gcb,'MaskVisibilities',{'on','off','on'});
would hide the control for the currently selected block’s second user-defined
mask parameter. Simulink expands or shrinks a dialog to show or hide a
control, respectively.
6-30
7
Conditionally Executed
Subsystems
Introduction . . . . . . . . . . . . . . . . . . . . 7-2
Enabled Subsystems . . . . . . . . . . . . . . . . 7-3
Creating an Enabled Subsystem . . . . . . . . . . . . 7-3
Blocks an Enabled Subsystem Can Contain . . . . . . . . 7-5
Triggered Subsystems . . . . . . . . . .
Creating a Triggered Subsystem . . . . . . .
Function-Call Subsystems . . . . . . . . . .
Blocks That a Triggered Subsystem Can Contain
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7-8
7-9
7-10
7-10
Triggered and Enabled Subsystems . .
Creating a Triggered and Enabled Subsystem
A Sample Triggered and Enabled Subsystem
Creating Alternately Executing Subsystems
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7-11
7-11
7-12
7-12
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7
Conditionally Executed Subsystems
Introduction
A conditionally executed subsystem is a subsystem whose execution depends on
the value of an input signal. The signal that controls whether a subsystem
executes is called the control signal. The signal enters the Subsystem block at
the control input.
Conditionally executed subsystems can be very useful when building complex
models that contain components whose execution depends on other
components.
Simulink supports three types of conditionally executed subsystems:
• An enabled subsystem executes while the control signal is positive. It starts
execution at the time step where the control signal crosses zero (from the
negative to the positive direction) and continues execution while the control
signal remains positive. Enabled subsystems are described in more detail on
“Enabled Subsystems” on page 7-3.
• A triggered subsystem executes once each time a “trigger event” occurs. A
trigger event can occur on the rising or falling edge of a trigger signal, which
can be continuous or discrete. Triggered subsystems are described in more
detail on “Triggered Subsystems” on page 7-8.
• A triggered and enabled subsystem executes once on the time step when a
trigger event occurs if the enable control signal has a positive value at that
step. See “Triggered and Enabled Subsystems” on page 7-11 for more
information.
7-2
Enabled Subsystems
Enabled Subsystems
Enabled subsystems are subsystems that execute at each simulation step
where the control signal has a positive value.
An enabled subsystem has a single control input, which can be scalar or vector
valued:
• If the input is a scalar, the subsystem executes if the input value is greater
than zero.
• If the input is a vector, the subsystem executes if any of the vector elements
is greater than zero.
For example, if the control input signal is a sine wave, the subsystem is
alternately enabled and disabled, as shown in this figure. An up arrow signifies
enable, a down arrow disable.
Simulink uses the zero-crossing slope method to determine whether an enable
is to occur. If the signal crosses zero and the slope is positive, the subsystem is
enabled. If the slope is negative at the zero crossing, the subsystem is disabled.
Creating an Enabled Subsystem
You create an enabled subsystem by copying an Enable block from the Signals
& Systems library into a subsystem. Simulink adds an enable symbol and an
enable control input port to the Subsystem block icon:
7-3
7
Conditionally Executed Subsystems
Setting Output Values While the Subsystem Is Disabled
Although an enabled subsystem does not execute while it is disabled, the
output signal is still available to other blocks. While an enabled subsystem is
disabled, you can choose to hold the subsystem outputs at their previous values
or reset them to their initial conditions.
Open each Outport block’s dialog box and select one of the choices for the
Output when disabled parameter, as shown in the dialog box below:
• Choose held to cause the output to maintain its most recent value.
• Choose reset to cause the output to revert to its initial condition. Set the
Initial output to the initial value of the output.
Select an option to set the
Outport output while the
subsystem is disabled.
The initial condition and the
value when reset.
Setting States When the Subsystem Becomes Re-enabled
When an enabled subsystem executes, you can choose whether to hold the
subsystem states at their previous values or reset them to their initial
conditions.
To do this, open the Enable block dialog box and select one of the choices for the
States when enabling parameter, as shown in the dialog box below:
7-4
Enabled Subsystems
• Choose held to cause the states to maintain their most recent values.
• Choose reset to cause the states to revert to their initial conditions.
Select an option to set the states
when the subsystem is re-enabled.
Outputting the Enable Control Signal
An option on the Enable block dialog box lets you output the enable control
signal. To output the control signal, select the Show output port check box:
Select this check box to show the
output port.
This feature allows you to pass the control signal down into the enabled
subsystem, which can be useful where logic within the enabled subsystem is
dependent on the value or values contained in the control signal.
Blocks an Enabled Subsystem Can Contain
An enabled subsystem can contain any block, whether continuous or discrete.
Discrete blocks in an enabled subsystem execute only when the subsystem
executes, and only when their sample times are synchronized with the
simulation sample time. Enabled subsystems and the model use a common
clock.
For example, this system contains four discrete blocks and a control signal. The
discrete blocks are:
• Block A, which has a sample time of 0.25 seconds.
• Block B, which has a sample time of 0.5 seconds.
7-5
7
Conditionally Executed Subsystems
• Block C, within the Enabled subsystem, which has a sample time of 0.125
seconds.
• Block D, also within the Enabled subsystem, which has a sample time of 0.25
seconds.
The enable control signal is generated by a Pulse Generator block, labeled
Signal E, which changes from 0 to 1 at 0.375 seconds and returns to 0 at 0.875
seconds.
The chart below indicates when the discrete blocks execute:
1
Signal E
0
- start of execution
for a block.
Block D
Block C
Block B
Block A
0
.125 .25 .375 .50 .625 .75 .875 1.0
Time (sec)
Blocks A and B execute independent of the enable signal because they are not
part of the enabled subsystem. When the enable signal becomes positive, blocks
7-6
Enabled Subsystems
C and D execute at their assigned sample rates until the enable signal becomes
zero again. Note that block C does not execute at 0.875 seconds when the
enable signal changes to zero.
7-7
7
Conditionally Executed Subsystems
Triggered Subsystems
Triggered subsystems are subsystems that execute each time a trigger event
occurs.
A triggered subsystem has a single control input, called the trigger input,
which determines whether the subsystem executes. You can choose from three
types of trigger events to force a triggered subsystem to begin execution:
• rising triggers execution of the subsystem when the control signal rises from
a negative or zero value to a positive value (or zero if the initial value is
negative).
• falling triggers execution of the subsystem when the control signal falls from
a positive or a zero value to a negative value (or zero if the initial value is
positive).
• either triggers execution of the subsystem when the signal is either rising or
falling.
For example, this figure shows when rising (R) and falling (F) triggers occur for
the given control signal.
0
F
R
F
A simple example of a trigger subsystem is illustrated below:
7-8
Triggered Subsystems
In this example, the subsystem is triggered on the rising edge of the square
wave trigger control signal.
Creating a Triggered Subsystem
You create a triggered subsystem by copying the Trigger block from the Signals
& Systems library into a subsystem. Simulink adds a trigger symbol and a
trigger control input port to the Subsystem block icon:
To select the trigger type, open the Trigger block dialog box and select one of
the choices for the Trigger type parameter, as shown in the dialog box below:
• rising forces a trigger whenever the trigger signal crosses zero in a positive
direction.
• falling forces a trigger whenever the trigger signal crosses zero in a negative
direction.
• either forces a trigger whenever the trigger signal crosses zero in either
direction.
Select the trigger type from
these choices.
Simulink uses different symbols on the Trigger and Subsystem blocks to
indicate rising and falling triggers (or either). This figure shows the trigger
symbols on Subsystem blocks:
7-9
7
Conditionally Executed Subsystems
Outputs and States Between Trigger Events
Unlike enabled subsystems, triggered subsystems always hold their outputs at
the last value between triggering events. Also, triggered subsystems cannot
reset their states when triggered; states of any discrete blocks are held between
trigger events.
Outputting the Trigger Control Signal
An option on the Trigger block dialog box lets you output the trigger control
signal. To output the control signal, select the Show output port check box.
Select this check box to show the
output port.
The Output data type field allows you to specify the data type of the output
signal as auto, int8, or double. The auto option causes the data type of the
output signal to be set to the data type (either int8 or double) of the port to
which the signal is connected.
Function-Call Subsystems
You can create a triggered subsystem whose execution is determined by logic
internal to an S-function instead of by the value of a signal. These subsystems
are called function-call subsystems. For more information about function-call
subsystems, see the companion guide Writing S-Functions.
Blocks That a Triggered Subsystem Can Contain
Triggered systems execute only at specific times during a simulation. As a
result, the only blocks that are suitable for use in a triggered subsystem are:
• Blocks with inherited sample time, such as the Logical Operator block or the
Gain block.
• Discrete blocks having their sample time set to –1, which indicates that the
sample time is inherited from the driving block.
7-10
Triggered and Enabled Subsystems
Triggered and Enabled Subsystems
A third kind of conditionally executed subsystem combines both types of
conditional execution. The behavior of this type of subsystem, called a triggered
and enabled subsystem, is a combination of the enabled subsystem and the
triggered subsystem, as shown by this flow diagram.
Trigger event
Is
the enable
input signal
>0?
No
Don’t execute the subsystem
Yes
Execute the subsystem
A triggered and enabled subsystem contains both an enable input port and a
trigger input port. When the trigger event occurs, Simulink checks the enable
input port to evaluate the enable control signal. If its value is greater than zero,
Simulink executes the subsystem. If both inputs are vectors, the subsystem
executes if at least one element of each vector is nonzero.
The subsystem executes once at the time step at which the trigger event occurs.
Creating a Triggered and Enabled Subsystem
You create a triggered and enabled subsystem by dragging both the Enable and
Trigger blocks from the Signals & Systems library into an existing subsystem.
Simulink adds enable and trigger symbols and enable and trigger and enable
control inputs to the Subsystem block icon.
7-11
7
Conditionally Executed Subsystems
You can set output values when a triggered and enabled subsystem is disabled
as you would for an enabled subsystem. For more information, see “Setting
Output Values While the Subsystem Is Disabled” on page 7–4. Also, you can
specify what the values of the states are when the subsystem is re-enabled. See
“Setting States When the Subsystem Becomes Re-enabled” on page 7–4.
Set the parameters for the Enable and Trigger blocks separately. The
procedures are the same as those described for the individual blocks.
A Sample Triggered and Enabled Subsystem
A simple example of a triggered and enabled subsystem is illustrated in the
model below.
Creating Alternately Executing Subsystems
You can use conditionally executed subsystems in combination with Merge
blocks (see Merge on page 8-126) to create sets of subsystems that execute
alternately, depending on the current state of the model. For example, the
following figure shows a model that uses two enabled blocks and a Merge block
7-12
Triggered and Enabled Subsystems
to model an inverter, that is, a device that converts AC current to pulsating DC
current.
In this example, the block labeled “pos” is enabled when the AC waveform is
positive; it passes the waveform unchanged to its output. The block labeled
“neg” is enabled when the waveform is negative; it inverts the waveform. The
Merge block passes the output of the currently enabled block to the Mux block,
which passes the output, along with the original waveform, to the Scope block
to create the following display.
7-13
7
Conditionally Executed Subsystems
7-14
8
Block Reference
What Each Block Reference Page Contains . . . . . . 8-2
Simulink Block Libraries . . . . . . . . . . . . . . 8-3
8
Block Reference
What Each Block Reference Page Contains
Blocks appear in alphabetical order and contain this information:
• The block name, icon, and block library that contains the block
• The purpose of the block
• A description of the block’s use
• The block dialog box and parameters
• The block characteristics, including some or all of these, as they apply to the
block:
- Direct Feedthrough – whether the block or any of its ports has direct
feedthrough. For more information, see “Algebraic Loops” on page 9-7.
- Sample Time – how the block’s sample time is determined, whether by the
block itself (as is the case with discrete and continuous blocks) or inherited
from the block that drives it or is driven by it. For more information, see
“Sample Time” on page 9-13.
- Scalar Expansion – whether or not scalar values are expanded to vectors.
Some blocks expand scalar inputs and/or parameters as appropriate. For
more information, see “Scalar Expansion of Inputs and Parameters” on
page 3-18.
- States – the number of discrete and continuous states.
- Vectorized – whether the block accepts and/or generates vector signals.
For more information, see “Vector Input and Output” on page 3-18.
- Zero Crossings – whether the block detects state events. For more
information, see “Zero Crossings” on page 9-3.
8-2
Simulink Block Libraries
Simulink Block Libraries
Simulink organizes its blocks into block libraries according to their behavior.
The simulink window displays the block library icons and names:
• The Sources library contains blocks that generate signals.
• The Sinks library contains blocks that display or write block output.
• The Discrete library contains blocks that describe discrete-time components.
• The Continuous library contains blocks that describe linear functions.
• The Nonlinear library contains blocks that describe nonlinear functions.
• The Math library contains blocks that describe general mathematics
functions.
• The Functions & Tables library contains blocks that describe general
functions and table look-up operations.
• The Signal & Systems library contains blocks that allow multiplexing and
demultiplexing, implement external input/output, pass data to other parts of
the model, create subsystems, and perform other functions.
• The Blocksets and Toolboxes library contains the Extras block library of
specialized blocks.
• The Demos library contains useful MATLAB and Simulink demos.
Table 8-1: Sources Library Blocks
Block Name
Purpose
Band-Limited White Noise
Introduce white noise into a continuous
system.
Chirp Signal
Generate a sine wave with increasing
frequency.
Clock
Display and provide the simulation time.
Constant
Generate a constant value.
Digital Clock
Generate simulation time at the specified
sampling interval.
8-3
8
Block Reference
Table 8-1: Sources Library Blocks (Continued)
Block Name
Purpose
Digital Pulse Generator
Generate pulses at regular intervals.
From File
Read data from a file.
From Workspace
Read data from a matrix defined in the
workspace.
Pulse Generator
Generate pulses at regular intervals.
Ramp
Generate a constantly increasing or
decreasing signal.
Random Number
Generate normally distributed random
numbers.
Repeating Sequence
Generate a repeatable arbitrary signal.
Signal Generator
Generate various waveforms.
Sine Wave
Generate a sine wave.
Step
Generate a step function.
Uniform Random Number
Generate uniformly distributed random
numbers.
Table 8-2: Sinks Library Blocks
8-4
Block Name
Purpose
Display
Show the value of the input.
Scope
Display signals generated during a
simulation.
Stop Simulation
Stop the simulation when the input is
nonzero.
To File
Write data to a file.
Simulink Block Libraries
Table 8-2: Sinks Library Blocks (Continued)
Block Name
Purpose
To Workspace
Write data to a matrix in the workspace.
XY Graph
Display an X-Y plot of signals using a
MATLAB figure window.
Table 8-3: Discrete Library Blocks
Block Name
Purpose
Discrete Filter
Implement IIR and FIR filters.
Discrete State-Space
Implement a discrete state-space system.
Discrete-Time Integrator
Perform discrete-time integration of a
signal.
Discrete Transfer Fcn
Implement a discrete transfer function.
Discrete Zero-Pole
Implement a discrete transfer function
specified in terms of poles and zeros.
First-Order Hold
Implement a first-order sample-and-hold.
Unit Delay
Delay a signal one sample period.
Zero-Order Hold
Implement zero-order hold of one sample
period.
Table 8-4: Continuous Library Blocks
Block Name
Purpose
Derivative
Output the time derivative of the input.
Integrator
Integrate a signal.
8-5
8
Block Reference
Table 8-4: Continuous Library Blocks (Continued)
Block Name
Purpose
Memory
Output the block input from the previous
time step.
State-Space
Implement a linear state-space system.
Transfer Fcn
Implement a linear transfer function.
Transport Delay
Delay the input by a given amount of time.
Variable Transport Delay
Delay the input by a variable amount of
time.
Zero-Pole
Implement a transfer function specified in
terms of poles and zeros.
Table 8-5: Math Library Blocks
8-6
Block Name
Purpose
Abs
Output the absolute value of the input.
Algebraic Constraint
Constrain the input signal to zero.
Combinatorial Logic
Implement a truth table.
Complex to
Magnitude-Angle
Output the phase and magnitude of a
complex input signal.
Complex to Real-Imag
Output the real and imaginary parts of a
complex input signal.
Derivative
Output the time derivative of the input.
Dot Product
Generate the dot product.
Gain
Multiply block input.
Logical Operator
Perform the specified logical operation on
the input.
Simulink Block Libraries
Table 8-5: Math Library Blocks (Continued)
Block Name
Purpose
Magnitude-Angle to
Complex
Output a complex signal from magnitude
and phase inputs.
Math Function
Perform a mathematical function.
Matrix Gain
Multiply the input by a matrix.
MinMax
Output the minimum or maximum input
value.
Product
Generate the product or quotient of block
inputs.
Real-Imag to Complex
Output a complex signal from real and
imaginary inputs.
Relational Operator
Perform the specified relational operation
on the input.
Rounding Function
Perform a rounding function.
Sign
Indicate the sign of the input.
Slider Gain
Vary a scalar gain using a slider.
Sum
Generate the sum of inputs.
Trigonometric Function
Perform a trigonometric function.
Table 8-6: Functions & Tables Library Blocks
Block Name
Purpose
Fcn
Apply a specified expression to the input.
Look-Up Table
Perform piecewise linear mapping of the
input.
8-7
8
Block Reference
Table 8-6: Functions & Tables Library Blocks (Continued)
Block Name
Purpose
Look-Up Table (2-D)
Perform piecewise linear mapping of two
inputs.
MATLAB Fcn
Apply a MATLAB function or expression to
the input.
S-Function
Access an S-function.
Table 8-7: Nonlinear Library Blocks
8-8
Block Name
Purpose
Backlash
Model the behavior of a system with play.
Coulomb & Viscous Friction
Model discontinuity at zero, with linear
gain elsewhere.
Dead Zone
Provide a region of zero output.
Manual Switch
Switch between two inputs.
Multiport Switch
Choose between block inputs.
Quantizer
Discretize input at a specified interval.
Rate Limiter
Limit the rate of change of a signal.
Relay
Switch output between two constants.
Saturation
Limit the range of a signal.
Switch
Switch between two inputs.
Simulink Block Libraries
Table 8-8: Signals & Systems Library Blocks
Block Name
Purpose
Bus Selector
Output selected input signals.
Configurable Subsystem
Represent any block selected from a
specified library.
Data Store Memory
Define a shared data store.
Data Store Read
Read data from a shared data store.
Data Store Write
Write data to a shared data store.
Data Type Conversion
Convert a signal to another data type.
Demux
Separate a vector signal into output
signals.
Enable
Add an enabling port to a subsystem.
From
Accept input from a Goto block.
Goto
Pass block input to From blocks.
Goto Tag Visibility
Define the scope of a Goto block tag.
Ground
Ground an unconnected input port.
Hit Crossing
Detect crossing point.
IC
Set the initial value of a signal.
Inport
Create an input port for a subsystem or an
external input.
Merge
Combine several input lines into a scalar
line.
Model Info
Display revision control information in a
model.
8-9
8
Block Reference
Table 8-8: Signals & Systems Library Blocks (Continued)
8-10
Block Name
Purpose
Mux
Combine several input lines into a vector
line.
Outport
Create an output port for a subsystem or an
external output.
Probe
Output an input signal’s width, sample
time, and/or signal type.
Subsystem
Represent a system within another system.
Terminator
Terminate an unconnected output port.
Trigger
Add a trigger port to a subsystem.
Width
Output the width of the input vector.
Abs
Purpose
8Abs
Library
Math
Description
The Abs block generates as output the absolute value of the input.
Data Type
Support
An Abs block accepts a real- or complex-valued input of type double and
generates a real output of type double.
Output the absolute value of the input.
Dialog Box
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
N/A
Vectorized
Yes
Zero Crossing
Yes, to detect zero
8-11
Algebraic Constraint
Purpose
8Algebraic Constraint
Library
Math
Description
The Algebraic Constraint block constrains the input signal f(z) to zero and
outputs an algebraic state z. The block outputs the value necessary to produce
a zero at the input. The output must affect the input through some feedback
path. This enables you to specify algebraic equations for index 1 differential/
algebraic systems (DAEs).
Constrain the input signal to zero.
By default, the Initial guess parameter is zero. You can improve the efficiency
of the algebraic loop solver by providing an Initial guess of the algebraic state
z that is close to the solution value.
For example, the model below solves these equations:
z2 + z1 = 1
z2 – z1 = 1
The solution is z2 = 1, z1 = 0, as the Display blocks show.
Data Type
Support
8-12
An Algebraic Constraint block accepts and outputs real values of type double.
Algebraic Constraint
Parameters
and Dialog Box
Initial guess
An initial guess of the solution value. The default is 0.
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
No
Vectorized
Yes
Zero Crossing
No
8-13
Backlash
Purpose
8Backlash
Library
Nonlinear
Description
The Backlash block implements a system in which a change in input causes an
equal change in output. However, when the input changes direction, an initial
change in input has no effect on the output. The amount of side-to-side play in
the system is referred to as the deadband. The deadband is centered about the
output. This figure shows the block’s initial state, with the default deadband
width of 1 and initial output of 0.
Model the behavior of a system with play.
-1.0
-0.5
0
0.5
1.0
Output
deadband
A system with play can be in one of three modes:
• Disengaged – in this mode, the input does not drive the output and the
output remains constant.
• Engaged in a positive direction – in this mode, the input is increasing (has a
positive slope) and the output is equal to the input minus half the deadband
width.
• Engaged in a negative direction – in this mode, the input is decreasing (has
a negative slope) and the output is equal to the input plus half the deadband
width.
If the initial input is outside the deadband, the Initial output parameter value
determines if the block is engaged in a positive or negative direction and the
output at the start of the simulation is the input plus or minus half the
deadband width.
For example, the Backlash block can be used to model the meshing of two
gears. The input and output are both shafts with a gear on one end, and the
output shaft is driven by the input shaft. Extra space between the gear teeth
introduces play. The width of this spacing is the Deadband width parameter.
If the system is disengaged initially, the output (the position of the driven gear)
is defined by the Initial output parameter.
8-14
Backlash
The figures below illustrate the block’s operation when the initial input is
within the deadband. The first figure shows the relationship between the input
and the output while the system is in disengaged mode (and the default
parameter values are not changed).
-1.0
-0.5
0
0.5
1.0
Input within deadband
The next figure shows the state of the block when the input has reached the end
of the deadband and engaged the output. The output remains at its previous
value.
-1.0
-0.5
0
0.5
1.0
Input reaches end of deadband (engaged)
The final figure shows how a change in input affects the output while they are
engaged.
-1.0
-0.5
0
0.5
1.0
Input moves in positive direction.
Output = Input - (deadband width/2)
If the input reverses its direction, it disengages from the output. The output
remains constant until the input either reaches the opposite end of the
deadband or reverses its direction again and engages at the same end of the
deadband. Now, as before, movement in the input causes equal movement in
the output.
For example, if the deadband width is 2 and the initial output is 5, the output,
y, at the start of the simulation is:
• 5 if the input, u, is between 4 and 6
• u + 1 if u < 4
• u - 1 if u > 6
8-15
Backlash
This sample model and the plot that follows it show the effect of a sine wave
passing through a Backlash block.
The Backlash block parameters are unchanged from their default values (the
deadband width is 1 and the initial output is 0). Notice in the plotted output
below that the Backlash block output is zero until the input reaches the end of
the deadband (at 0.5). Now, the input and output are engaged and the output
moves as the input does until the input changes direction (at 1.0). When the
input reaches 0, it again engages the output at the opposite end of the
deadband.
B
A
Input engages in
positive direction.
Change in input causes
equal change in output.
B
Input disengages. Change
in input does not affect
output.
C
Input engages in
negative direction.
Change in input causes
equal change in output.
D
Input disengages. Change
in input does not affect
output.
Input
A
C
Output
D
Data Type
Support
8-16
A Backlash block accepts and outputs real values of type double.
Backlash
Parameters
and Dialog Box
Deadband width
The width of the deadband. The default is 1.
Initial output
The initial output value. The default is 0.
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Yes
Vectorized
Yes
Zero Crossing
Yes, to detect engagement with lower and upper
thresholds
8-17
Band-Limited White Noise
Purpose
8Band-Limited White Noise
Library
Sources
Description
The Band-Limited White Noise block generates normally distributed random
numbers that are suitable for use in continuous or hybrid systems.
Introduce white noise into a continuous system.
The primary difference between this block and the Random Number block is
that the Band-Limited White Noise block produces output at a specific sample
rate, which is related to the correlation time of the noise.
Theoretically, continuous white noise has a correlation time of 0, a flat power
spectral density (PSD), and a covariance of infinity. In practice, physical
systems are never disturbed by white noise, although white noise is a useful
theoretical approximation when the noise disturbance has a correlation time
that is very small relative to the natural bandwidth of the system.
In Simulink, you can simulate the effect of white noise by using a random
sequence with a correlation time much smaller than the shortest time constant
of the system. The Band-Limited White Noise block produces such a sequence.
The correlation time of the noise is the sample rate of the block. For accurate
simulations, use a correlation time much smaller than the fastest dynamics of
the system. You can get good results by specifying
1 2π
t c ≈ ---------- -----------100 fmax
where fmax is the bandwidth of the system in rad/sec.
The Algorithm Used in the Block Implementation
To produce the correct intensity of this noise, the covariance of the noise is
scaled to reflect the implicit conversion from a continuous PSD to a discrete
noise covariance. The appropriate scale factor is 1/tc, where tc is the
correlation time of the noise. This scaling ensures that the response of a
continuous system to our approximate white noise has the same covariance as
the system would have if we had used true white noise. Because of this scaling,
the covariance of the signal from the Band-Limited White Noise block is not the
same as the Noise power (intensity) dialog box parameter. This parameter is
actually the height of the PSD of the white noise. While the covariance of true
8-18
Band-Limited White Noise
white noise is infinite, the approximation used in this block has the property
that the covariance of the block output is the Noise Power divided by tc.
Data Type
Support
A Band-Limited White Noise block outputs real values of type double.
Parameters
and Dialog Box
Noise power
The height of the PSD of the white noise. The default value is 0.1.
Sample time
The correlation time of the noise. The default value is 0.1.
Seed
The starting seed for the random number generator. The default value is
23341.
Characteristics
Sample Time
Discrete
Scalar Expansion
Of Noise power and Seed parameters and output
Vectorized
Yes
Zero Crossing
No
8-19
Bus Selector
Purpose
8Bus Selector
Library
Signals & Systems
Description
The Bus Selector block accepts input from a Mux block or another Bus Selector
block. This block has one input port. The number of output ports depends on
the state of the Muxed output checkbox. If you check Muxed output, then the
signals are combined at the output port and there is only one output port;
otherwise, there is one output port for each selected signal.
Select signals from an incoming bus.
Note Simulink hides the name of a bus selector block when you copy it from
the Simulink library to a model.
Data Type
Support
Parameters
and Dialog Box
8-20
A Bus Selector block accepts and outputs real or complex values of any data
type.
Bus Selector
Signals in the bus
The Signals in the bus listbox shows the signals in the input bus. Use the
Select>> button to select output signals from the Signals in the bus
listbox.
Selected signals
The Selected signals listbox shows the output signals. You can order the
signals by using the Up, Down, and Remove buttons. Port connectivity is
maintained when the signal order is changed.
If an output signal listed in the Selected signals listbox is not an input to
the Bus Selector block, the signal name will be preceded by ???.
The signal label at the ouput port is automatically set by the block except
when you check the Muxed output checkbox. If you try to change this label,
you will get an error message stating that you cannot change the signal
label of a line connected to the output of a Bus Selector block.
8-21
Chirp Signal
Purpose
8Chirp Signal
Library
Sources
Description
The Chirp Signal block generates a sine wave whose frequency increases at a
linear rate with time. You can use this block for spectral analysis of nonlinear
systems. The block generates a scalar or vector output.
Data Type
Support
A Chirp Signal block outputs a real-valued signal of type double.
Generate a sine wave with increasing frequency.
Parameters
and Dialog Box
Initial frequency
The initial frequency of the signal, specified as a scalar or vector value. The
default is 0.1 Hz.
Target time
The time at which the frequency reaches the Frequency at target time
parameter value, a scalar or vector value. The frequency continues to
change at the same rate after this time. The default is 100 seconds.
Frequency at target time
The frequency of the signal at the target time, a scalar or vector value. The
default is 1 Hz.
Characteristics
8-22
Sample Time
Continuous
Scalar Expansion
Of parameters
Chirp Signal
Vectorized
Yes
Zero Crossing
No
8-23
Clock
Purpose
8Clock
Library
Sources
Description
The Clock block outputs the current simulation time at each simulation step.
This block is useful for other blocks that need the simulation time.
Display and provide the simulation time.
When you need the current time within a discrete system, use the Digital Clock
block.
Data Type
Support
A Clock block outputs a real-valued signal of type double.
Parameters
and Dialog Box
Display time
Use the Display time check box to display the current simulation time
inside the Clock block icon, which will then have the following appearance.
Decimation
The Decimation parameter value is the increment at which the clock gets
updated; it can be any positive integer. For example, if the decimation is
1000, then for a fixed integration step of 1 millisecond, the clock will update
at 1 second, 2 seconds, and so on.
Characteristics
8-24
Sample Time
Continuous
Scalar Expansion
N/A
Vectorized
No
Zero Crossing
No
Combinatorial Logic
Purpose
8Combinatorial Logic
Library
Math
Description
The Combinatorial Logic block implements a standard truth table for modeling
programmable logic arrays (PLAs), logic circuits, decision tables, and other
Boolean expressions. You can use this block in conjunction with Memory blocks
to implement finite-state machines or flip-flops.
Implement a truth table.
You specify a matrix that defines all possible block outputs as the Truth table
parameter. Each row of the matrix contains the output for a different
combination of input elements. You must specify outputs for every combination
of inputs. The number of columns is the number of block outputs.
The relationship between the number of inputs and the number of rows is
number of rows = 2 ^ (number of inputs)
Simulink returns a row of the matrix by computing the row’s index from the
input vector elements. Simulink computes the index by building a binary
number where input vector elements having zero values are 0 and elements
having nonzero values are 1, then adds 1 to the result. For an input vector, u,
of m elements
row index = 1 + u(m)*20 + u(m–1)*21 + ... + u(1)*2m–1
Example of Two-Input AND Function
This example builds a two-input AND function, which returns 1 when both
input elements are 1, and 0 otherwise. To implement this function, specify the
Truth table parameter value as [0; 0; 0; 1]. The portion of the model that
provides the inputs to and the output from the Combinatorial Logic block might
look like this.
The table below indicates the combination of inputs that generate each output.
The input signal labeled “Input 1” corresponds to the column in the table
labeled Input 1. Similarly, the input signal “Input 2” corresponds to the column
8-25
Combinatorial Logic
with the same name. The combination of these values determines which row of
the Output column of the table gets passed as block output.
For example, if the input vector is [1 0], the input references the third row
(21*1 + 1). So, the output value is 0.
Row
Input 1
Input 2
Output
1
0
0
0
2
0
1
0
3
1
0
0
4
1
1
1
Example of Circuit
This sample circuit has three inputs: the two bits (a and b) to be summed and
a carry-in bit (c). It has two outputs, the carry-out bit (c') and the sum bit (s).
Here is the truth table and the outputs associated with each combination of
input values for this circuit:
Inputs
8-26
Outputs
a
b
c
c'
s
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
Combinatorial Logic
To implement this adder with the Combinatorial Logic block, you enter the
8-by-2 matrix formed by columns c' and s as the Truth table parameter.
Sequential circuits (that is, circuits with states) can also be implemented with
the Combinatorial Logic block by including an additional input for the state of
the block and feeding the output of the block back into this state input.
Data Type
Support
A Combinatorial Logic block accepts real signals of type boolean or double and
outputs the same type as the input. The elements of the truth table can be of
type boolean or double. If the elements are of type double, they may have any
values, not just “boolean” (0 or 1) values.If the data type of the truth table
elements differs from the data type of the output signal, Simulink converts the
truth table to the output type before computing the output.
Parameters
and Dialog Box
Truth table
The matrix of outputs. Each column corresponds to an element of the
output vector and each row corresponds to a row of the truth table.
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
No
Vectorized
Yes; the output width is the number of columns of the
Truth table parameter
Zero Crossing
No
8-27
Complex to Magnitude-Angle
Purpose
8Complex to Magnitude-Angle
Library
Math
Description
The Complex to Magnitude-Angle block accepts a complex-valued signal of type
double. It outputs the magnitude and/or phase angle of the input signal,
depending on the setting of the Output parameter. The outputs are real values
of type double. The input may be a vector of complex signals, in which case the
output signals are also vectors. The magnitude signal vector contains the
magnitudes of the corresponding complex input elements. The angle output
similarly contains the angles of the input elements.
Data Type
Support
See the description above.
Compute the magnitude and/or phase angle of a complex signal.
Parameters
and Dialog Box
Output
Determines the output of this block. Choose from the following values:
MagnitudeAndAngle (outputs the input signal’s magnitude and phase
angle in radians), Magnitude (outputs the input’s magnitude), Angle
(outputs the input’s phase angle in radians).
Characteristics
8-28
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
No
Vectorized
No
Zero Crossing
No
Complex to Real-Imag
Purpose
8Complex to Real-Imag
Library
Math
Description
The Complex to Real-Imag block accepts a complex-valued signal of type
double. It outputs the real and/or imaginary part of the input signal, depending
on the setting of the Output parameter. The outputs are real values of type
double. The input may be a vector of complex signals, in which case the output
signals are also vectors. The real signal vector contains the real parts of the
corresponding complex input elements. The imaginary output similarly
contains the imaginary parts of the input elements.
Data Type
Support
See the description above.
Output the real and imaginary parts of a complex input signal.
Parameters
and Dialog Box
Output
Determines the output of this block. Choose from the following values:
RealAndImag (outputs the input signal’s real and imaginary parts), Real
(outputs the input’s real part), Imag (outputs the input’s imaginary part).
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
No
Vectorized
No
Zero Crossing
No
8-29
Configurable Subsystem
Purpose
8Configurable Subsystem
Library
Signals & Systems
Description
A Configurable Subsystem block can represent any block contained in a
specified library of blocks. The Configurable Subsystem’s dialog box lets you
specify which block it represents and the values of the parameters of the
represented block.
Represents any block selected from a user-specified library of blocks.
Configurable Subsystem blocks simplify creation of models that represent
families of designs. For example, suppose that you want to model an
automobile that offers a choice of engines. To model such a design, you would
first create a library of models of the engine types available with the car. You
would then use a Configurable Subsystem block in your car model to represent
the choice of engines. To model a particular variant of the basic car design, a
user need only choose the engine type, using the configurable engine block’s
dialog.
A Configurable Subystem block’s appearance changes depending on which
block it represents. Initially, a Configurable Subystem block represents
nothing. In this state, it has no ports and displays the icon shown at the left of
this paragraph. When you select a library and block, the Configurable
Subystem shows the icon and a set of input and output ports corresponding to
input and output ports in the selected library.
Simulink uses the following rules to map library ports to Configurable
Subystem block ports:
• Map each uniquely named input/output port in the library to a separate
input/output port of the same name on the Configurable Subystem block.
• Map all identically named input/output ports in the library to the same input
port/output on the Configurable Subystem block.
• Terminate any input/output port not used by the currently selected library
block with a Terminator/Ground block.
This mapping allows a user to change the library block represented by a
Configurable Subsystem block without having to rewire connections to the
Configurable Subsystem block.
For example, suppose that a library contains two blocks A and B and that block
A has input ports labeled a, b, and c and an output port labeled d and that block
8-30
Configurable Subsystem
B has input ports labeled a and b and an output port labeled e. A Configurable
Subsystem block based onthis library would have three input ports labeled a,
b, and c, respectively, and two output ports labeled d and e, respectively, as
illustrated in the following figure.
In this example, port a on the Configurable Subystem block connects to port a
of the selected library block no matter which block is selected. On the other
hand, port c on the Configurable Subsystem block functions only if library block
A is selected. Otherwise, it simply terminates.
Note A Configurable Subsystem block does not provide ports that correspond
to non-I/O ports, such as the trigger and enable ports on triggered and enabled
subsystems. Thus, you cannot use a Configurable Subsystem block directly to
represent blocks that have such ports. You can do so indirectly, however, by
wrapping such blocks in subsystem blocks that have input or output ports
connected to the non-I/O ports.
Data Type
Support
A Configurable Subsystem block accepts and outputs signals of the same types
as are accepted or output by the block that it currently represents.
8-31
Configurable Subsystem
Parameters
A Configurable Subsystem’s dialog box changes, depending on whether the
and Dialog Box Configurable Subystem currently represents a library and which block, if any,
the Configurable Subsystem represents. Initially a Configurable Subsystem
does not represent anything; its dialog box displays only an empty Library
name parameter.
Library name
The relative path name of the library of blocks that this Configurable
Subsystem can represent, for example, simulink/Math.
To specify the library that you want the Configurable Subystem to represent,
enter the library’s name in the Library name field.
Note You cannot use the block dialog box to change the library represented
by an existing Configurable Subsystem block. You can, however, change the
library by setting the block’s Library parameter to the name of the new
library, using the set_param model creation command.
Note If you add or remove blocks or ports in a library, you must recreate any
Configurable Subsystem blocks that use the library.
When you specify the library, a new set of parameters replaces the Library
name field. The new set comprises a Block choice field, an Open subystems
when selected field, and the parameters, if any, of the block currently
represented by the Configurable Subsystem. The following figure shows the
8-32
Configurable Subsystem
dialog box for a Configurable Subystem block that represents the Simulink
Discrete block library.
Block choice
The block that this Configurable Subystem block current represents.
Open subsystems when selected
Checking this option causes Simulink to open a nonmasked block when you
select it. This parameter appears only when the selected block is a masked
block.
Note The other parameter fields in the dialog shown above are those of the
Discrete Transfer Function block, which the Configurable Subsystem block
represents in this example.
Characteristics
A Configurable Subsystem block has the characteristics of the block that it
currently represents.
8-33
Constant
Purpose
8Constant
Library
Sources
Description
The Constant block generates a specified real or complex value independent of
time. The block generates one output, which can be scalar or vector, depending
on the length of the Constant value parameter.
Data Type
Support
A Constant block outputs a signal whose numeric type (complex or real) and
data type are the same as that of the block’s Constant value parameter.
Generate a constant value.
Parameters
and Dialog Box
Constant value
The output of the block. If a vector, the output is a vector of constants with
the specified values. The default value is 1.
Characteristics
8-34
Sample Time
Constant
Scalar Expansion
No
Vectorized
Yes
Zero Crossing
No
Coulomb and Viscous Friction
Purpose
8Coulomb and Viscous Friction
Library
Nonlinear
Description
The Coulomb and Viscous Friction block models Coulomb (static) and viscous
(dynamic) friction. The block models a discontinuity at zero and a linear gain
otherwise. The offset corresponds to the Coulombic friction; the gain
corresponds to the viscous friction. The block is implemented as
Model discontinuity at zero, with linear gain elsewhere.
y = sign(u) * (Gain * abs(u) + Offset)
where y is the output, u is the input, and Gain and Offset are block
parameters.
The block accepts one input and generates one output.
Data Type
Support
A Coulomb and Viscous Friction block accepts and outputs real signals of type
double.
Parameters
and Dialog Box
Coulomb friction value
The offset, applied to all input values. The default is [1 3 2 0].
Coefficient of viscous friction
The signal gain at nonzero input points. The default is 1.
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
No
8-35
Data Store Memory
Vectorized
Yes
Zero Crossing
Yes, at the point where the static friction is overcome
Purpose
8Data Store Memory
Library
Signals & Systems
Description
The Data Store Memory block defines and initializes a named shared data
store, which is a memory region usable by the Data Store Read and Data Store
Write blocks.
Define a data store.
Each data store must be defined by a Data Store Memory block. The location of
the Data Store Memory block that defines a data store determines the Data
Store Read and Data Store Write blocks that can access the data store:
• If the Data Store Memory block is in the top-level system, the data store can
be accessed by Data Store Read and Data Store Write blocks located
anywhere in the model.
• If the Data Store Memory block is in a subsystem, the data store can be
accessed by Data Store Read and Data Store Write blocks located in the same
subsystem or in any subsystem below it in the model hierarchy.
You initialize the data store by specifying values in the Initial value
parameter. The size of the value determines the size of the data store. An error
occurs if a Data Store Write block does not write the same amount of data.
Data Type
Support
Parameters
and Dialog Box
8-36
A Data Store Memory block stores real signals of type double.
Data Store Memory
Data store name
The name of the data store being defined. The default is A.
Initial value
The initial values of the data store. The default value is 0.
Characteristics
Sample Time
N/A
Vectorized
Yes
8-37
Data Store Read
Purpose
8Data Store Read
Library
Signals & Systems
Description
The Data Store Read block reads data from a named data store, passing the
data as output. The data was previously initialized by a Data Store Memory
block and (possibly) written to that data store by a Data Store Write block.
Read data from a data store.
The data store from which the data is read is determined by the location of the
Data Store Memory block that defines the data store. For more information, see
Data Store Memory on page 8-36.
More than one Data Store Read block can read from the same data store.
Data Type
Support
A Data Store Read block outputs a real signal of type double.
Parameters
and Dialog Box
Data store name
The name of the data store from which this block reads data.
Sample time
The sample time, which controls when the block writes to the data store.
The default, -1, indicates that the sample time is inherited.
Characteristics
8-38
Sample Time
Continuous or discrete
Vectorized
Yes
Data Store Write
Purpose
8Data Store Write
Library
Signals & Systems
Description
The Data Store Write block writes the block input to a named data store.
Write data to a data store.
Each write operation performed by a Data Store Write block writes over the
data store, replacing the previous contents.
The data store to which this block writes is determined by the location of the
Data Store Memory block that defines the data store. For more information, see
Data Store Memory on page 8-36. The size of the data store is set by the Data
Store Memory block that defines and initializes the data store. Each Data Store
Write block that writes to that data store must write the same amount of data.
More than one Data Store Write block can write to the same data store.
However, if two Data Store Write blocks attempt to write to the same data store
at the same simulation step, results are unpredictable.
Data Type
Support
A Data Store Write block accepts a real signal of type double.
Parameters
and Dialog Box
Data store name
The name of the data store to which this block writes data.
Sample time
The sample time, which controls when the block writes to the data store.
The default, -1, indicates that the sample time is inherited.
8-39
Data Store Write
Characteristics
8-40
Sample Time
Continuous or discrete
Vectorized
Yes
Data Type Conversion
Purpose
8Data Type Conversion
Library
Signals & Systems
Description
The Data Type Conversion block converts an input signal to the data type
specifed by the block’s Data type parameter. The input can be any real or
complex-valued signal. If the input is real, the output is real. If the input is
complex, the output is complex.
Data Type
Support
See block description above.
Convert input signal to specified data type.
Parameters
and Dialog Box
Data type
Specifies the type to which to convert the input signal. The auto option
converts the input signal to the type required by the input port to which the
Data Type Conversion block’s output port is connected.
Saturate on integer overflow
This parameter is enable only for integer output. If selected, this option
causes the output of the Data Type Conversion block to saturate on integer
overflow. In particular, if the output data type is an integer type, the block
output is the maximum value representable by the output type or the
converted output, whichever is smaller in the absolute sense. If the option
is not selected, Simulink takes the action specified by Data overflow event
option on the Diagnostics page of the Simulation Parameters dialog box
(see “The Diagnostics Page” on page 4–24).
8-41
Data Type Conversion
Characteristics
8-42
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Of parameters
Vectorized
Yes
Zero Crossing
Yes, to detect when the limits are reached
Dead Zone
Purpose
8Dead Zone
Library
Nonlinear
Description
The Dead Zone block generates zero output within a specified region, called its
dead zone. The lower and upper limits of the dead zone are specified as the
Start of dead zone and End of dead zone parameters. The block output
depends on the input and dead zone:
Provide a region of zero output.
• If the input is within the dead zone (greater than the lower limit and less
than the upper limit), the output is zero.
• If the input is greater than or equal to the upper limit, the output is the input
minus the upper limit.
• If the input is less than or equal to the lower limit, the output is the input
minus the lower limit.
This sample model uses lower and upper limits of -0.5 and +0.5, with a sine
wave as input.
This plot shows the effect of the Dead Zone block on the sine wave. While the
input (the sine wave) is between -0.5 and 0.5, the output is zero.
Data Type
Support
A Dead Zone block accepts and outputs a real signal of type double.
8-43
Dead Zone
Parameters
and Dialog Box
Start of dead zone
The lower limit of the dead zone. The default is -0.5.
End of dead zone
The upper limit of the dead zone. The default is 0.5.
Characteristics
8-44
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Of parameters
Vectorized
Yes
Zero Crossing
Yes, to detect when the limits are reached
Demux
Purpose
8Demux
Library
Signals & Systems
Description
The Demux block separates a vector input signal into output lines, each of
which can carry a scalar or vector signal. Simulink determines the number and
widths of the output signals by the Number of outputs parameter.
Separate a vector signal into output signals.
Scalar Number of Outputs
If the Number of outputs parameter field contains a scalar value, the block
separates the input signal into that number of output signals. The widths of the
output signals depend on the width of the input vector and the number of
outputs:
• If the input signal width is equal to the number of outputs, the block
separates the input signal vector into scalar signals. In this model, the
Demux block separates a three-element vector signal into three scalar
signals. The Number of outputs parameter is 3.
• If the input signal width is evenly divisible by the number of outputs, the
block separates the input signal into vector signals of equal width. In this
model, the Demux block separates a 12-element vector signal into three
vector signals, each with a width of four elements.
8-45
Demux
• If the input signal width is not evenly divisible by the number of outputs (and
they’re not the same), the block separates the input signal into vector signals
of unequal width and Simulink issues a warning message. In this model, the
Demux block separates a four-element vector signal into three signals. The
first signal contains the first two elements of the input signal.
Vector Number of Outputs
If the Number of outputs parameter is a vector, the number of output lines is
equal to the number of elements in the vector. The output signal widths depend
on the input vector width and the values of the elements of the parameter. You
can explicitly size output signals or let Simulink determine their widths.
• If the Number of outputs vector elements are all positive values, the block
generates signals with the specified widths. In this model, the input signal
is a vector of width 7 and the Number of outputs parameter is [2 4 1].
• If the Number of outputs vector elements include positive and –1 values, the
block generates output signals with the specified widths for those outputs
having positive values and dynamically sizes those outputs having
–1 values.
In this model, the input signal is a vector of width seven and the Number of
outputs parameter is [–1 3 –1]. In this example, Simulink explicitly
generates a three-element vector signal as the second output and
8-46
Demux
dynamically sizes the other two outputs by dividing the remaining input
elements as evenly as possible. In this case, the four elements divide equally.
In the next example, the Number of outputs is specified as [–1 4 –1]. This
parameter causes Simulink to generate unequal output vectors.
• If the Number of outputs vector elements are all –1, the number of outputs
is equal to the number of vector elements, and the widths are dynamically
sized. Specifying the parameter in this way is the same as specifying the
parameter as a scalar whose value is the number of elements. For example,
entering [–1 –1 –1] is the same as specifying a parameter value of 3.
Simulink draws the specified number of output ports on the block, resizing the
block if necessary. When the number of ports is increased or decreased, ports
are added or removed from the bottom of the block icon.
Using a Variable to Provide the Number of Outputs Parameter
When you specify the Number of outputs parameter as a variable, Simulink
issues an error message if the variable is undefined in the workspace.
Note Simulink hides the name of a bus selector block when you copy it from
the Simulink library to a model.
8-47
Demux
Data Type
Support
A Demux block accepts and outputs signals of any numeric (complex or real)
and data type.
Parameters
and Dialog Box
Number of outputs
The number and width of outputs. The total of the output widths must
match the width of the input line.
8-48
Derivative
Purpose
8Derivative
Library
Continuous
Description
The Derivative block approximates the derivative of its input by computing
Output the time derivative of the input.
∆u
------∆t
where ∆u is the change in input value and ∆t is the change in time since the
previous simulation time step. The block accepts one input and generates one
output. The value of the input signal before the start of the simulation is
assumed to be zero. The initial output for the block is zero.
The accuracy of the results depends on the size of the time steps taken in the
simulation. Smaller steps allow a smoother and more accurate output curve
from this block. Unlike blocks that have continuous states, the solver does not
take smaller steps when the input changes rapidly.
When the input is a discrete signal, the continuous derivative of the input is an
impulse when the value of the input changes, otherwise it is 0. You can obtain
the discrete derivative of a discrete signal using
1
y ( k ) = ------ ( u ( k ) – u ( k – 1 ) )
∆t
and taking the z-transform
–1
1–z
Y(z)
z–1
------------ = ----------------- = ------------∆t
u(z)
∆t ⋅ z
Using linmod to linearize a model that contains a Derivative block can be
troublesome. For information about how to avoid the problem, see
“Linearization” on page 5–4.
Data Type
Support
A Derivative block accepts and outputs a real signal of type double.
8-49
Derivative
Dialog Box
Characteristics
8-50
Direct Feedthrough
Yes
Sample Time
Continuous
Scalar Expansion
N/A
States
0
Vectorized
Yes
Zero Crossing
No
Digital Clock
Purpose
8Digital Clock
Library
Sources
Description
The Digital Clock block outputs the simulation time only at the specified
sampling interval. At other times, the output is held at the previous value.
Output simulation time at the specified sampling interval.
Use this block rather than the Clock block (which outputs continuous time)
when you need the current time within a discrete system.
Data Type
Support
A Digital Clock block outputs a real signal of type double.
Parameters
and Dialog Box
Sample time
The sampling interval. The default value is 1 second.
Characteristics
Sample Time
Discrete
Scalar Expansion
No
Vectorized
No
Zero Crossing
No
8-51
Discrete Filter
Purpose
8Discrete Filter
Library
Discrete
Description
The Discrete Filter block implements Infinite Impulse Response (IIR) and
Finite Impulse Response (FIR) filters. You specify the coefficients of the
numerator and denominator polynomials in ascending powers of z-1 as vectors
using the Numerator and Denominator parameters. The order of the
denominator must be greater than or equal to the order of the numerator. See
Discrete Transfer Fcn on page 8-65 for more information about coefficients.
Implement IIR and FIR filters.
The Discrete Filter block represents the method often used by signal processing
engineers, who describe digital filters using polynomials in z-1 (the delay
operator). The Discrete Transfer Fcn block represents the method often used
by control engineers, who represent a discrete system as polynomials in z. The
methods are identical when the numerator and denominator are the same
length. A vector of n elements describes a polynomial of degree n-1.
The block icon displays the numerator and denominator according to how they
are specified. For a discussion of how Simulink displays the icon, see Transfer
Fcn on page 8-203.
Data Type
Support
A Discrete Filter block accepts and outputs a real signal of type double.
Parameters
and Dialog Box
Numerator
The vector of numerator coefficients. The default is [1].
8-52
Discrete Filter
Denominator
The vector of denominator coefficients. The default is [1 2].
Sample time
The time interval between samples.
Characteristics
Direct Feedthrough
Only if the lengths of the Numerator and
Denominator parameters are equal
Sample Time
Discrete
Scalar Expansion
No
States
Length of Denominator parameter -1
Vectorized
No
Zero Crossing
No
8-53
Discrete Pulse Generator
Purpose
8Discrete Pulse Generator
Library
Sources
Description
The Discrete Pulse Generator block generates a series of pulses at regular
intervals.
Generate pulses at regular intervals.
The pulse width is the number of sample periods the pulse is high. The period
is the number of sample periods the pulse is high and low. The phase delay is
the number of sample periods before the pulse starts. The phase delay can be
positive or negative but must not be larger than the period. The sample time
must be greater than zero.
Use the Discrete Pulse Generator block for discrete or hybrid systems. To
generate continuous signals, use the Pulse Generator block (see Pulse
Generator on page 8-146).
Data Type
Support
A Discrete Pulse Generator block accepts and outputs a real signal of type
double.
Parameters
and Dialog Box
Amplitude
The amplitude of the pulse. The default is 1.
Period
The pulse period in number of samples. The default is 2.
8-54
Discrete Pulse Generator
Pulse width
The number of sample periods that the pulse is high. The default is 1.
Phase delay
The delay before each pulse is generated, in number of samples. The
default is 0.
Sample time
The sample period. The default is 1.
Characteristics
Sample Time
Discrete
Scalar Expansion
Of parameters
Vectorized
Yes
Zero Crossing
No
8-55
Discrete State-Space
Purpose
8Discrete State-Space
Library
Discrete
Description
The Discrete State-Space block implements the system described by
Implement a discrete state-space system.
x ( n + 1 ) = Ax ( n ) + Bu ( n )
y ( n ) = Cx ( n ) + Du ( n )
where u is the input, x is the state, and y is the output. The matrix coefficients
must have these characteristics, as illustrated in the diagram below:
• A must be an n-by-n matrix, where n is the number of states.
• B must be an n-by-m matrix, where m is the number of inputs.
• C must be an r-by-n matrix, where r is the number of outputs.
• D must be an r-by-m matrix.
n
m
n
A
B
r
C
D
The block accepts one input and generates one output. The input vector width
is determined by the number of columns in the B and D matrices. The output
vector width is determined by the number of rows in the C and D matrices.
Simulink converts a matrix containing zeros to a sparse matrix for efficient
multiplication.
Data Type
Support
8-56
A Discrete State Space block accepts and outputs a real signal of type double.
Discrete State-Space
Parameters
and Dialog Box
A, B, C, D
The matrix coefficients, as defined in the above equations.
Initial conditions
The initial state vector. The default is 0.
Sample time
The time interval between samples.
Characteristics
Direct Feedthrough
Only if D ≠ 0
Sample Time
Discrete
Scalar Expansion
Of the initial conditions
States
Determined by the size of A
Vectorized
Yes
Zero Crossing
No
8-57
Discrete-Time Integrator
Purpose
8Discrete-Time Integrator
Library
Discrete
Description
The Discrete-Time Integrator block can be used in place of the Integrator block
when constructing a purely discrete system.
Perform discrete-time integration of a signal.
The Discrete-Time Integrator block allows you to:
• Define initial conditions on the block dialog box or as input to the block.
• Output the block state.
• Define upper and lower limits on the integral.
• Reset the state depending on an additional reset input.
These features are described below.
Integration Methods
The block can integrate using these methods: Forward Euler, Backward Euler,
and Trapezoidal. For a given step k, Simulink updates y(k) and x(k+1). T is
the sampling period (delta T in the case of triggered sampling time). Values are
clipped according to upper or lower limits. In all cases, x(0)=IC (clipped if
necessary):
• Forward Euler method (the default), also known as Forward Rectangular, or
left-hand approximation. For this method, 1/s is approximated by T/(z–1).
This gives us y(k) = y(k–1) + T * u(k–1).
Let x(k) = y(k), then we have:
x(k+1) = x(k) + T * u(k)
y(k) = x(k)
(clip if necessary)
With this method, input port 1 does not have direct feedthrough.
8-58
Discrete-Time Integrator
• Backward Euler method, also known as Backward Rectangular or
right-hand approximation. For this method, 1/s is approximated by
T*z/(z–1). This gives us y(k) = y(k–1) + T * u(k).
Let x(k) = y(k–1), then we have:
x(k+1) = y(k)
y(k) = x(k) + T * u(k)
(clip if necessary)
With this method, input port 1 has direct feedthrough.
• Trapezoidal method. For this method, 1/s is approximated by
T/2*(z+1)/(z–1). This gives us y(k) = y(k–1) + T/2 * (u(k) + u(k–1)).
When T is fixed (equal to the sampling period), let
x(k) = y(k–1) + T/2 * u(k–1), then we have:
x(k+1) = y(k) + T/2 * u(k)
(clip if necessary)
y(k) = x(k) + T/2 * u(k)
(clip if necessary)
Here, x(k+1) is the best estimate of the next output. It isn’t quite the state,
in the sense that x(k) != y(k).
When T is variable (that is, obtained from the triggering times), we have:
x(k+1) = y(k)
y(k) = x(k) + T/2 * (u(k) + u(k–1)) (clip if necessary)
With this method, input port 1 has direct feedthrough.
The block icon reflects the selected integration method, as this figure shows.
Defining Initial Conditions
You can define the initial conditions as a parameter on the block dialog box or
input them from an external signal:
8-59
Discrete-Time Integrator
• To define the initial conditions as a block parameter, specify the Initial
condition source parameter as internal and enter the value in the Initial
condition parameter field.
• To provide the initial conditions from an external source, specify the Initial
condition source parameter as external. An additional input port appears
under the block input, as shown in this figure.
Using the State Port
In two known situations, you must use the state port instead of the output port:
• When the output of the block is fed back into the block through the reset port
or the initial condition port, causing an algebraic loop. For an example of this
situation, see the bounce model.
• When you want to pass the state from one conditionally executed subsystem
to another, which may cause timing problems. For an example of this
situation, see the clutch model.
You can correct these problems by passing the state through the state port
rather than the output port. Although the values are the same, Simulink
generates them at slightly different times, which protects your model from
these problems. You output the block state by selecting the Show state port
check box.
By default, the state port appears on the top of the block, as shown in this
figure.
Limiting the Integral
To prevent the output from exceeding specifiable levels, select the Limit
output check box and enter the limits in the appropriate parameter fields.
Doing so causes the block to function as a limited integrator. When the output
8-60
Discrete-Time Integrator
is outside the limits, the integral action is turned off to prevent integral wind
up. During a simulation, you can change the limits but you cannot change
whether the output is limited. The output is determined as follows:
• When the integral is less than the Lower saturation limit and the input is
negative, the output is held at the Lower saturation limit.
• When the integral is between the Lower saturation limit and the Upper
saturation limit, the output is the integral.
• When the integral is greater than the Upper saturation limit and the input
is positive, the output is held at the Upper saturation limit.
To generate a signal that indicates when the state is being limited, select the
Show saturation port check box. A saturation port appears below the block
output port, as shown in this figure.
The signal has one of three values:
• 1 indicates that the upper limit is being applied.
• 0 indicates that the integral is not limited.
• -1 indicates that the lower limit is being applied.
When the Limit output option is selected, the block has three zero crossings:
one to detect when it enters the upper saturation limit, one to detect when it
enters the lower saturation limit, and one to detect when it leaves saturation.
Resetting the State
The block can reset its state to the specified initial condition based on an
external signal. To cause the block to reset its state, select one of the External
reset choices. A trigger port appears below the block’s input port and indicates
the trigger type, as shown in this figure.
8-61
Discrete-Time Integrator
Select rising to trigger the state reset when the reset signal has a rising edge.
Select falling to trigger the state reset when the reset signal has a falling edge.
Select either to trigger the reset when either a rising or falling signal occurs.
The reset port has direct feedthrough. If the block output is fed back into this
port, either directly or through a series of blocks with direct feedthrough, an
algebraic loop results. To resolve this loop, feed the block state into the reset
port instead. To access the block’s state, select the Show state port check box.
Choosing All Options
When all options are selected, the icon looks like this.
Data Type
Support
Parameters
and Dialog Box
8-62
A Discrete-Time Integrator block accepts and outputs real signals of type
double.
Discrete-Time Integrator
Integrator method
The integration method. The default is ForwardEuler.
External reset
Resets the states to their initial conditions when a trigger event (rising,
falling, or either) occurs in the reset signal.
Initial condition source
Gets the states’ initial conditions from the Initial condition parameter (if
set to internal) or from an external block (if set to external).
Initial condition
The states’ initial conditions. Set the Initial condition source parameter
value to internal.
Limit output
If checked, limits the states to a value between the Lower saturation limit
and Upper saturation limit parameters.
Upper saturation limit
The upper limit for the integral. The default is inf.
Lower saturation limit
The lower limit for the integral. The default is -inf.
Show saturation port
If checked, adds a saturation output port to the block.
Show state port
If checked, adds an output port to the block for the block’s state.
Sample time
The time interval between samples. The default is 1.
Characteristics
Direct Feedthrough
Yes, of the reset and external initial condition source
ports
Sample Time
Discrete
Scalar Expansion
Of parameters
States
Inherited from driving block and parameter
8-63
Discrete-Time Integrator
8-64
Vectorized
Yes
Zero Crossing
One for detecting reset; one each to detect upper and
lower saturation limits, one when leaving saturation
Discrete Transfer Fcn
Purpose
8Discrete Transfer Fcn
Library
Discrete
Description
The Discrete Transfer Fcn block implements the z-transform transfer function
described by the following equations
Implement a discrete transfer function.
n
n–1
n–m
num 0 z + num 1 z
+ … + num m z
num ( z )
H ( z ) = --------------------- = -------------------------------------------------------------------------------------------------------------n
n
–
1
den ( z )
+ … + den n
den 0 z + den 1 z
where m+1 and n+1 are the number of numerator and denominator
coefficients, respectively. num and den contain the coefficients of the
numerator and denominator in descending powers of z. num can be a vector or
matrix, den must be a vector, and both are specified as parameters on the block
dialog box. The order of the denominator must be greater than or equal to the
order of the numerator.
Block input is scalar; output width is equal to the number of rows in the
numerator.
The Discrete Transfer Fcn block represents the method typically used by
control engineers, representing discrete systems as polynomials in z. The
Discrete Filter block represents the method typically used by signal processing
engineers, who describe digital filters using polynomials in z-1 (the delay
operator). The two methods are identical when the numerator is the same
length as the denominator.
The Discrete Transfer Fcn block displays the numerator and denominator
within its icon depending on how they are specified. See Transfer Fcn on page
8-203 for more information.
Data Type
Support
A Discrete Transfer Function block accepts and outputs real signals of type
double.
8-65
Discrete Transfer Fcn
Parameters
and Dialog Box
Numerator
The row vector of numerator coefficients. A matrix with multiple rows can
be specified to generate multiple output. The default is [1].
Denominator
The row vector of denominator coefficients. The default is [1 0.5].
Sample time
The time interval between samples. The default is 1.
Characteristics
8-66
Direct Feedthrough
Only if the lengths of the Numerator and
Denominator parameters are equal
Sample Time
Discrete
Scalar Expansion
No
States
Length of Denominator parameter -1
Vectorized
No
Zero Crossing
No
Discrete Zero-Pole
Purpose
8Discrete Zero-Pole
Library
Discrete
Description
The Discrete Zero-Pole block implements a discrete system with the specified
zeros, poles, and gain in terms of the delay operator z. A transfer function can
be expressed in factored or zero-pole-gain form, which, for a single-input,
single-output system in MATLAB, is
Implement a discrete transfer function specified in terms of poles and zeros.
( z – Z 1 ) ( z – Z 2 )… ( z – Z m )
Z(z)
H ( z ) = K ----------- = K ---------------------------------------------------------------------P(z)
( z – P 1 ) ( z – P 2 )… ( z – P n )
where Z represents the zeros vector, P the poles vector, and K the gain. The
number of poles must be greater than or equal to the number of zeros
(n ≥ m). If the poles and zeros are complex, they must be complex conjugate
pairs.
The block icon displays the transfer function depending on how the parameters
are specified. See Zero-Pole on page 8-222 for more information.
Data Type
Support
A Discrete Zero-Pole block accepts and outputs real signals of type double.
Parameters
and Dialog Box
Zeros
The matrix of zeros. The default is [1].
8-67
Discrete Zero-Pole
Poles
The vector of poles. The default is [0 0.5].
Gain
The gain. The default is 1.
Sample time
The time interval between samples.
Characteristics
8-68
Direct Feedthrough
Yes, if the number of zeros and poles are equal
Sample Time
Discrete
Scalar Expansion
No
States
Length of Poles vector
Vectorized
No
Zero Crossing
No
Display
Purpose
8Display
Library
Sinks
Description
The Display block shows the value of its input.
Show the value of the input.
You can control the display format by selecting a Format choice:
• short, which displays a 5-digit scaled value with fixed decimal point
• long, which displays a 15-digit scaled value with fixed decimal point
• short_e, which displays a 5-digit value with a floating decimal point
• long_e, which displays a 16-digit value with a floating decimal point
• bank, which displays a value in fixed dollars and cents format (but with no $
or commas)
To use the block as a floating display, select the Floating display check box.
The block’s input port disappears and the block displays the value of the signal
on a selected line. If you select the Floating display option, you must turn off
Simulink’s buffer reuse feature. See “Disable optimized I/O storage” on page
4-25 for more information.
The amount of data displayed and the time steps at which the data is displayed
are determined by block parameters:
• The Decimation parameter enables you to display data at every nth sample,
where n is the decimation factor. The default decimation, 1, displays data at
every time step.
• The Sample time parameter enables you to specify a sampling interval at
which to display points. This parameter is useful when using a variable-step
solver where the interval between time steps may not be the same. The
default value of –1 causes the block to ignore sampling interval when
determining which points to display.
If the block input is a vector, you can resize the block to show more than just
the first element. You can resize the block vertically or horizontally; the block
adds display fields in the appropriate direction. A black triangle indicates that
the block is not displaying all input vector elements. For example, the figure
below shows a model that passes a vector to a Display block. The top model
8-69
Display
shows the block before it is resized; notice the black triangle. The bottom model
shows the resized block displaying both input elements.
Displays only one element
of input vector but indicates
there are more
Displays both elements
of input vector
Data Type
Support
A Display block accepts and outputs real or complex signals of any data type.
Parameters
and Dialog Box
Format
The format of the data displayed. The default is short.
Decimation
How often to display data. The default value, 1, displays every input point.
Floating display
If checked, the block’s input port disappears, which enables the block to be
used as a floating Display block.
Sample time
The sample time at which to display points.
8-70
Display
Characteristics
Sample Time
Inherited from driving block
Vectorized
Yes
8-71
Dot Product
Purpose
8Dot Product
Library
Math
Description
The Dot Product block generates the dot product of its two input vectors. The
scalar output, y, is equal to the MATLAB operation
Generate the dot product.
y = u1' * u2
where u1 and u2 represent the vector inputs. If both inputs are vectors, they
must be the same length. The elements of the input vectors may be real- or
complex-valued signals of data type double. The signal type (complex or real)
of the output depends on the signal types of the inputs.
Input 1
Input 2
Output
real
real
real
real
complex
complex
complex
real
complex
complex
complex
complex
To perform element-by-element multiplication without summing, use the
Product block.
Data Type
Support
A Dot Product block accepts and outputs signals of type double.
Dialog Box
Characteristics
8-72
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Yes
Dot Product
States
0
Vectorized
Yes
Zero Crossing
No
8-73
Enable
Purpose
8Enable
Library
Signals & Systems
Description
Adding an Enable block to a subsystem makes it an enabled subsystem. An
enabled subsystem executes while the input received at the Enable port is
greater than zero.
Add an enabling port to a subsystem.
At the start of simulation, Simulink initializes the states of blocks inside an
enabled subsystem to their initial conditions. When an enabled subsystem
restarts (executes after having been disabled), the States when enabling
parameter determines what happens to the states of blocks contained in the
enabled subsystem:
• reset resets the states to their initial conditions (zero if not defined).
• held holds the states at their previous values.
You can output the enabling signal by selecting the Show output port check
box. Selecting this option allows the system to process the enabling signal. The
width of the signal is the width of the enabling signal.
A subsystem can contain no more than one Enable block.
Data Type
Support
The data type of the input of the Enable port may be boolean or double. See
Chapter 7, “Conditionally Executed Subsystems” for more information about
enabled subsystems.
Parameters
and Dialog Box
States when enabling
Specifies how to handle internal states when the subsystem becomes
re-enabled.
8-74
Enable
Show output port
If checked, Simulink draws the Enable block output port and outputs the
enabling signal.
Characteristics
Sample Time
Determined by the signal at the enable port
Vectorized
Yes
8-75
Fcn
Purpose
8Fcn
Library
Functions & Tables
Description
The Fcn block applies the specified C language style expression to its input.
The expression can be made up of one or more of these components:
Apply a specified expression to the input.
• u — the input to the block. If u is a vector, u(i) represents the ith element
of the vector; u(1) or u alone represents the first element.
• Numeric constants
• Arithmetic operators (+ – * /)
• Relational operators (== != > < >= <=) — The expression returns 1 if the
relation is TRUE; otherwise, it returns 0.
• Logical operators (&& || !) — The expression returns 1 if the relation is
TRUE; otherwise, it returns 0.
• Parentheses
• Mathematical functions — abs, acos, asin, atan, atan2, ceil, cos, cosh, exp,
fabs, floor, hypot, ln, log, log10, pow, power, rem, sgn, sin, sinh, sqrt, tan,
and tanh.
• Workspace variables — Variable names that are not recognized in the list of
items above are passed to MATLAB for evaluation. Matrix or vector
elements must be specifically referenced (e.g., A(1,1) instead of A for the first
element in the matrix).
The rules of precedence obey the C language standards:
1 ( )
2 + – (unary)
3 pow (exponentiation)
4 !
5 * /
6 + –
7 > < <= >=
8 = !=
9 &&
10 ||
8-76
Fcn
The expression differs from a MATLAB expression in that the expression
cannot perform matrix computations. Also, this block does not support the
colon operator (:).
Block input can be a scalar or vector. The output is always a scalar. For vector
output, consider using the Math Function block. If a block is a vector and the
function operates on input elements individually (for example, the sin
function), the block operates on only the first vector element.
Data Type
Support
A Fcn block accepts and outputs signals of type double.
Parameters
and Dialog Box
Expression
The C language style expression applied to the input. Expression
components are listed above. The expression must be mathematically well
formed (i.e., matched parentheses, proper number of function arguments,
etc.).
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
No
Vectorized
No
Zero Crossing
No
8-77
First-Order Hold
Purpose
8First-Order Hold
Library
Discrete
Description
The First-Order Hold block implements a first-order sample-and-hold that
operates at the specified sampling interval. This block has little value in
practical applications and is included primarily for academic purposes.
Implement a first-order sample-and-hold.
You can see the difference between the Zero-Order Hold and First-Order Hold
blocks by running the demo program fohdemo. This figure compares the output
from a Sine Wave block and a First-Order Hold block.
Data Type
Support
A First-Order Hold block accepts and outputs signals of type double.
Parameters
and Dialog Box
Sample time
The time interval between samples.
8-78
First-Order Hold
Characteristics
Direct Feedthrough
No
Sample Time
Continuous
Scalar Expansion
No
States
1 continuous and 1 discrete per input element
Vectorized
Yes
Zero Crossing
No
8-79
From
Purpose
8From
Library
Signals & Systems
Description
The From block accepts a signal from a corresponding Goto block, then passes
it as output. The data type of the output is the same as that of the input from
the Goto block. From and Goto blocks allow you to pass a signal from one block
to another without actually connecting them. To associate a Goto block with a
From block, enter the Goto block’s tag in the Goto tag parameter.
Accept input from a Goto block.
A From block can receive its signal from only one Goto block, although a Goto
block can pass its signal to more than one From block.
This figure shows that using a Goto block and a From block is equivalent to
connecting the blocks to which those blocks are connected. In the model at the
left, Block1 passes a signal to Block2. That model is equivalent to the model at
the right, which connects Block1 to the Goto block, passes that signal to the
From block, then on to Block2.
Block1
Block2
Block1
A
A
Goto
From
Block2
Associated Goto and From blocks can appear anywhere in a model with this
exception: if either block is in a conditionally executed subsystem, the other
block must be either in the same subsystem or in a subsystem below it in the
model hierarchy (but not in another conditionally executed subsystem).
However, if a Goto block is connected to a state port, the signal can be sent to
a From block inside another conditionally executed subsystem. For more
information about conditionally executed subsystems, see Chapter 7.
The visibility of a Goto block tag determines the From blocks that can receive
its signal. For more information, see Goto on page 8-91, and Goto Tag
Visibility on page 8-94. The block icon indicates the visibility of the Goto
block tag:
• A local tag name is enclosed in square brackets ([]).
• A scoped tag name is enclosed in braces ({}).
• A global tag name appears without additional characters.
8-80
From
Data Type
Support
A From block outputs signals of any real or complex data type.
Parameters
and Dialog Box
Goto tag
The tag of the Goto block passing the signal to this From block.
Characteristics
Sample Time
Inherited from block driving the Goto block
Vectorized
Yes
8-81
From File
Purpose
8From File
Library
Sources
Description
The From File block outputs data read from the specified file. The block icon
displays the name of the file supplying the data.
Read data from a file.
The file must contain a matrix of two or more rows. The first row must contain
monotonically increasing time points. Other rows contain data points that
correspond to the time point in that column. The matrix is expected to have this
form.
t1
t2
…t final
u1 1 u1 2 …u1 final
…
un 1 un 2 …un final
The width of the output depends on the number of rows in the file. The block
uses the time data to determine its output, but does not output the time values.
This means that in a matrix containing m rows, the block outputs a vector of
length m–1, consisting of data from all but the first row of the appropriate
column.
If an output value is needed at a time that falls between two values in the file,
the value is linearly interpolated between the appropriate values. If the
required time is less than the first time value or greater than the last time
value in the file, Simulink extrapolates using the first two or last two points to
compute a value.
If the matrix includes two or more columns at the same time value,the output
is the data point for the first column encountered. For example, for a matrix
that has this data:
time values:
data points:
0 1 2 2
2 3 4 5
At time 2, the output is 4, the data point for the first column encountered at
that time value.
8-82
From File
Simulink reads the file into memory at the start of the simulation. As a result,
you cannot read data from the same file named in a To File block in the same
model.
Using Data Saved by a To File or a To Workspace Block
The From File block can read data written by a To File block without any
modifications. To read data written by a To Workspace block and saved to a file:
• The data must include the simulation times. The easiest way to include time
data in the simulation output is to specify a variable for time on the
Workspace I/O page of the Simulation Parameters dialog box. See Chapter
4 for more information.
• The form of the data as it is written to the workspace is different from the
form expected by the From File block. Before saving the data to a file,
transpose it. When it is read by the From File block, it will be in the correct
form.
Data Type
Support
A From File block outputs real signals of type double.
Parameters
and Dialog Box
File name
The name of the file that contains the data used as input. The default file
name is untitled.mat.
Sample time
Sample rate of data read from the file.
8-83
From File
Characteristics
8-84
Sample Time
Inherited from driven block
Scalar Expansion
No
Vectorized
Yes
Zero Crossing
No
From Workspace
Purpose
8From Workspace
Library
Sources
Description
The From Workspace block reads data from the MATLAB workspace. The
block’s Data parameter specifies the workspace data via a MATLAB expression
that evaluates to a matrix or structure containing a table of signal values and
time steps. The format of the matrix or structure is the same as that used to
load inport data from the workspace (see “Loading Input from the Base
Workspace” on page 4–17). The From Workspace icon displays the expression
in the Data parameter.
Read data from the workspace.
If the input table does not specify the times of the input data values, each value
is assumed to occur at t = (n-1) * st where n is the nth input value and st
is the block’s sample time.
The output of a From Workspace block at each time step depends on the
settings of the block’s Interpolate data and Hold final data value parameters.
The following table summarizes the output for the various combinations of
parameter settings.
Intrp.
Option
Hold
Option
Block Output
ti < t < tf
Block Output
t > tf
On
Off
Interpolated between
data values
Extrapolated from final
data value
On
On
Interpolated between
data values
Final data value
Off
Off
Most recent data value
Zero
Off
On
Most recent data value
Final data value
If the input table contains more than one entry for the same time step,
Simulink uses the signals specified by the last entry. For example, suppose the
input table has this data:
time:
signal:
0 1 2 2
2 3 4 5
8-85
From Workspace
At time 2, the output is 5, the signal value for the lastentry for time 2.
Note A From Workspace block can directly read the output of a To
Workspace block (see To Workspace on page 8-199) if the output is in
structure or structure-with-time format (see “Loading Input from the Base
Workspace” on page 4–17 for a description of these formats). To read a matrix
written by a To Workspace block requires that a time column be added to the
matrix.
Data Type
Support
A From Workspace block can output a real or complex signal of any data type.
Parameters
and Dialog Box
Data
An expression that evaluates to a matrix or a structure containing a table
of simulation times and corresponding signal values. For example, suppose
that the workspace contains a column vector of times named T and a matrix
of corresponding signal values named U. Then the default expression for
this parameter, [T,U], yields a matrix containing the required input table.
If the required signal-versus-time matrix or structure already exists in the
workspace, simply enter the name of the structure or matrix in this field.
8-86
From Workspace
Sample time
Sample rate of data from workspace.
Interpolate data
This option causes the block to linearly interpolate (or extrapolate, if the
Hold final data value parameter is off) at time steps for which no
corresponding workspace data exists. Otherwise, the current output equals
the output at the most recent time for which data exists.
Hold final data value
This option causes the block to hold its output to the last value for which
data is available.
Characteristics
Sample Time
Inherited from driven block
Scalar Expansion
No
Vectorized
Yes
Zero Crossing
No
8-87
Function-Call Generator
Purpose
8Function-Call Generator
Library
Signals & Systems
Description
The Function-Call Generator block executes a function-call subsystem (for
example, a Stateflow state chart configured as a function-call system) at the
rate specified by the block’s Sample time parameter. To execute multiple
function-call subsystems in a prescribed order, first connect a Function-Call
Generator block to a Demux block that has as many output ports as there are
function-call subsystems to be controlled. Then connect the outports of the
Demux block to the systems to be controlled. The system connected to the first
demux port executes first, the system connected to the second demux port
executes second, and so on.
Data Type
Support
A Function-Call block outputs a real signal of type double.
Execute a function-call subsystem at a specified rate.
Parameters
and Dialog Box
Sample time
The time interval between samples.
Characteristics
8-88
Direct Feedthrough
No
Sample Time
User-specified
Scalar Expansion
No
Vectorized
Yes
Zero Crossing
No
Gain
Purpose
8Gain
Library
Math
Description
The Gain block generates its output by multiplying its input by a specified
constant, variable, or expression.You can enter the gain as a numeric value, or
as a variable or expression. To multiply the input by a matrix, use the Matrix
Gain block (see Matrix Gain on page 8-123).
Multiply block input.
The Gain block icon displays the value entered in the Gain parameter field if
the block is large enough. If the gain is specified as a variable, the block
displays the variable name, although if the variable is specified in parentheses,
the block evaluates the variable each time the block is redrawn and displays its
value. If the Gain parameter value is too long to be displayed in the block, the
string –K– is displayed.
To modify the gain during a simulation using a slider control (see Slider Gain
on page 8-183).
Data Type
Support
A Gain block accepts a real- or complex-valued scalar or vector of any data type
except boolean and outputs a signal of the same data type as its input. The
elements of an input vector must be of the same type. A Gain blocks Gain
parameter can also be a real- or complex-valued scalar or vector of any data
type. A Gain block observes the following type rules:
• If the input is real and the gain is complex, the output is complex.
• If the gain parameter’s data type differs from the input signal’s data type and
the input data type can represent the gain, Simulink converts the gain to the
input type before computing the output. Otherwise, Simulink halts the
simulation and signals an error. For example, if the input data type is uint8
and the gain is -1, an error results. If typecasting the gain parameter to the
input data type results in a loss of precision, Simulink issues a warning and
continues the simulation.
• If the output data type is an integer type and the gain block’s Saturate on
integer overflow option is selected, the block saturates if the output exceeds
the maximum value representable by the block’s output data type. In other
words, the block outputs one plus the maximum positive or minimum
negative value representable by the output data type. For example, if the
8-89
Gain
output type is int8, the actual output is 128 if the computed output is greater
than 128 and -128 if the computed output is less than -128.
Parameters
and Dialog Box
Gain
The gain, specified as a scalar, vector, variable name, or expression. The
default is 1. If not specified, the data type of the Gain parameter is double.
Saturate on integer overflow
If selected, this option causes the output of the Gain block to saturate on
integer overflow. In particular, if the output data type is an integer type,
the block output is the maximum value representable by the output type or
the computed output, whichever is smaller in the absolute sense. If the
option is not selected, Simulink takes that action specified by the Data
overflow event option on the Diagnostics page of the Simulation
Parameters dialog box (see “The Diagnostics Page” on page 4–24).
Characteristics
8-90
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Of input and Gain parameter
States
0
Vectorized
Yes
Zero Crossing
No
Goto
Purpose
8Goto
Library
Signals & Systems
Description
The Goto block passes its input to its corresponding From blocks. The input can
be a real- or complex-valued signal or vector of any data type. From and Goto
blocks allow you to pass a signal from one block to another without actually
connecting them.
Pass block input to From blocks.
A Goto block can pass its input signal to more than one From block, although
a From block can receive a signal from only one Goto block. The input to that
Goto block is passed to the From blocks associated with it as though the blocks
were physically connected. For limitations on the use of From and Goto blocks,
see From on page 8-80. Goto blocks and From blocks are matched by the use of
Goto tags, defined as the Tag parameter.
The Tag visibility parameter determines whether the location of From blocks
that access the signal is limited:
• local, the default, means that From and Goto blocks using the tag must be
in the same subsystem. A local tag name is enclosed in square brackets ([]).
• scoped means that From and Goto blocks using the same tag must be in the
same subsystem or in any subsystem below the Goto Tag Visibility block in
the model hierarchy. A scoped tag name is enclosed in braces ({}).
• global means that From and Goto blocks using the same tag can be
anywhere in the model.
Use local tags when the Goto and From blocks using the same tag name reside
in the same subsystem. You must use global or scoped tags when the Goto and
From blocks using the same tag name reside in different subsystems. When
you define a tag as global, all uses of that tag access the same signal. A tag
8-91
Goto
defined as scoped can be used in more than one place in the model. This
example shows a model that uses two scoped tags with the same name (A).
Data Type
Support
A Goto block accepts real or complex signals of any data type.
Parameters
and Dialog Box
Tag
The Goto block identifier. This parameter identifies the Goto block whose
scope is defined in this block.
Tag visibility
The scope of the Goto block tag: local, scoped, or global. The default is
local.
8-92
Goto
Characteristics
Sample Time
Inherited from driving block
Vectorized
Yes
8-93
Goto Tag Visibility
Purpose
8Goto Tag Visibility
Library
Signals & Systems
Description
The Goto Tag Visibility block defines the accessibility of Goto block tags that
have scoped visibility. The tag specified as the Goto tag parameter is
accessible by From blocks in the same subsystem that contains the Goto Tag
Visibility block and in subsystems below it in the model hierarchy.
Define scope of Goto block tag.
A Goto Tag Visibility block is required for Goto blocks whose Tag visibility
parameter value is scoped. It is not used if the tag visibility is either local or
global. The block icon shows the tag name enclosed in braces ({}).
Data Type
Support
Not applicable.
Parameters
and Dialog Box
Goto tag
The Goto block tag whose visibility is defined by the location of this block.
Characteristics
8-94
Sample Time
N/A
Vectorized
N/A
Ground
Purpose
8Ground
Library
Signals & Systems
Description
The Ground block can be used to connect blocks whose input ports are not
connected to other blocks. If you run a simulation with blocks having
unconnected input ports, Simulink issues warning messages. Using Ground
blocks to “ground” those blocks avoids warning messages. The Ground block
outputs a signal with zero value. The data type of the signal is the same as that
of the port to which it is connected.
Data Type
Support
A Ground block outputs a signal of the same numeric type (real or complex) and
data type as the port to which it is connected. For example, consider the
following model.
Ground an unconnected input port.
In this example, the output of the constant block determines the data type
(int8) of the port to which the ground block is connected. That port in turn
determines the type of the signal output by the ground block.
Parameters
and Dialog Box
Characteristics
Sample Time
Inherited from driven block
Vectorized
Yes
8-95
Hit Crossing
Purpose
8Hit Crossing
Library
Signals & Systems
Description
The Hit Crossing block detects when the input reaches the Hit crossing offset
parameter value in the direction specified by the Hit crossing direction
parameter. This block locates transitions to, from, and through the offset. The
block finds the crossing point to within machine tolerance.
Detect crossing point.
The block accepts one input of type double. If the Show output port check box
is selected, the block output indicates when the crossing occurs. If the input
signal is exactly the value of the offset value, the block outputs a value of 1 at
that time step. If the input signals at two adjacent points bracket the offset
value (but neither value is exactly equal to the offset), the block outputs a value
of 1 at the second time step. If the Show output port check box is not selected,
the block ensures that the simulation finds the crossing point but does not
generate output.
The Hit Crossing block serves as an “Almost Equal” block, useful in working
around limitations in finite mathematics and computer precision. Used for
these reasons, this block may be more convenient than adding logic to your
model to detect this condition.
The hardstop and clutch demos illustrate the use of the Hit Crossing block. In
the hardstop demo, the Hit Crossing block is in the Friction Model subsystem.
In the clutch demo, the Hit Crossing block is in the Lockup Detection
subsystem.
Data Type
Support
8-96
A Hit Crossing block outputs a signal of type boolean unless boolean
compatibility mode is enabled (see “Enabling Strict Boolean Type Checking” on
page 3-45) in which case, the block outputs a signal of type double.
Hit Crossing
Parameters
and Dialog Box
Hit crossing offset
The value whose crossing is to be detected.
Hit crossing direction
The direction from which the input signal approaches the hit crossing offset
for a crossing to be detected.
Show output port
If checked, draw an output port.
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Yes
Vectorized
Yes
Zero Crossing
Yes, to detect the crossing
8-97
IC
Purpose
8IC
Library
Signals & Systems
Description
The IC block sets the initial condition of the signal connected to its output port.
Set the initial value of a signal.
For example, these blocks illustrate how the IC block initializes a signal
labeled “test signal.”
At t = 0, the signal value is 3. Afterwards, the signal value is 6.
The IC block is also useful in providing an initial guess for the algebraic state
variables in the loop. For more information, see Chapter 10.
Data Type
Support
A IC block accepts and outputs a signal of type double.
Dialog Box
Initial value
The initial value for the signal. The default is 1.
Characteristics
8-98
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Parameter only
States
0
Vectorized
Yes
Zero Crossing
No
Inport
Purpose
8Inport
Library
Signals & Systems
Description
Inports are the links from outside a system into the system.
Create an input port for a subsystem or an external input.
Simulink assigns Inport block port numbers according to these rules:
• It automatically numbers the Inport blocks within a top-level system or
subsystem sequentially, starting with 1.
• If you add an Inport block, it is assigned the next available number.
• If you delete an Inport block, other port numbers are automatically
renumbered to ensure that the Inport blocks are in sequence and that no
numbers are omitted.
• If you copy an Inport block into a system, its port number is not renumbered
unless its current number conflicts with an Inport block already in the
system. If the copied Inport block port number is not in sequence, you must
renumber the block or you will get an error message when you run the
simulation or update the block diagram.
If the Inport block provides a vector signal, you can specify the width of the
input to the Inport block as the Port width parameter or let Simulink
determine it automatically by providing a value of -1 (the default).
The Sample time parameter is the rate at which the signal is coming into the
system. The default (-1) causes the block to inherit its sample time from the
block driving it. It may be appropriate to set this parameter for Inport blocks
in the top-level system or in models where Inport blocks are driven by blocks
whose sample time cannot be determined.
Inport Blocks in a Subsystem
Inport blocks in a subsystem represent inputs to the subsystem. A signal
arriving at an input port on a Subsystem block flows out of the associated
Inport block in that subsystem.
The Inport block associated with an input port on a Subsystem block is the
block whose Port number parameter matches the relative position of the input
port on the Subsystem block. For example, the Inport block whose Port
8-99
Inport
number parameter is 1 gets its signal from the block connected to the top-most
port on the Subsystem block.
If you renumber the Port number of an Inport block, the block becomes
connected to a different input port, although the block continues to receive its
signal from the same block outside the subsystem.
The Inport block name appears in the Subsystem block icon as a port label. To
suppress display of the label, select the Inport block and choose Hide Name
from the Format menu. Then, choose Update Diagram from the Edit menu.
Inport Blocks in a Top-Level System
Inport blocks in a top-level system have two uses: to supply external inputs
from the workspace, which you can do by using either the Simulation
Parameters dialog box or the sim command, and to provide a means for
analysis functions to perturb the model:
• To supply external inputs from the workspace, using the Simulation
Parameters dialog (see “Loading Input from the Base Workspace” on page
4-17) or the ut argument of the sim command (see sim on page 4-30).
• To provide a means for perturbation of the model by the linmod and trim
analysis functions. Inport blocks define the points where inputs are injected
into the system. For information about using Inport blocks with analysis
commands, see Chapter 5.
Data and
Numeric Type
Support
An inport accepts real- or complex-valued signals of any data type. The data
type and numeric type of the output of an inport is the same as that of the
corresponding input signal. You must specify the signal type and data type of
an external (i.e., workspace) input to a root-level inport, using the inport’s
Signal type and Data type parameters.
The elements of an signal vector connected to a root-level inport must be of the
same numeric type and data type. Signal elements connected to a subsystem
import may be of differing numeric and data types except in one instance. If the
subsystem contains an Enable or Trigger block and the inport is connected
8-100
Inport
directly to an outport, the input elements must be of the same type. For
example, consider the follow enabled subsystem.
In this example, the elements of a signal vector connected to In1 must be of the
same type. The elements connected to In2, however, may be of differing types.
Parameters
and Dialog Box
Port number
The port number of the Inport block.
Port width
The width of the input signal to the Inport. Specify -1 to have it
automatically determined.
Sample time
The rate at which the signal is coming into the system.
8-101
Inport
Note The next three parameters apply only to root-level inports. They do not
appear on subsystem inport dialogs.
Data type
The data type of the external input.
Signal type
The signal type (real or complex) of the external input.
Interpolate data
Selecting this option causes this block to interpolate or extrapolate output
at time steps for which no corresponding workspace data exists.
Characteristics
8-102
Sample Time
Inherited from driving block
Vectorized
Yes
Integrator
Purpose
8Integrator
Library
Continuous
Description
The Integrator block integrates its input. The output of the integrator is simply
its state, the integral. The Integrator block allows you to:
Integrate a signal.
• Define initial conditions on the block dialog box or as input to the block.
• Output the block state.
• Define upper and lower limits on the integral.
• Reset the state depending on an additional reset input.
Use the Discrete-Time Integrator block (see Discrete-Time Integrator on
page 8-58), when constructing a purely discrete system.
Defining Initial Conditions
You can define the initial conditions as a parameter on the block dialog box or
input them from an external signal:
• To define the initial conditions as a block parameter, specify the Initial
condition source parameter as internal and enter the value in the Initial
condition parameter field.
• To provide the initial conditions from an external source, specify the Initial
condition source parameter as external. An additional input port appears
under the block input, as shown in this figure.
Using the State Port
In two known situations, you must use the state port instead of the output port:
• When the output of the block is fed back into the block through the reset port
or the initial condition port, causing an algebraic loop. For an example of this
situation, see the bounce model.
• When you want to pass the state from one conditionally executed subsystem
to another, which may cause timing problems. For an example of this
situation, see the clutch model.
8-103
Integrator
You can correct these problems by passing the state through the state port
rather than the output port. Although the values are the same, Simulink
generates them at slightly different times, which protects your model from
these problems.You output the block state by selecting the Show state port
check box. By default, the state port appears on the top of the block, as shown
in this figure.
Limiting the Integral
To prevent the output from exceeding specifiable levels, select the Limit
output check box and enter the limits in the appropriate parameter fields.
Doing so causes the block to function as a limited integrator. When the output
is outside the limits, the integral action is turned off to prevent integral wind
up. During a simulation, you can change the limits but you cannot change
whether the output is limited. The output is determined as follows:
• When the integral is less than the Lower saturation limit and the input is
negative, the output is held at the Lower saturation limit.
• When the integral is between the Lower saturation limit and the Upper
saturation limit, the output is the integral.
• When the integral is greater than the Upper saturation limit and the input
is positive, the output is held at the Upper saturation limit.
To generate a signal that indicates when the state is being limited, select the
Show saturation port check box. A saturation port appears below the block
output port, as shown on this figure.
The signal has one of three values:
• 1 indicates that the upper limit is being applied.
• 0 indicates that the integral is not limited.
• -1 indicates that the lower limit is being applied.
8-104
Integrator
When this option is selected, the block has three zero crossings: one to detect
when it enters the upper saturation limit, one to detect when it enters the lower
saturation limit, and one to detect when it leaves saturation.
Resetting the State
The block can reset its state to the specified initial condition based on an
external signal. To cause the block to reset its state, select one of the External
reset choices. A trigger port appears below the block’s input port and indicates
the trigger type, as shown in this figure.
Select rising to trigger the state reset when the reset signal has a rising edge.
Select falling to trigger the state reset when the reset signal has a falling edge.
Select either to trigger the reset when either a rising or falling signal occurs.
The reset port has direct feedthrough. If the block output is fed back into this
port, either directly or through a series of blocks with direct feedthrough, an
algebraic loop results. To resolve this loop, feed the block state into the reset
port instead. To access the block’s state, select the Show state port check box.
Specifying the Absolute Tolerance for the Block State
When your model contains states having vastly different magnitudes, defining
the absolute tolerance for the model might not provide sufficient error control.
To define the absolute tolerance for an Integrator block’s state, provide a value
for the Absolute tolerance parameter. If the block has more than one state,
the same value is applied to all states.
For more information about error control, see “Error Tolerances” on page 4-13.
Choosing All Options
When all options are selected, the icon looks like this.
8-105
Integrator
Data Type
Support
An Integrator block accepts and outputs signals of type double on its data
ports. Its external reset port accepts signals of type double or boolean.
Parameters
and Dialog Box
External reset
Resets the states to their initial conditions when a trigger event (rising,
falling, or either) occurs in the reset signal.
Initial condition source
Gets the states’ initial conditions from the Initial condition parameter (if
set to internal) or from an external block (if set to external).
Initial condition
The states’ initial conditions. Set the Initial condition source parameter
value to internal.
Limit output
If checked, limits the states to a value between the Lower saturation limit
and Upper saturation limit parameters.
Upper saturation limit
The upper limit for the integral. The default is inf.
Lower saturation limit
The lower limit for the integral. The default is -inf.
8-106
Integrator
Show saturation port
If checked, adds a saturation output port to the block.
Show state port
If checked, adds an output port to the block for the block’s state.
Absolute tolerance
Absolute tolerance for the block’s states.
Characteristics
Direct Feedthrough
Yes, of the reset and external initial condition source
ports
Sample Time
Continuous
Scalar Expansion
Of parameters
States
Inherited from driving block or parameter
Vectorized
Yes
Zero Crossing
If the Limit output option is selected, one for
detecting reset; one each to detect upper and lower
saturation limits, one when leaving saturation
8-107
Logical Operator
Purpose
8Logical Operator
Library
Math
Description
The Logical Operator block performs any of these logical operations on its
inputs: AND, OR, NAND, NOR, XOR, and NOT. The output depends on the
number of inputs, their vector size, and the selected operator. The output is 1
if TRUE and 0 if FALSE. The block icon shows the selected operator.
Perform the specified logical operation on the input.
• For two or more inputs, the block performs the operation between all of the
inputs. If the inputs are vectors, the operation is performed between
corresponding elements of the vectors to produce a vector output.
• For a single vector input, the block applies the operation (except the NOT
operator) to all elements of that vector. The NOT operator accepts only one
input, which can be a scalar or vector. If the input is a vector, the output is a
vector of the same size containing the logical complements of the elements of
the input vector.
When configured as a multi-input XOR gate, this block performs an addition
modulo two operation as mandated by the IEEE standard for logic elements.
Data Type
Support
Parameters
and Dialog Box
8-108
An Logical Operator block accepts signals of type boolean on its input ports,
unless boolean compatibility mode is enabled (see “Enabling Strict Boolean
Type Checking” on page 3-45), in which case the block also accepts inputs of
type double. A nonzero input of type double is treated as TRUE (1), a zero
input as FALSE (0). All inputs must be of the same type. The output of the
block is of the same type as the input.
Logical Operator
Operator
The logical operator to be applied to the block inputs. Valid choices are the
operators listed above.
Number of input ports
The number of block inputs. The value must be appropriate for the selected
operator.
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Of inputs
Vectorized
Yes
Zero Crossing
No
8-109
Look-Up Table
Purpose
8Look-Up Table
Library
Functions & Tables
Description
The Look-Up Table block maps an input to an output using linear interpolation
of the values defined in the block’s parameters.
Perform piecewise linear mapping of the input.
You define the table by specifying (either as row or column vectors) the Vector
of input values and Vector of output values parameters. The block produces
an output value by comparing the block input with values in the input vector:
• If it finds a value that matches the block’s input, the output is the
corresponding element in the output vector.
• If it does not find a value that matches, it performs linear interpolation
between the two appropriate elements of the table to determine an output
value. If the block input is less than the first or greater than the last input
vector element, the block extrapolates using the first two or the last two
points.
To map two inputs to an output, use the Look-Up Table (2-D) block. For more
information, see Look-Up Table (2-D) on page 8-113.
To create a table with step transitions, repeat an input value with different
output values. For example, these input and output parameter values create
the input/output relationship described by the plot that follows:
Vector of input values:
Vector of output values:
[–2 –1 –1 0 0 0 1 1 2]
[–1 –1 –2 –2 1 2 2 1 1]
the output value
This example has three step discontinuities: at u = -1, 0, and +1.
8-110
Look-Up Table
When there are two points at a given input value, the block generates output
according to these rules:
• When u is less than zero, the output is the value connected with the point
first encountered when moving away from the origin in a negative direction.
In this example, when u is -1, y is -2, marked with a solid circle.
• When u is greater than zero, the output is the value connected with the point
first encountered when moving away from the origin in a positive direction.
In this example, when u is 1, y is 2, marked with a solid circle.
• When u is at the origin and there are two output values specified for zero
input, the actual output is their average. In this example, if there were no
point at u = 0 and y = 1, the output would be 0, the average of the two points
at u = 0. If there are three points at zero, the block generates the output
associated with the middle point. In this example, the output at the origin is
1.
The Look-Up Table block icon displays a graph of the input vector versus the
output vector. When a parameter is changed on the block’s dialog box, the
graph is automatically redrawn when you press the Apply or Close button.
Data Type
Support
A Look-Up Table block accepts and outputs signals of type double.
Parameters
and Dialog Box
Vector of input values
The vector of values containing possible block input values. This vector
must be the same size as the output vector. The input vector must be
monotonically increasing.
8-111
Look-Up Table
Vector of output values
The vector of values containing block output values. This vector must be
the same size as the input vector.
Characteristics
8-112
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
No
Vectorized
Yes
Zero Crossing
No
Look-Up Table (2-D)
Purpose
8Look-Up Table (2-D)
Library
Functions & Tables
Description
The Look-Up Table (2-D) block maps the block inputs to an output using linear
interpolation of a table of values defined by the block’s parameters.
Perform piecewise linear mapping of two inputs.
You define the possible output values as the Table parameter. You define the
values that correspond to its rows and columns with the Row and Column
parameters. The block generates an output value by comparing the block
inputs with the Row and the Column parameters. The first input identifies a
row, and the second input identifies a column, as shown by this figure.
The block generates output based on the input values:
• If the inputs match row and column parameter values, the output is the table
value at the intersection of the row and column.
• If the inputs do not match row and column parameter values, the block
generates output by linearly interpolating between the appropriate table
values. If either or both block inputs are less than the first or greater than
the last row or column parameter values, the block extrapolates from the
first two or last two points.
If either the Row or Column parameter has a repeating value, the block
chooses a value using the technique described for the Look-Up Table block.
The Look-Up Table block allows you to map a single input value into a vector
of output values (see Look-Up Table on page 8-110).
Example
In this example, the block parameters are defined as:
Row:
Column:
Table:
[1 2]
[3 4]
[10 20; 30 40]
8-113
Look-Up Table (2-D)
The first figure shows the block outputting a value at the intersection of block
inputs that match row and column values. The first input is 1 and the second
input is 4. These values select the table value at the intersection of the first row
(row parameter value 1) and second column (column parameter value 4).
3
4
1 10 20
2 30 40
In the second figure, the first input is 1.7 and the second is 3.4. These values
cause the block to interpolate between row and column values, as shown in the
table at the left. The value at the intersection (28) is the output value.
3 3.4 4
1 10 14 20
1.7 24 28 34
2 30 34 40
Data Type
Support
A Look-Up Table (2-D) block accepts and outputs signals of type double.
Parameters
and Dialog Box
Row
The row values for the table, entered as a vector. The vector values must
increase monotonically.
8-114
Look-Up Table (2-D)
Column
The column values for the table, entered as a vector. The vector values
must increase monotonically.
Table
The table of output values. The matrix size must match the dimensions
defined by the Row and Column parameters.
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from driving blocks
Scalar Expansion
Of one input if the other is a vector
Vectorized
Yes
Zero Crossing
No
8-115
Magnitude-Angle to Complex
Purpose
8Magnitude-Angle to Complex
Library
Math
Description
The Magnitude-Angle to Complex block converts magnitude and/or phase
angle inputs to a complex-valued output signal. The inputs must be real-valued
signals of type double. The angle input is assumed to be in radians. The data
type of the complex output signal is double.
Convert a magnitude and/or a phase angle signal to a complex signal.
The inputs may be both vectors of equal size, or one input may be a vector and
the other a scalar. If the block has a vector input, the output is a vector of
complex signals. The elements of a magnitude input vector are mapped to
magnitudes of the corresponding complex output elements. An angle input
vector is similarly mapped to the angles of the complex output signals. If one
input is a scalar, it is mapped to the corresponding component (magnitude or
angle) of all the complex output signals.
Data Type
Support
See block description above.
Parameters
and Dialog Box
Input
Specifies the kind of input: a magnitude input, an angle input, or both.
Angle (Magnitude)
If the input is an angle signal, specifies the constant magnitude of the
output signal. If the input is a magnitude, specifies the constant phase
angle in radians of the output signal.
8-116
Magnitude-Angle to Complex
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Of the input when the function requires two inputs
Vectorized
Yes
Zero Crossing
No
8-117
Manual Switch
Purpose
8Manual Switch
Library
Nonlinear
Description
The Manual Switch block is a toggle switch that selects one of its two inputs to
pass through to the output. To toggle between inputs, double-click on the block
icon (there is no dialog box). The selected input is propagated to the output,
while the unselected input is discarded. You can set the switch before the
simulation is started or throw it while the simulation is executing to
interactively control the signal flow. The Manual Switch block retains its
current state when the model is saved.
Data Type
Support
A Manual Switch block accepts all input types. Both inputs must be of the same
numeric and data type. The block’s output has the same numeric type (real or
complex) and data type as its input.
Switch between two inputs.
Parameters
None
and Dialog Box
Characteristics
8-118
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
N/A
Vectorized
Yes
Zero Crossing
No
Math Function
Purpose
8Math Function
Library
Math
Description
The Math Function block performs numerous common mathematical
functions.
Perform a mathematical function.
You can select one of these functions from the Function list: exp, log, 10u,
log10, square, sqrt, pow, reciprocal, hypot, rem, and mod. The block output is
the result of the function operating on the input or inputs.
The name of the function appears on the block icon. Simulink automatically
draws the appropriate number of input ports.
Use the Math Function block instead of the Fcn block when you want
vectorized output because the Fcn block can produce only scalar output.
Data Type
Support
A Math Function block accepts complex or real-valued signals or signal vectors
of type double.The output signal type is real or complex, depending on the
setting of the Output signal type parameter.
Parameters
and Dialog Box
Function
The mathematical function.
8-119
Math Function
Output signal type
The dialog allows you to select the output signal type of the Math Function
block as real, complex, or auto.
Input
Characteristics
8-120
Output Signal Type
Function
Signal
Auto
Real
Complex
Exp, log, log^, log10,
square, sqrt, pow,
reciprocal, conjugate
real
complex
real
complex
real
error
complex
complex
magnitude squared
real
complex
real
real
real
real
complex
complex
hypot, rem, mod
real
complex
real
error
real
error
complex
error
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Of the input when the function requires two inputs
Vectorized
Yes
Zero Crossing
No
MATLAB Fcn
Purpose
8MATLAB Fcn
Library
Functions & Tables
Description
The MATLAB Fcn block applies the specified MATLAB function or expression
to the input. The specified function or expression is applied to the input. The
output of the function must match the output width of the block or an error
occurs.
Apply a MATLAB function or expression to the input.
Here are some sample valid expressions for this block:
sin
atan2(u(1), u(2))
u(1)^u(2)
Note This block is slower than the Fcn block because it calls the MATLAB
parser during each integration step. Consider using built-in blocks (such as
the Fcn block or the Math Function block) instead, or writing the function as
an M-file or MEX-file S-function, then accessing it using the S-Function block.
Data Type
Support
A MATLAB Fcn block accepts one complex- or real-valued input of type double
and generates real or complex output of type double, depending on the setting
of the Output signal type parameter.
Parameters
and Dialog Box
MATLAB function
The function or expression. If you specify a function only, it is not necessary
to include the input argument in parentheses.
8-121
MATLAB Fcn
Output width
The output width. If the output width is to be the same as the input width,
specify -1. Otherwise, you must specify the correct width or an error will
result.
Output signal type
The dialog allows you to select the output signal type of the MATLAB Fcn
as real, complex, or auto. A value of auto sets the block’s output type to be
the same as the type of the input signal. If the block has no input signal,
auto sets the output type to the port type to which the output is connected.
Characteristics
8-122
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
N/A
Vectorized
Yes
Zero Crossing
No
Matrix Gain
Purpose
8Matrix Gain
Library
Math
Description
The Matrix Gain block implements a matrix gain. It generates its output by
multiplying its vector input by a specified matrix
Multiply the input by a matrix.
y = Ku
where K is the gain and u is the input.
If the specified matrix has m rows and n columns, then the input to this block
should be a vector of length n. The output is a vector of length m.
The block icon always displays K.
If the matrix contains zeros, Simulink converts the matrix gain to a sparse
matrix for efficient multiplication.
Data Type
Support
A Matrix Gain block accepts and outputs real-valued signals of type double.
Parameters
and Dialog Box
Gain matrix
The gain, specified as a matrix. The default is eye(3,3).
Characteristics
Direct Feedthrough
Yes
Sample Time
Continuous
Scalar Expansion
No
States
0
Vectorized
Yes
Zero Crossing
No
8-123
Memory
Purpose
8Memory
Library
Continuous
Description
The Memory block outputs its input from the previous time step, applying a one
integration step sample-and-hold to its input signal.
Output the block input from the previous integration step.
This sample model (which, to provide more useful information, would be part
of a larger model) demonstrates how to display the step size used in a
simulation. The Sum block subtracts the time at the previous step, generated
by the Memory block, from the current time, generated by the clock.
Note Avoid using the Memory block when integrating with ode15s or
ode113, unless the input to the block does not change.
Data Type
Support
A Memory block accepts signals of any numeric type (complex or real) and data
type, including user-defined types. If the input type is user-defined, the initial
condition must be 0.
Parameters
and Dialog Box
Initial condition
The output at the initial integration step.
Inherit sample time
Check this box to cause the sample time to be inherited from the driving
block.
8-124
Memory
Characteristics
Direct Feedthrough
No
Sample Time
Continuous, but inherited if the Inherit sample time
check box is selected
Scalar Expansion
Of the Initial condition parameter
Vectorized
Yes
Zero Crossing
No
8-125
Merge
Purpose
8Merge
Library
Signals & Systems
Description
The Merge block combines its inputs into a single output line whose value at
any time is equal to the most recently computed output of its driving blocks.
You can specify any number of inputs by setting the block’s Number of Inputs
parameter. All inputs must be the same width, for example, all scalar or all
vectors of width three.You can specify an initial output value by setting the
blocks Initial Output parameter. If you do not specify an initial output and one
or more of the driving blocks do, the Merge block’s initial output equals the
most recently evaluated initial output of the driving blocks.
Combine input lines into a scalar output line
Merge blocks facilitate creation of alternately executing subsystems. See
“Creating Alternately Executing Subsystems” on page 7-12 for an application
example.
Simulink restricts the kinds of connections you can make to the inputs of a
Merge block. In particular, it permits only connections that establish a
one-to-one mapping from the outputs of nonvirtual blocks to the inputs of a
Merge block. For example, you can use a Go To/From block pair to connect the
scalar or vector output of a nonvirtual block in one part of a diagram to the
input of a Merge block in another part of the diagram. The following diagram
illustrates valid ways to connect nonvirtual blocks to a Merge block.
8-126
Merge
You cannot use a Merge block to connect multiple nonvirtual outputs to a single
input on a Merge block. The following diagram illustrates invalid ways to
connect nonvirtual blocks to a Merge block.
Not a data input
Maps two outputs to one input
Not an input from a block
Connects two ports to one Merge
Simulink checks for invalid connections in a block diagram at the start of a
simulation. If it detects an invalid connection, it stops and displays an error
message.
Data Type
Support
A Merge block accepts signals of any numeric type (complex or real) and data
type, including user-defined types. If the input type is user-defined, the initial
condition must be 0.
Parameters
and Dialog Box
Number of inputs
The number of input ports to merge. Ports may be scalar or vector.
8-127
Merge
Initial output
Initial value of output. If unspecified, the initial output equals the initial
output, if any, of one of the driving blocks.
Characteristics
8-128
Sample Time
Inherited from the driving block
Vectorized
Yes
Scalar Expansion
No
MinMax
Purpose
8MinMax
Library
Math
Description
The MinMax block outputs either the minimum or the maximum element or
elements of the input(s). You can choose which function to apply by selecting
one of the choices from the Function parameter list.
Output the minimum or maximum input value.
If the block has one input port, the block outputs a scalar that is the minimum
or maximum element of the input vector.
If the block has more than one input port, the block performs an
element-by-element comparison of the input vectors. Each element of the block
output vector is the result of the comparison of the elements of the input
vectors.
Data Type
Support
A MinMax block accepts and outputs real-valued signals of type double.
Parameters
and Dialog Box
Function
The function (min or max) to apply to the input.
Number of input ports
The number of inputs to the block.
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from the driving block
Scalar Expansion
Of the inputs
8-129
MinMax
8-130
Vectorized
Yes
Zero Crossing
Yes, to detect minimum and maximum values
Model Info
Purpose
8Model Info
Library
Signals & Systems
Description
The Model Info block displays revision control information about a model as an
annotation block in the model’s block diagram. The following diagram
illustrates use of a Model Info block to display information about the vdp model.
Display revision control information in a model.
A Model Info block can show revision control information embedded in the
model itself and/or information maintained by an external revision control or
configuration management system. A Model Info block’s dialog allows you to
specify the content and format of the text displayed by the block.
Data Type
Support
Not applicable.
8-131
Model Info
Dialog Box
The Model Info block dialog box includes the following fields:
Editable text. Enter the text to be displayed by the Model Info block in this field.
You can freely embed variables of the form %<propname>, where propname is
the name of a model or revision control system property, in the entered text.
The value of the property replaces the variable in the displayed text. For
example, suppose that the current version of the model is 1.1. Then the entered
text
Version %<ModelVersion>
appears as
Version 1.1
in the displayed text. The model and revision control system properties that
you can reference in this way are listed in the Model properties and
Configuration manager properties fields.
Model properties. Lists revision control properties stored in the model. Selecting
a property and then selecting the adjacent arrow button enters the
corresponding variable in the Editable text field. For example, selecting
CreatedBy enters %<CreatedBy%> in the Editable text field. See “Version
8-132
Model Info
Control Properties” on page 3–77 for a description of the usage of the properties
specified in this field.
RCS properties. This field appears only if you previously specified an external
configuration manager for this model (see “Configuration manager” on page 3–
73). The title of the field changes to reflect the selected configuration manager
(for example, RCS Properties). The field lists version control information
maintained by the external system that you can include in the Model Info
block. To include an item from the list, select it and then click the adjacent
arrow button.
Note The selected item does not appear in the Model Info block until you
check the model in or out of the repository maintained by the configuration
manager and you have closed and reopened the model.
8-133
Multiport Switch
Purpose
8Multiport Switch
Library
Nonlinear
Description
The Multiport Switch block chooses between a number of inputs.
Choose between block inputs.
The first (top) input is the control input and the other inputs are data inputs.
The value of the control input determines which data input to pass through to
the output port.
If the control input is not an integer value, the Multiport Switch truncates the
value to the nearest integer and issues a warning. If the (truncated) control
input is less than one or greater than the number of input ports, the switch
issues an out-of-bounds error. Otherwise, the switch passes the data input that
corresponds to the (truncated) control input. The following table summarizes
the Multiport Switch’s behavior.
(Truncated) Control Input
Passes This Data Input
Less than 1
Out of bounds error
1
First input
2
Second input
etc.
etc.
Greater than the number of
data inputs
Out of bounds error
Data inputs can be scalar or vector. The control input can be a scalar or a
vector. The block output is determined by these rules:
• If inputs are scalar, the output is a scalar.
• If the block has more than one data input, at least one of which is a vector,
the output is a vector. Any scalar inputs are expanded to vectors.
• If the block has only one data input and that input is a vector, the block
output is the element of the vector that corresponds to the truncated value of
the control input.
8-134
Multiport Switch
Data Type
Support
The control input of a Multiport Switch block accepts a real-valued signal of
any built-in data type except boolean. The data inputs accept real- or
complex-valued inputs of any type. All data inputs must be of the same data
and numeric type. The signal type of the block’s output is the same as that of
its data inputs.
Parameters
and Dialog Box
Number of inputs
The number of data inputs to the block.
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from driving block(s)
Scalar Expansion
Yes
Vectorized
Yes
Zero Crossing
No
8-135
Mux
Purpose
8Mux
Library
Signals & Systems
Description
The Mux block combines several input lines into one vector line. Each input
line can carry a scalar or vector signal. The output of a Mux block is a vector.
Combine several input lines into a vector line.
You can assign names to the input signals by:
• Labeling the lines that represent the incoming signals
• Entering a comma-separated list of signal names as the value of the Mux
block’s Number of inputs parameter; for example, if you enter
position,velocity in this parameter, the Mux block will have two inputs,
named position and velocity.
The default name for an unlabeled line or unconnected port is signalN, where
N is the input port number. This option is useful when you are defining a signal
bus from which individual signals can be extracted by using the Bus Selector
block.
If you define the Number of inputs parameter as a scalar, Simulink
determines the input widths by checking the output ports of the blocks feeding
the Mux block. If any input is a vector, all of its elements are combined by the
block.
If it is necessary to define input widths explicitly, you can specify them as a
vector. Include elements with -1 values for those inputs whose widths are to be
determined dynamically (during the simulation). If an input signal width does
not match the expected width, Simulink displays an error message.
For example, [4 1 2] indicates three inputs forming a seven-element output
vector: the first four output elements are from the first input, the fifth element
comes from the second input, and the sixth and seventh elements come from
the third input. If it is not important that these inputs have fixed widths, you
could specify the Number of inputs as 3.
To specify three inputs where the first input vector must have four elements,
you could specify [4 –1 –1]. Simulink determines the widths of the second and
third inputs and sizes the output width accordingly.
8-136
Mux
Simulink draws the Mux block with the specified number of inputs. If you
change the number of input ports, Simulink adds or removes them from the
bottom of the block icon.
Using a Variable to Provide the Number of Inputs Parameter
When you specify the Number of inputs parameter as a variable, Simulink
issues an error message if the variable is undefined in the workspace.
Note Simulink hides the name of a Mux block when you copy it from the
Simulink block library to a model.
Data Type
Support
A Mux block accepts real or complex signals of any data type, including
mixed-type vectors.
Parameters
and Dialog Box
Number of inputs
The number and width of inputs. The width of the output line equals the
sum of the widths of the input lines. You can enter a comma-separated list
of signal names for this parameter field when the Display option
parameter is names.
8-137
Mux
Display option
The appearance of the block icon in your model.
8-138
Display Option
Appearance of Block in Model
none
Mux appears inside block icon
names
Displays signal names next to each port
bar
Displays the block icon in a solid foreground color
Outport
Purpose
8Outport
Library
Signals & Systems
Description
Outports are the links from a system to a destination outside the system.
Create an output port for a subsystem or an external output.
Simulink assigns Outport block port numbers according to these rules:
• It automatically numbers the Outport blocks within a top-level system or
subsystem sequentially, starting with 1.
• If you add an Outport block, it is assigned the next available number.
• If you delete an Outport block, other port numbers are automatically
renumbered to ensure that the Outport blocks are in sequence and that no
numbers are omitted.
• If you copy an Outport block into a system, its port number is not
renumbered unless its current number conflicts with an Outport block
already in the system. If the copied Outport block port number is not in
sequence, you must renumber the block or you will get an error message
when you run the simulation or update the block diagram.
Outport Blocks in a Subsystem
Outport blocks in a subsystem represent outputs from the subsystem. A signal
arriving at an Outport block in a subsystem flows out of the associated output
port on that Subsystem block. The Outport block associated with an output
port on a Subsystem block is the block whose Port number parameter matches
the relative position of the output port on the Subsystem block. For example,
the Outport block whose Port number parameter is 1 sends its signal to the
block connected to the top-most output port on the Subsystem block.
If you renumber the Port number of an Outport block, the block becomes
connected to a different output port, although the block continues to send the
signal to the same block outside the subsystem.
When you create a subsystem by selecting existing blocks, if more than one
Outport block is included in the grouped blocks, Simulink automatically
renumbers the ports on the blocks.
8-139
Outport
The Outport block name appears in the Subsystem block icon as a port label.
To suppress display of the label, select the Outport block and choose Hide
Name from the Format menu.
Outport Blocks in a Conditionally Executed Subsystem
When an Outport block is in a triggered and/or enabled subsystem, you can
specify what happens to its output when the subsystem is disabled: it can be
reset to an initial value or held at its most recent value. The Output when
disabled popup menu provides these options. The Initial output parameter is
the value of the output before the subsystem executes and, if the reset option
is chosen, while the subsystem is disabled.
Outport Blocks in a Top-Level System
Outport blocks in a top-level system have two uses: to supply external outputs
to the workspace, which you can do by using either the Simulation
Parameters dialog box or the sim command, and to provide a means for
analysis functions to obtain output from the system.
• To supply external outputs to the workspace, using the Simulation
Parameters dialog box (see “Saving Output to the Workspace” on page 4-20)
or the sim command (see sim on page 4-30). For example, if a system has
more than one Outport block, the following command
[t,x,y] = sim(...);
writes y as a matrix, with each column containing data for a different
Outport block. The column order matches the order of the port numbers for
the Outport blocks.
If you specify more than one variable name after the second (state)
argument, data from each Outport block is written to a different variable.
For example, if the system has two Outport blocks, to save data from Outport
block 1 to speed and the data from Outport block 2 to dist, you could specify
this command:
[t,x,speed,dist] = sim(...);
• To provide a means for the linmod and trim analysis functions to obtain
output from the system. For more information about using Outport blocks
with analysis commands, see Chapter 5.
8-140
Outport
Numeric and
Data Type
Support
An Outport block accepts complex or real signals of any MATLAB data type as
input. The numeric and data type of the block’s output is the same as that of
its input. The elements of a signal vector connected to an Outport block can be
of differing numeric and data types except in the following circumstance. If the
outport is in a conditionally executed subsystem and the initial output is not
specified, all elements of an input vector must be of the same numeric and data
type.
Simulink’s data type conversion rules apply to an outport’s Initial output
parameter. If the initial value is in the range of the block’s output data type,
Simulink converts the initial value to the output data type. If the conversion
entails a loss of precision, Simulink issues a warning message. If the specified
initial output is out of range of the output data type, Simulink halts the
simulation and signals an error. Note that the block’s output data type is the
data type of the signal connected to its input.
Parameters
and Dialog Box
Port number
The port number of the Outport block.
Output when disabled
For conditionally executed subsystems, what happens to the block output
when the system is disabled.
Initial output
For conditionally executed subsystems, the block output before the
subsystem executes and while it is disabled.
8-141
Outport
Characteristics
8-142
Sample Time
Inherited from driving block
Vectorized
Yes
Product
Purpose
8Product
Library
Math
Description
The Product block multiplies or divides block inputs, depending on the value of
the Number of inputs parameter:
Generate the product or quotient of block inputs.
• If the value is a combination of * and / symbols, the number of block inputs
is equal to the number of symbols. The block icon shows the appropriate
symbol adjacent to each input port. The block output is the product of all
inputs marked * divided by all inputs marked /.
For example, this block icon is the result of entering */ as the parameter
value.
• If the value is a scalar greater than 1, the block multiplies all inputs. If any
input is a vector, the block output is an element-by-element product across
the inputs. If all inputs are scalars, the output is a scalar. For a block having
n inputs, if any input is a vector, each element of the output is generated as
y i = u1 i × u2 i × … × un i
• If the value is 1, the block output is the scalar product of the elements of the
input vector.
y = Πu i
This model represents using the Product block in this way. The solid line
input signal indicates that the input is a vector.
If necessary, Simulink resizes the block to show all input ports. If the number
of inputs is changed, ports are added or deleted from the bottom of the block.
Data Type
Support
The Product block accepts real- or complex-valued signals of any data type. All
input signals must be of the same data type. The output signal data type is the
same as the input’s.
8-143
Product
Parameters
and Dialog Box
Number of inputs
Either the number of inputs to the block or a combination of * and /
symbols. The default is 2.
Saturate on integer overflow
If selected, this option causes the output of the Product block to saturate on
integer overflow. In particular, if the output data type is an integer type,
the block output is the maximum value representable by the output type or
the computed output, whichever is smaller in the absolute sense. If the
option is not selected, Simulink takes the action specified by the Data
overflow event option on the Diagnostics page of the Simulation
Parameters dialog (see “The Diagnostics Page” on page 4–24).
Characteristics
8-144
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Yes
Vectorized
Yes
Zero Crossing
No
Probe
Purpose
8Probe
Library
Signals & Systems
Description
The Probe block outputs selected information about the signal on its input. The
block can output the input signal’s width, sample time, and/or a flag indicating
whether the input is a complex-valued signal. The block has one input port.
The number of output ports depends on the information that you select for
probing, that is, signal width, sample time, and/or complex signal flag. Each
probed value is output as a separate signal on a separate output port. The block
accepts real or complex-valued signals or vectors of any built-in data type. It
outputs signals of type double. During simulation, the block’s icon displays the
probed data.
Data Type
Support
A Probe block accepts and outputs signals of type double.
Probe a line for its width, sample time, and/or complex signal flag.
Parameters
and Dialog Box
Probe width
If checked, output width of probed line.
Probe sample time
If checked, output sample time of probed line.
Probe complex signal
If checked, output 1 if probed signal is complex; otherwise, 0.
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Yes
8-145
Pulse Generator
Vectorized
Yes
Zero Crossing
No
Purpose
8Pulse Generator
Library
Sources
Description
The Pulse Generator block generates a series of pulses at regular intervals.
Generate pulses at regular intervals.
Use the Pulse Generator block for continuous systems. To generate discrete
signals, use the Discrete Pulse Generator block (see Discrete Pulse
Generator on page 8-54).
Data Type
Support
A Pulse Generator block outputs signals of type double.
Parameters
and Dialog Box
Period
The pulse period in seconds. The default is 1 second.
Duty cycle
The duty cycle: the percentage of the pulse period that the signal is on. The
default is 50 percent.
Amplitude
The pulse amplitude. The default is 1.
8-146
Pulse Generator
Start time
The delay before the pulse is generated, in seconds. The default is 0
seconds.
Characteristics
Sample Time
Inherited
Scalar Expansion
Of parameters
Vectorized
Yes
Zero Crossing
No
8-147
Quantizer
Purpose
8Quantizer
Library
Nonlinear
Description
The Quantizer block passes its input signal through a stair-step function so
that many neighboring points on the input axis are mapped to one point on the
output axis. The effect is to quantize a smooth signal into a stair-step output.
The output is computed using the round-to-nearest method, which produces an
output that is symmetric about zero
Discretize input at a specified interval.
y = q * round(u/q)
where y is the output, u the input, and q the Quantization interval parameter.
Data Type
Support
A Quantizer block accepts and outputs signals of type double.
Parameters
and Dialog Box
Quantization interval
The interval around which the output is quantized. Permissible output
values for the Quantizer block are n*q, where n is an integer and q the
Quantization interval. The default is 0.5.
Characteristics
8-148
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Of parameter
Vectorized
Yes
Zero Crossing
No
Ramp
Purpose
8Ramp
Library
Sources
Description
The Ramp block generates a signal that starts at a specified time and value and
changes by a specified rate.
Data Type
Support
A Ramp block outputs signals of type double.
Generate constantly increasing or decreasing signal.
Parameters
and Dialog Box
Slope
The rate of change of the generated signal. The default is 1.
Start time
The time at which the signal begins to be generated. The default is 0.
Initial output
The initial value of the signal. The default is 0.
Characteristics
Sample Time
Inherited from driven block
Scalar Expansion
Yes
Vectorized
Yes
Zero Crossing
Yes
8-149
Random Number
Purpose
8Random Number
Library
Sources
Description
The Random Number block generates normally distributed random numbers.
The seed is reset to the specified value each time a simulation starts.
Generate normally distributed random numbers.
By default, the sequence produced has a mean of 0 and a variance of 1,
although you can vary these parameters. The sequence of numbers is
repeatable and can be produced by any Random Number block with the same
seed and parameters. To generate a vector of random numbers with the same
mean and variance, specify the Initial seed parameter as a vector.
To generate uniformly distributed random numbers, use the Uniform Random
Number block (see Uniform Random Number on page 8-212).
Avoid integrating a random signal because solvers are meant to integrate
relatively smooth signals. Instead, use the Band-Limited White Noise block.
Data Type
Support
A Random Number block accepts and outputs signals of type double.
Parameters
and Dialog Box
Mean
The mean of the random numbers. The default is 0.
Variance
The variance of the random numbers. The default is 1.
8-150
Random Number
Initial seed
The starting seed for the random number generator. The default is 0.
Sample time
The time interval between samples. The default is 0, causing the block to
have continuous sample time.
Characteristics
Sample Time
Continuous or discrete
Scalar Expansion
Of parameters
Vectorized
Yes
Zero Crossing
No
8-151
Rate Limiter
Purpose
8Rate Limiter
Library
Nonlinear
Description
The Rate Limiter block limits the first derivative of the signal passing through
it. The output changes no faster than the specified limit. The derivative is
calculated using this equation:
Limit the rate of change of a signal.
u( i ) – y( i – 1 )
rate = -----------------------------------t(i ) – t( i – 1)
u(i) and t(i) are the current block input and time, and y(i–1) and t(i–1) are the
output and time at the previous step. The output is determined by comparing
rate to the Rising slew rate and Falling slew rate parameters:
• If rate is greater than the Rising slew rate parameter (R), the output is
calculated as:
y ( i ) = ∆t ⋅ R + y ( i – 1 )
• If rate is less than the Falling slew rate parameter (F), the output is
calculated as:
y ( i ) = ∆t ⋅ F + y ( i – 1 )
• If rate is between the bounds of R and F, the change in output is equal to the
change in input:
y( i ) = u( i )
Data Type
Support
Parameters
and Dialog Box
8-152
A Rate Limiter block accepts and outputs signals of type double.
Rate Limiter
Rising slew rate
The limit of the derivative of an increasing input signal.
Falling slew rate
The limit of the derivative of a decreasing input signal.
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Of input and parameters
Vectorized
Yes
Zero Crossing
No
8-153
Real-Imag to Complex
Purpose
8Real-Imag to Complex
Library
Math
Description
The Real-Imag to Complex block converts real and/or imaginary inputs to a
complex-valued output signal. The inputs must be real-valued signals of type
double. The data type of the complex output signal is double.
Convert a magnitude and/or a phase angle signal to a complex signal.
The inputs may be both vectors of equal size, or one input may be a vector and
the other a scalar. If the block has a vector input, the output is a vector of
complex signals. The elements of a real input vector are mapped to real parts
of the corresponding complex output elements. An imaginary input vector is
similarly mapped to the imaginary parts of the complex output signals. If one
input is a scalar, it is mapped to the corresponding component (real or
imaginary) of all the complex output signals.
Data Type
Support
See description above.
Parameters
and Dialog Box
Input
Specifies the kind of input: a real input, an imaginary input, or both.
Real (Imag) part
If the input is a real-part signal, this parameter specifies the constant
imaginary part of the output signal. If the input is the imaginary part, this
parameter specifies the constant real part of the output signal. Note that
the title of this field changes to reflect its usage.
8-154
Real-Imag to Complex
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Of the input when the function requires two inputs
Vectorized
Yes
Zero Crossing
No
8-155
Relational Operator
Purpose
8Relational Operator
Library
Math
Description
The Relational Operator block performs a relational operation on its two inputs
and produces output according to the following table.
Perform the specified relational operation on the input.
Operator
Output
==
TRUE if the first input is equal to the second input
~=
TRUE if the first input is not equal to the second input
<
TRUE if the first input is less than the second input
<=
TRUE if the first input is less than or equal to the second
input
>=
TRUE if the first input is greater than or equal to the
second input
>
TRUE if the first input is greater than the second input
If the result is TRUE, the output is 1; if FALSE, it is 0. You can specify inputs
as scalars, vectors, or a combination of a scalar and a vector:
• For scalar inputs, the output is a scalar.
• For vector inputs, the output is a vector, where each element is the result of
an element-by-element comparison of the input vectors.
• For mixed scalar/vector inputs, the output is a vector, where each element is
the result of a comparison between the scalar and the corresponding vector
element.
The block icon displays the selected operator.
Data Type
Support
8-156
A Relational Operator block accepts real signals of any data type. It outputs a
signal of type boolean, unless boolean compatibility mode is enabled (see
“Enabling Strict Boolean Type Checking” on page 3-45), in which case the block
outputs a signal of type double.
Relational Operator
Parameters
and Dialog Box
Operator
The relational operator to be applied to the block inputs.
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Of inputs
Vectorized
Yes
Zero Crossing
Yes, to detect when the output changes
8-157
Relay
Purpose
8Relay
Library
Nonlinear
Description
The Relay block allows the output to switch between two specified values.
When the relay is on, it remains on until the input drops below the value of the
Switch off point parameter. When the relay is off, it remains off until the
input exceeds the value of the Switch on point parameter. The block accepts
one input and generates one output.
Switch output between two constants.
Specifying a Switch on point value greater than the Switch off point value
models hysteresis, whereas specifying equal values models a switch with a
threshold at that value. The Switch on point value must be greater than or
equal to the Switch off point.
Data Type
Support
A Relay block accepts and outputs real signals of type double.
Parameters
and Dialog Box
Switch on point
The on threshold for the relay. The default is eps.
Switch off point
The off threshold for the relay. The default is eps.
Output when on
The output when the relay is on. The default is 1.
8-158
Relay
Output when off
The output when the relay is off. The default is 0.
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Yes
Vectorized
Yes
Zero Crossing
Yes, to detect switch on and switch off points
8-159
Repeating Sequence
Purpose
8Repeating Sequence
Library
Sources
Description
The Repeating Sequence block allows you to specify an arbitrary signal to be
repeated regularly over time. When the simulation reaches the maximum time
value in the Time values vector, the signal is repeated.
Generate a repeatable arbitrary signal.
This block is implemented using the one-dimensional Look-Up Table block,
performing linear interpolation between points.
Data Type
Support
A Repeating Sequence block outputs real signals of type double.
Parameters
and Dialog Box
Time values
A vector of monotonically increasing time values. The default is [0 2].
Output values
A vector of output values. Each corresponds to the time value in the same
column. The default is [0 2].
Characteristics
8-160
Sample Time
Continuous
Scalar Expansion
No
Vectorized
No
Zero Crossing
No
Rounding Function
Purpose
8Rounding Function
Library
Math
Description
The Rounding Function block performs common mathematical rounding
functions.
Perform a rounding function.
You can select one of these functions from the Function list: floor, ceil,
round, and fix. The block output is the result of the function operating on the
input or inputs. The Rounding Function block accepts and outputs real- or
complex-valued signals of type double.
The name of the function appears on the block icon.
Use the Rounding Function block instead of the Fcn block when you want
vectorized output because the Fcn block can produce only scalar output.
Data Type
Support
A Rounding Function block accepts and outputs real signals of type double.
Parameters
and Dialog Box
Function
The rounding function.
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
N/A
Vectorized
Yes
Zero Crossing
No
8-161
Saturation
Purpose
8Saturation
Library
Nonlinear
Description
The Saturation block imposes upper and lower bounds on a signal. When the
input signal is within the range specified by the Lower limit and Upper limit
parameters, the input signal passes through unchanged. When the input
signal is outside these bounds, the signal is clipped to the upper or lower bound.
Limit the range of a signal.
When the parameters are set to the same value, the block outputs that value.
Data Type
Support
A Saturation block accepts and outputs real signals of type double.
Parameters
and Dialog Box
Upper limit
The upper bound on the input signal. While the signal is above this value,
the block output is set to this value.
Lower limit
The lower bound on the input signal. While the signal is below this value,
the block output is set to this value.
Characteristics
8-162
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Of parameters and input
Vectorized
Yes
Zero Crossing
Yes, to detect when the signal reaches a limit, and
when it leaves the limit
Scope
Purpose
8Scope
Library
Sinks
Description
The Scope block displays its input with respect to simulation time. The Scope
block can have multiple axes (one per port); all axes have a common time range
with independent y-axes. The Scope allows you to adjust the amount of time
and the range of input values displayed. You can move and resize the Scope
window and you can modify the Scope’s parameter values during the
simulation.
Display signals generated during a simulation.
When you start a simulation, Simulink does not open Scope windows, although
it does write data to connected Scopes. As a result, if you open a Scope after a
simulation, the Scope’s input signal or signals will be displayed.
If the signal is continuous, the Scope produces a point-to-point plot. If the signal
is discrete, the Scope produces a stairstep plot.
The Scope provides toolbar buttons that enable you to zoom in on displayed
data, display all the data input to the Scope, preserve axes settings from one
simulation to the next, limit data displayed, and save data to the workspace.
The toolbar buttons are labeled in this figure, which shows the Scope window
as it appears when you open a Scope block.
Zoom in both x and y directions.
Zoom in x direction.
Zoom in y direction.
Auto-scale.
Save axes settings.
Properties.
Print.
8-163
Scope
Displaying Vector Signals
When displaying a vector signal, the Scope uses different colors in this order:
yellow, magenta, cyan, red, green, and dark blue. When more than six signals
are displayed, the Scope cycles through the colors in the order listed above.
Y-Axis Limits
You set y-limits by right clicking on an axes and choosing Properties.... The
following dialog box appears.
Y-min
Enter the minimum value for the y-axis.
Y-max
Enter the maximum value for the y-axis.
Title
Enter the title of the plot. You can include a signal label in the title by
typing %<SignalLabel> as part of the title string (%<SignalLabel> is
replaced by the signal label).
8-164
Scope
Time Offset
This figure shows the Scope block displaying the output of the vdp model. The
simulation was run for 40 seconds. Note that this scope shows the final 20
seconds of the simulation. The Time offset field displays the time
corresponding to 0 on the horizontal axis. Thus, you have to add the offset to
the fixed time range values on the x-axis to get the actual time.
8-165
Scope
Auto-Scaling the Scope Axes
This figure shows the same output after pressing the Auto-scale toolbar
button, which automatically scales both axes to display all stored simulation
data. In this case, the y-axis was not scaled because it was already set to the
appropriate limits.
The Auto-scale button
If you click on the Auto-scale button while the simulation is running, the axes
are auto-scaled based on the data displayed on the current screen, and the
auto-scale limits are saved as the defaults. This enables you to use the same
limits for another simulation.
Zooming
You can zoom in on data in both the x and y directions at the same time, or in
either direction separately. The zoom feature is not active while the simulation
is running.
To zoom in on data in both directions at the same time, make sure the left-most
Zoom toolbar button is selected. Then, define the zoom region using a bounding
box. When you release the mouse button, the Scope displays the data in that
area. You can also click on a point in the area you want to zoom in on.
If the scope has multiple y-axes, and you zoom in on one set of x-y axes, the
x-limits on all sets of x-y axes are changed so that they match, since all x-y axes
must share the same time base (x-axis).
8-166
Scope
This figure shows a region of the displayed data enclosed within a bounding
box.
Zoom in both directions
This figure shows the zoomed region, which appears after you release the
mouse button.
To zoom in on data in just the x direction, click on the middle Zoom toolbar
button. Define the zoom region by positioning the pointer at one end of the
region, pressing and holding down the mouse button, then moving the pointer
8-167
Scope
to the other end of the region. This figure shows the Scope after defining the
zoom region but before releasing the mouse button.
Zoom in x direction
When you release the mouse button, the Scope displays the magnified region.
You can also click on a point in the area you want to zoom in on.
Zooming in the y direction works the same way except that you press the
right-most Zoom toolbar button before defining the zoom region. Again, you
can also click on a point in the area you want to zoom in on.
Saving the Axes Settings
The Save axes settings toolbar button enables you to store the current x- and
y-axis settings so you can apply them to the next simulation.
the Save axes settings button
You might want to do this after zooming in on a region of the displayed data so
you can see the same region in another simulation. The time range is inferred
from the current x-axis limits.
8-168
Scope
Scope Properties
You can change axes limits, set the number of axes, time range, tick labels,
sampling parameters, and saving options by choosing the Properties toolbar
button.
the Properties button
When you click on the Properties button, this dialog box appears.
The dialog box has two tabs: General and Data history.
General Parameters
You can set the axes parameters, time range, and tick labels in the General
tab. You can also choose the floating scope option with this tab.
Number of axes
Set the number of y-axes in this data field. With the exception of the
floating scope, there is no limit to the number of axes the Scope block can
contain. All axes share the same time base (x-axis), but have independent
y-axes. Note that the number of axes is equal to the number of input ports.
Time range
Change the x-axis limits by entering a number or auto in the Time range
field. Entering a number of seconds causes each screen to display the
amount of data that corresponds to that number of seconds. Enter auto to
set the x-axis to the duration of the simulation. Do not enter variable names
in these fields.
8-169
Scope
Tick labels
You can choose to have tick labels on all axes, on one axis, or on the bottom
axis only in the Tick labels drop box.
Floating scope
You can check the Floating scope check box if you want to have a floating
scope. A floating Scope is a Scope block that can display the signals carried
on one or more lines.
To add a floating Scope to a model, copy a Scope block into the model
window, then open the block. Select the Properties button on the block’s
toolbar. Then, select the General tab and select the Floating scope check
box.
To use a floating Scope during a simulation, first open the block. To display
the signals carried on a line, select the line. Hold down the Shift key while
clicking on another line to select multiple lines. It may be necessary to
press the Auto-scale data button on the Scope’s toolbar to find the signal
and adjust the axes to the signal values. Note that floating scopes cannot
have multiple axes.
A model can contain more than one floating Scope, although generally, it is
not useful to have more than one floating Scope in a window because they
will display the same signals.
If you plan to use a floating scope during a simulation, you should disable
buffer reuse. See “Disable optimized I/O storage” on page 4-25 for more
information.
Sampling
To specify a decimation factor, enter a number in the data field to the right
of the Decimation choice. To display data at a sampling interval, select the
Sample time choice and enter a number in the data field.
8-170
Scope
Controlling Data Collection and Display
You can control the amount of data that the Scope stores and displays by
setting fields on the Data History tab.
You can also choose to save data to the workspace in this tab. You apply the
current parameters and options by clicking on the Apply or OK button. The
values that appear in these fields are the values that will be used in the next
simulation.
Limit rows to last
You can limit the number of rows by checking the Limit rows to last check
box and entering a value in its data field. The Scope relies on its data
history for zooming and auto-scaling operations. If the number of rows is
limited to 1,000 and the simulation generates 2,000 rows, only the last
1,000 are available for regenerating the display.
Save data to workspace
You can automatically save the data collected by the Scope at the end of the
simulation by checking the Save data to workspace check box. If you
check this option, then the Variable name and Format fields become
active.
Variable name
Enter a variable name in the Variable name field. The specified name
must be unique among all data logging variables being used in the model.
Other data logging variables are defined on other Scope blocks, To
Workspace blocks, and simulation return variables such as time, states,
and outputs. Being able to save Scope data to the workspace means that it
8-171
Scope
is not necessary to send the same data stream to both a Scope block and a
To Workspace block.
Format
Data can be saved in one of three formats: Matrix, Structure, or Structure
with time. Use Matrix only for a Scope with one axes. For Scopes with
more than one axes, use Structure if you do not want to store time data
and use Structure with time if you want to store time data. See Data
Logging.
Printing the Contents of a Scope Window
To print the contents of a Scope window, open the Scope Properties dialog by
clicking on the Print icon, the right-most icon on the Scope toolbar.
the Print icon
Data Type
Support
A Scope block accepts real signals, including homogenous vectors, of any type.
Characteristics
Sample Time
Inherited from driving block or settable
States
0
8-172
Selector
Purpose
8Selector
Library
Signals & Systems
Description
The Selector block generates as output selective elements of the input vector.
Select input elements.
The Elements parameter defines the order of the input vector elements in the
output vector. The parameter must be specified as a vector unless only one
element is being selected. For example, this model shows the Selector block icon
and the output for an input vector of [2 4 6 8 10] and an Elements parameter
value of [5 1 3].
The block icon displays the ordering of input vector elements graphically. If the
block is not large enough, it displays the block name.
The Selector block accepts signals of any signal and data type, including
mixed-type signal vectors. The elements of the output vector have the same
type as the corresponding selected input elements.
Data Type
Support
A Selector block accepts and outputs signals of any numeric type (real or
complex) and data type.
Parameters
and Dialog Box
Elements
The order that the input elements are to appear in the output vector.
8-173
Selector
Input port width
The number of elements in the input vector.
Characteristics
8-174
Sample Time
Inherited from driving block
Vectorized
Yes
S-Function
Purpose
8S-Function
Library
Functions & Tables
Description
The S-Function block provides access to S-functions from a block diagram. The
S-function named as the S-function name parameter can be an M-file or
MEX-file written as an S-function.
Access an S-function.
The S-Function block allows additional parameters to be passed directly to the
named S-function. The function parameters can be specified as MATLAB
expressions or as variables separated by commas. For example,
A, B, C, D, [eye(2,2);zeros(2,2)]
Note that although individual parameters can be enclosed in square brackets,
the list of parameters must not be enclosed in square brackets.
The S-Function block displays the name of the specified S-function and is
always drawn with one input port and one output port, regardless of the
number of inputs and outputs of the contained subsystem.
Vector lines are used when the S-function contains more than one input or
output. The input vector width must match the number of inputs contained in
the S-function. The block directs the first element of the input vector to the first
input of the S-function, the second element to the second input, and so on.
Likewise, the output vector width must match the number of S-function
outputs.
Data Type
Support
Depends on the implementation of the S-Function block.
Parameters
and Dialog Box
8-175
S-Function
S-function name
The S-function name.
S-function parameters
Additional S-function parameters.
Characteristics
8-176
Direct Feedthrough
Depends on contents of S-function
Sample Time
Depends on contents of S-function
Scalar Expansion
Depends on contents of S-function
Vectorized
Depends on contents of S-function
Zero Crossing
No
Sign
Purpose
8Sign
Library
Math
Description
The Sign block indicates the sign of the input:
Indicate the sign of the input.
• The output is 1 when the input is greater than zero.
• The output is 0 when the input is equal to zero.
• The output is -1 when the input is less than zero.
Data Type
Support
A Sign block accepts and outputs real signals of type double.
Dialog Box
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
N/A
Vectorized
Yes
Zero Crossing
Yes, to detect when the input crosses through zero
8-177
Signal Generator
Purpose
8Signal Generator
Library
Sources
Description
The Signal Generator block can produce one of three different waveforms: sine
wave, square wave, and sawtooth wave. The signal parameters can be
expressed in Hertz (the default) or radians per second. This figure shows each
signal displayed on a Scope using default parameter values.
Generate various waveforms.
Sine Wave
Square Wave
Sawtooth Wave
A negative Amplitude parameter value causes a 180-degree phase shift. You
can generate a phase-shifted wave at other than 180 degrees in a variety of
ways, including inputting a Clock block signal to a MATLAB Fcn block and
writing the equation for the particular wave.
8-178
Signal Generator
You can vary the output settings of the Signal Generator block while a
simulation is in progress. This is useful to determine quickly the response of a
system to different types of inputs.
Data Type
Support
A Signal Generator block outputs real signals of type double.
Parameters
and Dialog Box
Wave form
The wave form: a sine wave, square wave, or sawtooth wave. The default is
a sine wave.
Amplitude
The signal amplitude. The default is 1.
Frequency
The signal frequency. The default is 1.
Units
The signal units, Hertz or radians/sec. The default is Hertz.
Characteristics
Sample Time
Inherited
Scalar Expansion
Of parameters
Vectorized
Yes
Zero Crossing
No
8-179
Sine Wave
Purpose
8Sine Wave
Library
Sources
Description
The Sine Wave block provides a sinusoid. The block can operate in either
continuous or discrete mode.
Generate a sine wave.
The output of the Sine Wave block is determined by:
y = Amplitude × sin ( frequency × time + phase )
The value of the Sample time parameter determines whether the block
operates in continuous mode or discrete mode:
• 0 (the default) causes the block to operate in continuous mode.
• >0 causes the block to operate in discrete mode.
• –1 causes the block to operate in the same mode as the block receiving the
signal.
Using the Sine Wave Block in Discrete Mode
A Sample time parameter value greater than zero causes the block to behave
as if it were driving a Zero-Order Hold block whose sample time is set to that
value.
Using the Sine Wave block in this way allows you to build models with sine
wave sources that are purely discrete, rather than models that are hybrid
continuous/discrete systems. Hybrid systems are inherently more complex and,
as a result, take longer to simulate.
The Sine Wave block in discrete mode uses an incremental algorithm rather
than one based on absolute time. As a result, the block can be useful in models
intended to run for an indefinite length of time, such as in vibration or fatigue
testing.
The incremental algorithm computes the sine based on the value computed at
the previous sample time. This method makes use of the following identities:
sin ( t + ∆t ) = sin ( t ) cos ( ∆t ) + sin ( ∆t ) cos ( t )
cos ( t + ∆t ) = cos ( t ) cos ( ∆t ) – sin ( t ) sin ( ∆t )
8-180
Sine Wave
These identities can be written in matrix form.
sin ( t + ∆t )
cos ( ∆t ) sin ( ∆t ) sin ( t )
=
cos ( t + ∆t )
– sin ( ∆t ) cos ( ∆t ) cos ( t )
Since ∆t is constant, the following expression is a constant.
cos ( ∆t ) sin ( ∆t )
– sin ( ∆t ) cos ( ∆t )
Therefore the problem becomes one of a matrix multiply of the value of sin(t) by
a constant matrix to obtain sin(t+∆t). This algorithm may also be faster on
computers that do not have hardware floating-point support for trigonometric
functions.
Using the Sine Wave Block in Continuous Mode
A Sample time parameter value of zero causes the block to behave in
continuous mode. When operating in continuous mode, the Sine Wave block can
become inaccurate due to loss of precision as time becomes very large.
Data Type
Support
A Sine Wave block accepts and outputs real signals of type double.
Parameters
and Dialog Box
Amplitude
The amplitude of the signal. The default is 1.
8-181
Sine Wave
Frequency
The frequency, in radians/second. The default is 1 rad/sec.
Phase
The phase shift, in radians. The default is 0 radians.
Sample time
The sample period. The default is 0.
Characteristics
8-182
Sample Time
Continuous, discrete, or inherited
Scalar Expansion
Of parameters
Vectorized
Yes
Zero Crossing
No
Slider Gain
Purpose
8Slider Gain
Library
Math
Description
The Slider Gain block allows you to vary a scalar gain during a simulation
using a slider. The block accepts one input and generates one output.
Data Type
Support
Data type support for the Slider Gain block is the same as that for the Gain
block (see Gain on page 8-89).
Vary a scalar gain using a slider.
Dialog Box
Low
The lower limit of the slider range. The default is 0.
High
The upper limit of the slider range. The default is 2.
The edit fields indicate (from left to right) the lower limit, the current value,
and the upper limit. You can change the gain in two ways: by manipulating the
slider, or by entering a new value in the current value field. You can change the
range of gain values by changing the lower and upper limits. Close the dialog
box by clicking on the Close button.
If you click on the slider’s left or right arrow, the current value changes by
about 1% of the slider’s range. If you click on the rectangular area to either side
of the slider’s indicator, the current value changes by about 10% of the slider’s
range.
To apply a vector gain to the block input, consider using the Gain block,
described on page Gain on page 8-89. To apply a matrix gain, use the Matrix
Gain block, described on Matrix Gain on page 8-123.
8-183
Slider Gain
Characteristics
8-184
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Of the gain
States
0
Vectorized
Yes
Zero Crossing
No
State-Space
Purpose
8State-Space
Library
Continuous
Description
The State-Space block implements a system whose behavior is defined by:
Implement a linear state-space system.
·
x = Ax + Bu
y = Cx + Du
where x is the state vector, u is the input vector, and y is the output vector. The
matrix coefficients must have these characteristics, as illustrated in the
diagram below:
• A must be an n-by-n matrix, where n is the number of states.
• B must be an n-by-m matrix, where m is the number of inputs.
• C must be an r-by-n matrix, where r is the number of outputs.
• D must be an r-by-m matrix.
n
m
n
A
B
r
C
D
The block accepts one input and generates one output. The input vector width
is determined by the number of columns in the B and D matrices. The output
vector width is determined by the number of rows in the C and D matrices.
Simulink converts a matrix containing zeros to a sparse matrix for efficient
multiplication.
Data Type
Support
A State-Space block accepts and outputs real signals of type double.
8-185
State-Space
Parameters
and Dialog Box
A, B, C, D
The matrix coefficients.
Initial conditions
The initial state vector.
Characteristics
8-186
Direct Feedthrough
Only if D ≠ 0
Sample Time
Continuous
Scalar Expansion
Of the initial conditions
States
Depends on the size of A
Vectorized
Yes
Zero Crossing
No
Step
Purpose
8Step
Library
Sources
Description
The Step block provides a step between two definable levels at a specified time.
If the simulation time is less than the Step time parameter value, the block’s
output is the Initial value parameter value. For simulation time greater than
or equal to the Step time, the output is the Final value parameter value.
Generate a step function.
The Step block generates a scalar or vector output, depending on the length of
the parameters.
Data Type
Support
A Step block outputs real signals of type double.
Parameters
and Dialog Box
Step time
The time, in seconds, when the output jumps from the Initial value
parameter to the Final value parameter. The default is 1 second.
Initial value
The block output until the simulation time reaches the Step time
parameter. The default is 0.
Final value
The block output when the simulation time reaches and exceeds the Step
time parameter. The default is 1.
8-187
Step
Sample time
Sample rate of step.
Characteristics
8-188
Sample Time
Inherited from driven block
Scalar Expansion
Of parameters
Vectorized
Yes
Zero Crossing
Yes, to detect step times
Stop Simulation
Purpose
8Stop Simulation
Library
Sinks
Description
The Stop Simulation block stops the simulation when the input is nonzero.
Stop the simulation when the input is nonzero.
The simulation completes the current time step before terminating. If the block
input is a vector, any nonzero vector element causes the simulation to stop.
You can use this block in conjunction with the Relational Operator block to
control when the simulation stops. For example, this model stops the
simulation when the input signal reaches 10.
Data Type
Support
A Stop Simulation block accepts real signals of type double.
Dialog Box
Characteristics
Sample Time
Inherited from driving block
Vectorized
Yes
8-189
Subsystem
Purpose
8Subsystem
Library
Signals & Systems
Description
A Subsystem block represents a system within another system. You create a
subsystem in these ways:
Represent a system within another system.
• Copy the Subsystem block from the Connections library into your model. You
can then add blocks to the subsystem by opening the Subsystem block and
copying blocks into its window.
• Select the blocks and lines that are to make up the subsystem using a
bounding box, then choose Create Subsystem from the Edit menu. Simulink
replaces the blocks with a Subsystem block. When you open the block, the
window displays the blocks you selected, adding Inport and Outport blocks
to reflect signals entering and leaving the subsystem.
The number of input ports drawn on the Subsystem block’s icon corresponds to
the number of Inport blocks in the subsystem. Similarly, the number of output
ports drawn on the block corresponds to the number of Outport blocks in the
subsystem. If Inport and Outport block names are not hidden, they appear as
port labels on the Subsystem block.
For more information about subsystems, see “Creating Subsystems” in
Chapter 3.
Data Type
Support
See Inport on page 8-99 and Outport on page 8-139.
Dialog Box
None
Characteristics
Sample Time
Depends on the blocks in the subsystem
Vectorized
Depends on the blocks in the subsystem
Zero Crossing
Yes, for enable and trigger ports if present
8-190
Sum
Purpose
8Sum
Library
Math
Description
The Sum block adds scalar and/or vector inputs, or elements of a single vector
input, depending on the number of block inputs:
Generate the sum of inputs.
• If the block has more than one input, the block output is an
element-by-element sum across the inputs. If all inputs are scalars, the
output is a scalar. For a block having n inputs, if any input is a vector, each
element of the output is generated as
: y i = u1 i + u2 i + … + un i
This model represents using the Sum block in this way. The broken lines
indicate that each signal can be a scalar or vector. The output is a scalar only
if all inputs are scalars.
• If the block has one vector input, the block output is the scalar sum of the
elements of the input:
y = Σu i
This model represents using the Sum block in this way. The solid line input
signal indicates that the input is a vector.
Σ
Note Simulink hides the name of a Sum block when you copy it from the
Simulink block library to a model.
Data Type
Support
The Sum block accepts real- or complex-valued signals of any data type. All the
inputs must be of the same data type. The output data type is the same as the
input data type.
8-191
Sum
Parameters
and Dialog Box
Icon shape
You can choose a circular or rectangular shape for the Sum block in the
Icon shape drop box. If the Sum block has multiple inputs, it may be more
convenient to have a circular shape than a rectangular shape.
List of signs
The List of signs parameter can have a constant or a combination of +, -,
and | symbols. Specifying a constant causes Simulink to redraw the block
with that number of ports, all with positive polarity. A combination of plus
and minus signs specifies the polarity of each port, where the number of
ports equals the number of symbols used.
The Sum block draws plus and minus signs beside the appropriate ports
and redraws its ports to match the number of signs specified in the List of
signs parameter. If the number of signs is changed, ports are added or
deleted from the icon. If necessary, Simulink resizes the block to show all
input ports. You can also manipulate the position of the input ports by
inserting spacers (|) between the signs in the List of signs parameter. The
spacers create extra space between the ports. For example, ++|-- will
create an extra space between the second + port and the first - port:
Saturate on integer overflow
If selected, this option causes the output of the Sum block to saturate on
integer overflow. In particular, if the output data type is an integer type,
the block output is the maximum value representable by the output type or
the computed output, whichever is smaller in the absolute sense. If the
option is not selected, Simulink takes the action specified by Data
8-192
Sum
overflow event option on the Diagnostics page of the Simulation
Parameters dialog (see “The Diagnostics Page” on page 4–24).
Characteristics
Direct Feedthrough
Yes
Sample Time
Inherited from driving blocks
Scalar Expansion
Yes
States
0
Vectorized
Yes
Zero Crossing
No
8-193
Switch
Purpose
8Switch
Library
Nonlinear
Description
The Switch block propagates one of two inputs to its output depending on the
value of a third input, called the control input. If the signal on the control
(second) input is greater than or equal to the Threshold parameter, the block
propagates the first input; otherwise, it propagates the third input. This figure
shows the use of the block ports.
Switch between two inputs.
To drive the switch with a logic input (i.e., 0 or 1), set the threshold to 0.5.
Data Type
Support
A Switch block accepts real- or complex-valued signals of any data type as
switched inputs (inputs 1 and 3). Both switched inputs must be of the same
type. The block output signal has the data type of the selected input. The data
type of the threshhold input must be bool or double.
Parameters
and Dialog Box
Threshold
The value of the control (the second input) at which the switch flips to its
other state. You can specify this parameter as either a scalar or a vector
equal in width to the input vectors.
Characteristics
8-194
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Yes
Switch
Vectorized
Yes
Zero Crossing
Yes, to detect when the switch condition occurs
8-195
Terminator
Purpose
8Terminator
Library
Signals & Systems
Description
The Terminator block can be used to cap blocks whose output ports are not
connected to other blocks. If you run a simulation with blocks having
unconnected output ports, Simulink issues warning messages. Using
Terminator blocks to cap those blocks avoids warning messages.
Data Type
Support
A Terminator block accepts signals of any numeric type or data type.
Terminate an unconnected output port.
Parameters
and Dialog Box
Characteristics
8-196
Sample Time
Inherited from driving block
Vectorized
Yes
To File
Purpose
8To File
Library
Sinks
Description
The To File block writes its input to a matrix in a MAT-file. The block writes
one column for each time step: the first row is the simulation time; the
remainder of the column is the input data, one data point for each element in
the input vector. The matrix has this form:
Write data to a file.
t1
t2
…t final
u1 1 u1 2 …u1 final
…
un 1 un 2 …un final
The From File block can use data written by a To File block without any
modifications. However, the form of the matrix expected by the From
Workspace block is the transpose of the data written by the To File block.
The block writes the data as well as the simulation time after the simulation is
completed. The block icon shows the name of the specified output file.
The amount of data written and the time steps at which the data is written are
determined by block parameters:
• The Decimation parameter allows you to write data at every nth sample,
where n is the decimation factor. The default decimation, 1, writes data at
every time step.
• The Sample time parameter allows you to specify a sampling interval at
which to collect points. This parameter is useful when using a variable-step
solver where the interval between time steps may not be the same. The
default value of -1 causes the block to inherit the sample time from the
driving block when determining which points to write.
If the file exists at the time the simulation starts, the block overwrites its
contents.
Data Type
Support
A To File block accepts real signals of type double.
8-197
To File
Parameters
and Dialog Box
Filename
The name of the MAT-file that holds the matrix.
Variable name
The name of the matrix contained in the named file.
Decimation
A decimation factor. The default value is 1.
Sample time
The sample time at which to collect points.
Characteristics
8-198
Sample Time
Inherited from driving block
Vectorized
Yes
To Workspace
Purpose
8To Workspace
Library
Sinks
Description
The To Workspace block writes its input to the workspace. The block writes its
output to a matrix or structure that has the name specified by the block’s
Variable name parameter. The Save format parameter determines the output
format:
Write data to the workspace.
Matrix
The matrix has this form:
u1 1
u2 1
…
un 1
u1 2
u2 2
…
un 2
…
u1 final u2 final … un final
The amount of data written and the time steps at which the data is written are
determined by block parameters:
• The Maximum number of rows parameter indicates how many data rows to
save. If the simulation generates more rows than the specified maximum, the
simulation saves only the most recently generated rows. To capture all the
data, set this value to inf.
• The Decimation parameter allows you to write data at every nth sample,
where n is the decimation factor. The default decimation, 1, writes data at
every time step.
• The Sample time parameter allows you to specify a sampling interval at
which to collect points. This parameter is useful when using a variable-step
solver where the interval between time steps may not be the same. The
default value of -1 causes the block to inherit the sample time from the
driving block when determining which points to write.
During the simulation, the block writes data to an internal buffer. When the
simulation is completed or paused, that data is written to the workspace. The
block icon shows the name of the matrix to which the data is written.
8-199
To Workspace
Structure
This format consists of a structure with three fields: time, signals, and
blockName. The time field is empty. The blockName field contains the name of
the To Workspace block. The signals field contains a structure with two fields:
values and label. The values field contains the matrix of signal values.
Structure with Time
This format is the same as Structure except that the time field contains a
vector of simulation time steps.
Using Saved Data with a From File Block
If the data written using a To Workspace block is to be saved and read later by
a From File block, the time must be added to the data and the matrix must be
transposed. For more information, see From File on page 8-82.
Using Saved Data with a From Workspace Block
If the data written using a To Workspace block is intended to be “played back”
in another simulation using a From Workspace block, the data must contain
the simulation time values. The way you include times depends on the save
format.
If the save format is a structure, you can include the simulation time by
choosing Structure with Time as the value of Save format. The block stores
the simulation times as a vector in the time member of the output structure.
If the save format is a matrix, you must add a column of simulation times to
the matrix. You can add a column with time values in two ways:
• By multiplexing the output of a Clock block as the first element of the vector
input line of the To Workspace block.
• By specifying time as a return value on the Simulation Parameters dialog
box or from the command line, described in Chapter 4. When the simulation
8-200
To Workspace
is completed, you can concatenate the time vector (t) to the matrix using a
command like this:
matrix = [t; matrix];
Examples
In a simulation where the start time is 0, the Maximum number of rows is
100, the Decimation is 1, and the Sample time is 0.5. The To Workspace block
collects a maximum of 100 points, at time values of 0, 0.5, 1.0, 1.5, … seconds.
Specifying a Decimation of 1 directs the block to write data at each step.
In a similar example, the Maximum number of rows is 100 and the Sample
time is 0.5, but the Decimation is 5. In this example, the block collects up to
100 points, at time values of 0, 2.5, 5.0, 7.5, … seconds. Specifying a
Decimation of 5 directs the block to write data at every fifth sample. The
sample time ensures that data is written at these points.
In another example, all parameters are as defined in the first example except
that the Maximum number of rows is 3. In this case, only the last three rows
collected are written to the workspace. If the simulation stop time is 100, data
corresponds to times 99.0, 99.5, and 100.0 seconds (three points).
Data Type
Support
A To Workspace block can save input of any real or complex data type to the
MATLAB workspace.
8-201
To Workspace
Parameters
and Dialog Box
Variable name
The name of the matrix that holds the data.
Maximum number of rows
The maximum number of rows (one row per time step) to be saved. The
default is 1000 rows.
Decimation
A decimation factor. The default is 1.
Sample time
The sample time at which to collect points.
Save format
Format in which to save simulation output to the workspace. The default
is as a structure.
Characteristics
8-202
Sample Time
Inherited
Vectorized
Yes
Transfer Fcn
Purpose
8Transfer Fcn
Library
Continuous
Description
The Transfer Fcn block implements a transfer function where the input (u) and
output (y) can be expressed in transfer function form as the following equation
Implement a linear transfer function.
nn – 1
nn – 2
num ( s )
num ( 1 )s
y(s)
+ num ( 2 )s
+ … + num ( nn )
H ( s ) = ----------- = --------------------- = ------------------------------------------------------------------------------------------------------------------------------nd – 1
nd – 2
u( s )
den ( s )
+ den ( 2 )s
+ … + den ( nd )
den ( 1 )s
where nn and nd are the number of numerator and denominator coefficients,
respectively. num and den contain the coefficients of the numerator and
denominator in descending powers of s. num can be a vector or matrix, den
must be a vector, and both are specified as parameters on the block dialog box.
The order of the denominator must be greater than or equal to the order of the
numerator.
A Transfer Fcn block takes a scalar input. If the numerator of the block’s
transfer function is a vector, the block’s output is also scalar. However, if the
numerator is a matrix, the transfer function expands the input into an output
vector equal in width to the number of rows in the numerator. For example, a
two-row numerator results in a block with scalar input and vector output. The
width of the output vector is two.
Initial conditions are preset to zero. If you need to specify initial conditions,
convert to state-space form using tf2ss and use the State-Space block. The
tf2ss utility provides the A, B, C, and D matrices for the system. For more
information, type help tf2ss or consult the Control System Toolbox User’s
Guide.
The Transfer Fcn Block Icon
The numerator and denominator are displayed on the Transfer Fcn block icon
depending on how they are specified:
• If each is specified as an expression, a vector, or a variable enclosed in
parentheses, the icon shows the transfer function with the specified
coefficients and powers of s. If you specify a variable in parentheses, the
variable is evaluated. For example, if you specify Numerator as [3,2,1] and
8-203
Transfer Fcn
Denominator as (den) where den is [7,5,3,1], the block icon looks like
this:
• If each is specified as a variable, the icon shows the variable name followed
by “(s)”. For example, if you specify Numerator as num and Denominator as
den, the block icon looks like this:
Data Type
Support
A Transfer Fcn block accepts and outputs signals of any data type.
Parameters
and Dialog Box
Numerator
The row vector of numerator coefficients. A matrix with multiple rows can
be specified to generate multiple output. The default is [1].
Denominator
The row vector of denominator coefficients. The default is [1 1].
Characteristics
8-204
Direct Feedthrough
Only if the lengths of the Numerator and
Denominator parameters are equal
Sample Time
Continuous
Scalar Expansion
No
States
Length of Denominator -1
Transfer Fcn
Vectorized
Yes, in the sense that the block expands scalar input
into vector output when the transfer function
numerator is a matrix. See block description above.
Zero Crossing
No
8-205
Transport Delay
Purpose
8Transport Delay
Library
Continuous
Description
The Transport Delay block delays the input by a specified amount of time. It
can be used to simulate a time delay.
Delay the input by a given amount of time.
At the start of the simulation, the block outputs the Initial input parameter
until the simulation time exceeds the Time delay parameter, when the block
begins generating the delayed input. The Time delay parameter must be
nonnegative.
The block stores input points and simulation times during a simulation in a
buffer whose initial size is defined by the Initial buffer size parameter. If the
number of points exceeds the buffer size, the block allocates additional memory
and Simulink displays a message after the simulation that indicates the total
buffer size needed. Because allocating memory slows down the simulation,
define this parameter value carefully if simulation speed is an issue. For long
time delays, this block might use a large amount of memory, particularly for a
vectorized input.
When output is required at a time that does not correspond to the times of the
stored input values, the block interpolates linearly between points. When the
delay is smaller than the step size, the block extrapolates from the last output
point, which may produce inaccurate results. Because the block does not have
direct feedthrough, it cannot use the current input to calculate its output value.
To illustrate this point, consider a fixed-step simulation with a step size of 1
and the current time at t = 5. If the delay is 0.5, the block needs to generate a
point at t = 4.5. Because the most recent stored time value is at t = 4, the block
performs forward extrapolation.
The Transport Delay block does not interpolate discrete signals. Instead, it
returns the discrete value at t - tdelay.
This block differs from the Unit Delay block, which delays and holds the output
on sample hits only.
Using linmod to linearize a model that contains a Transport Delay block can be
troublesome. For more information about ways to avoid the problem, see
“Linearization” in Chapter 5.
8-206
Transport Delay
Data Type
Support
A Transport Delay block accepts and outputs real signals of type double.
Parameters
and Dialog Box
Time delay
The amount of simulation time that the input signal is delayed before
propagating it to the output. The value must be nonnegative.
Initial input
The output generated by the block between the start of the simulation and
the Time delay.
Initial buffer size
The initial memory allocation for the number of points to store.
Characteristics
Direct Feedthrough
No
Sample Time
Continuous
Scalar Expansion
Of input and all parameters except Initial buffer size
Vectorized
Yes
Zero Crossing
No
8-207
Trigger
Purpose
8Trigger
Library
Signals & Systems
Description
Adding a Trigger block to a subsystem makes it a triggered subsystem. A
triggered subsystem executes once on each integration step when the value of
the signal that passes through the trigger port changes in a specifiable way
(described below). A subsystem can contain no more than one Trigger block. For
more information about triggered subsystems, see Chapter 7.
Add a trigger port to a subsystem.
The Trigger type parameter allows you to choose the type of event that
triggers execution of the subsystem:
• rising triggers execution of the subsystem when the control signal rises from
a negative or zero value to a positive value (or zero if the initial value is
negative).
• falling triggers execution of the subsystem when the control signal falls from
a positive or a zero value to a negative value (or zero if the initial value is
positive).
• either triggers execution of the subsystem when the signal is either rising or
falling.
• function-call causes execution of the subsystem to be controlled by logic
internal to an S-function (for more information, see “Function-Call
Subsystems” in Chapter 7).
You can output the trigger signal by selecting the Show output port check box.
Selecting this option allows the system to determine what caused the trigger.
The width of the signal is the width of the triggering signal. The signal value is:
• 1 for a signal that causes a rising trigger
• -1 for a signal that causes a falling trigger
• 0 otherwise
Data Type
Support
8-208
A Trigger block accepts signals of type boolean or double.
Trigger
Parameters
and Dialog Box
Trigger type
The type of event that triggers execution of the subsystem
Show output port
If checked, Simulink draws the Trigger block output port and outputs the
trigger signal.
Output data type
Specifies the data type (double or int8) of the trigger output. If you select
auto, Simulink sets the data type to be the same as that of the port to which
the output is connected.If the port’s data type is not double or int8,
Simulink signals an error.
Characteristics
Sample Time
Determined by the signal at the trigger port
Vectorized
Yes
8-209
Trigonometric Function
Purpose
8Trigonometric Function
Library
Math
Description
The Trigonometric Function block performs numerous common trigonometric
functions.
Perform a trigonometric function.
You can select one of these functions from the Function list: sin, cos, tan,
asin, acos, atan, atan2, sinh, cosh, and tanh. The block output is the result of
the function operating on the input or inputs.
The name of the function appears on the block icon. Simulink automatically
draws the appropriate number of input ports. The block accepts and outputs
real or complex signals of type double.
Use the Trigonometric Function block instead of the Fcn block when you want
vectorized output because the Fcn block can produce only scalar output.
Data Type
Support
A Trigonometric Function block accepts and outputs real or complex signals of
type double.
Parameters
and Dialog Box
Function
The trigonometric function.
Output signal type
Type of signal (complex or real) to output.
Characteristics
8-210
Direct Feedthrough
Yes
Sample Time
Inherited from driving block
Scalar Expansion
Of the input when the function requires two inputs
Trigonometric Function
Vectorized
Yes
Zero Crossing
No
8-211
Uniform Random Number
Purpose
8Uniform Random Number
Library
Sources
Description
The Uniform Random Number block generates uniformly distributed random
numbers over a specifiable interval with a specifiable starting seed. The seed
is reset each time a simulation starts. The generated sequence is repeatable
and can be produced by any Uniform Random Number block with the same
seed and parameters. To generate a vector of random numbers, specify the
Initial seed parameter as a vector.
Generate uniformly distributed random numbers.
To generate normally distributed random numbers, use the Random Number
block, described on Random Number on page 8-150.
Avoid integrating a random signal because solvers are meant to integrate
relatively smooth signals. Instead, use the Band-Limited White Noise block.
Data Type
Support
A Uniform Random Number block outputs a real signal of type double.
Parameters
and Dialog Box
Minimum
The minimum of the interval. The default is -1.
Maximum
The maximum of the interval. The default is 1.
Initial seed
The starting seed for the random number generator. The default is 0.
8-212
Uniform Random Number
Sample time
The sample period. The default is 0.
Characteristics
Sample Time
Continuous, discrete, or inherited
Scalar Expansion
No
Vectorized
Yes
Zero Crossing
No
8-213
Unit Delay
Purpose
8Unit Delay
Library
Discrete
Description
The Unit Delay block delays and holds its input signal by one sampling
interval. If the input to the block is a vector, all elements of the vector are
delayed by the same sample delay. This block is equivalent to the z-1
discrete-time operator.
Delay a signal one sample period.
If an undelayed sample-and-hold function is desired, use a Zero-Order Hold
block, or if a delay of greater than one unit is desired, use a Discrete Transfer
Fcn block. (See the description of the Transport Delay block for an example
that uses the Unit Delay block.)
Data Type
Support
A Unit block accepts real or complex signals of data type, including
user-defined types. If the data type of the input signal is user-defined, the
initial condition must be 0
Parameters
and Dialog Box
Initial condition
The block output for the first simulation period, during which the output of
the Unit Delay block is undefined. Careful selection of this parameter can
minimize unwanted output behavior during this time. The default is 0.
Sample time
The time interval between samples. The default is 1.
Characteristics
8-214
Direct Feedthrough
No
Sample Time
Discrete
Scalar Expansion
Of the Initial condition parameter or the input
Unit Delay
States
Inherited from driving block or parameters
Vectorized
Yes
Zero Crossing
No
8-215
Variable Transport Delay
Purpose
8Variable Transport Delay
Library
Continuous
Description
The Variable Transport Delay block can be used to simulate a variable time
delay. The block might be used to model a system with a pipe where the speed
of a motor pumping fluid in the pipe is variable.
Delay the input by a variable amount of time.
The block accepts two inputs: the first input is the signal that passes through
the block; the second input is the time delay, as show in this icon.
The Maximum delay parameter defines the largest value the time delay input
can have. The block clips values of the delay that exceed this value. The
Maximum delay must be greater than or equal to zero. If the time delay
becomes negative, the block clips it to zero and issues a warning message.
During the simulation, the block stores time and input value pairs in an
internal buffer. At the start of the simulation, the block outputs the Initial
input parameter until the simulation time exceeds the time delay input. Then,
at each simulation step the block outputs the signal at the time that
corresponds to the current simulation time minus the delay time.
When output is required at a time that does not correspond to the times of the
stored input values, the block interpolates linearly between points. If the time
delay is smaller than the step size, the block extrapolates an output point. This
may result in less accurate results. The block cannot use the current input to
calculate its output value because the block does not have direct feedthrough
at this port. To illustrate this point, consider a fixed-step simulation with a step
size of 1 and the current time at t = 5. If the delay is 0.5, the block needs to
generate a point at t = 4.5. Because the most recent stored time value is at t = 4,
the block performs forward extrapolation.
The Variable Transport Delay block does not interpolate discrete signals.
Instead, it returns the discrete value at t - tdelay.
8-216
Variable Transport Delay
Data Type
Support
A Variable Transport Delay block accepts and outputs real signals of type
double.
Parameters
and Dialog Box
Maximum delay
The maximum value of the time delay input. The value cannot be negative.
The default is 10.
Initial input
The output generated by the block until the simulation time first exceeds
the time delay input. The default is 0.
Buffer size
The number of points the block can store. The default is 1024.
Characteristics
Direct Feedthrough
Yes, of the time delay (second) input
Sample Time
Continuous
Scalar Expansion
Of input and all parameters except Buffer size
Vectorized
Yes
Zero Crossing
No
8-217
Width
Purpose
8Width
Library
Signals & Systems
Description
The Width block generates as output the width of its input vector.
Output the width of the input vector.
The Width block accepts real- or complex-valued signals of any data type,
including mixed-type signal vectors.
Data Type
Support
A Width block accepts and outputs real signals of type double.
Parameters
and Dialog Box
Characteristics
8-218
Sample Time
Constant
Vectorized
Yes
XY Graph
Purpose
8XY Graph
Library
Sinks
Description
The XY Graph block displays an X-Y plot of its inputs in a MATLAB figure
window.
Display an X-Y plot of signals using a MATLAB figure window.
The block has two scalar inputs. The block plots data in the first input (the x
direction) against data in the second input (the y direction). This block is useful
for examining limit cycles and other two-state data. Data outside the specified
range is not displayed.
Simulink opens a figure window for each XY Graph block in the model at the
start of the simulation.
For a demo that illustrates the use of the XY Graph block, enter lorenzs in the
command window.
Data Type
Support
An XY Graph block accepts real signals of type double.
Parameters
and Dialog Box
x-min
The minimum x-axis value. The default is -1.
x-max
The maximum x-axis value. The default is 1.
8-219
XY Graph
y-min
The minimum y-axis value. The default is -1.
y-max
The maximum y-axis value. The default is 1.
Sample time
The time interval between samples. The default is -1, which means that
the sample time is determined by the driving block.
Characteristics
8-220
Sample Time
Inherited from driving block
States
0
Zero-Order Hold
Purpose
8Zero-Order Hold
Library
Discrete
Description
The Zero-Order Hold block implements a sample-and-hold function operating
at the specified sampling rate. The block accepts one input and generates one
output, both of which can be scalar or vector..
Implement zero-order hold of one sample period.
This block provides a mechanism for discretizing one or more signals or
resampling the signal at a different rate. You can use it in instances where you
need to model sampling without requiring one of the other more complex
discrete function blocks. For example, it could be used in conjunction with a
Quantizer block to model an A/D converter with an input amplifier.
Data Type
Support
A Zero-Order Hold block accepts real- or complex-valued signals of any data
type.
Parameters
and Dialog Box
Sample time
The time interval between samples. The default is 1.
Characteristics
Direct Feedthrough
Yes
Sample Time
Discrete
Scalar Expansion
Yes
States
0
Vectorized
Yes
Zero Crossing
No
8-221
Zero-Pole
Purpose
8Zero-Pole
Library
Continuous
Description
The Zero-Pole block implements a system with the specified zeros, poles, and
gain in terms of the Laplace operator s.
Implement a transfer function specified in terms of poles and zeros.
A transfer function can be expressed in factored or zero-pole-gain form, which,
for a single-input single-output system in MATLAB, is
Z(s)
( s – Z ( 1 ) ) ( s – Z ( 2 ) )… ( s – Z ( m ) )
H ( s ) = K ------------ = K --------------------------------------------------------------------------------------( s – P ( 1 ) ) ( s – P ( 2 ) )… ( s – P ( n ) )
P( x )
where Z represents the zeros vector, P the poles vector, and K the gain. Z can
be a vector or matrix, P must be a vector, K can be a scalar or vector whose
length equals the number of rows in Z. The number of poles must be greater
than or equal to the number of zeros. If the poles and zeros are complex, they
must be complex conjugate pairs.
Block input and output widths are equal to the number of rows in the zeros
matrix.
The Zero-Pole Block Icon
The Zero-Pole block displays the transfer function in its icon depending on how
the parameters are specified:
8-222
Zero-Pole
• If each is specified as an expression or a vector, the icon shows the transfer
function with the specified zeros, poles, and gain. If you specify a variable in
parentheses, the variable is evaluated.
For example, if you specify Zeros as [3,2,1], Poles as (poles), where poles
is defined in the workspace as [7,5,3,1], and Gain as gain, the icon looks
like this:
• If each is specified as a variable, the icon shows the variable name followed
by “(s)” if appropriate. For example, if you specify Zeros as zeros, Poles as
poles, and Gain as gain, the icon looks like this.
Data Type
Support
A Zero-Pole block accepts real signals of type double.
Parameters
and Dialog Box
Zeros
The matrix of zeros. The default is [1].
Poles
The vector of poles. The default is [0 –1].
Gain
The vector of gains. The default is [1].
8-223
Zero-Pole
Characteristics
8-224
Direct Feedthrough
Only if the lengths of the Poles and Zeros
parameters are equal
Sample Time
Continuous
Scalar Expansion
No
States
Length of Poles vector
Vectorized
No
Zero Crossing
No
9
Additional Topics
How Simulink Works
Zero Crossings . . . .
Algebraic Loops . . .
Invariant Constants .
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9-2
9-3
9-7
9-11
Discrete-Time Systems . . . . . .
Discrete Blocks . . . . . . . . . .
Sample Time . . . . . . . . . . .
Purely Discrete Systems . . . . . . .
Multirate Systems . . . . . . . . .
Sample Time Colors . . . . . . . .
Mixed Continuous and Discrete Systems
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9-13
9-13
9-13
9-13
9-14
9-15
9-17
9
Additional Topics
How Simulink Works
Each block within a Simulink model has these general characteristics: a vector
of inputs, u, a vector of outputs, y, and a vector of states, x:
x
(states)
u
(input)
y
(output)
The state vector may consist of continuous states, discrete states, or a
combination of both. The mathematical relationships between these quantities
are expressed by these equations.
xd
y = f o ( t, x, u )
output
= f u ( t, x, u )
update
k+1
x' c = f d ( t, x, u )
where x =
derivative
xc
xd
k
Simulation consists of two phases: initialization and simulation. During the
initialization phase:
1 The block parameters are passed to MATLAB for evaluation. The resulting
numerical values are used as the actual block parameters.
2 The model hierarchy is flattened. Each subsystem that is not a conditionally
executed subsystem is replaced by the blocks it contains.
3 Blocks are sorted into the order in which they need to be updated. The
sorting algorithm constructs a list such that any block with direct
feedthrough is not updated until the blocks driving its inputs are updated.
It is during this step that algebraic loops are detected. For more information
about algebraic loops, see “Algebraic Loops” on page 9-7.
4 The connections between blocks are checked to ensure that the vector length
of the output of each block is the same as the input expected by the blocks it
drives.
9-2
How Simulink Works
Now the simulation is ready to run. A model is simulated using numerical
integration. Each of the supplied ODE solvers (simulation methods) depends
on the ability of the model to provide the derivatives of its continuous states.
Calculating these derivatives is a two-step process. First, each block’s output is
calculated in the order determined during the sorting. Then, in a second pass,
each block calculates its derivatives based on the current time, its inputs, and
its states. The resulting derivative vector is returned to the solver, which uses
it to compute a new state vector at the next time point. Once a new state vector
is calculated, the sampled data blocks and Scope blocks are updated.
Zero Crossings
Simulink uses zero crossings to detect discontinuities in continuous signals.
Zero crossings play an important role in:
• The handling of state events
• The accurate integration of discontinuous signals
State Event Handling
A system experiences a state event when a change in the value of a state causes
the system to undergo a distinct change. A simple example of a state event is a
bouncing ball hitting the floor. When simulating such a system using a
variable-step solver, the solver typically does not take steps that exactly
correspond to the times that the ball makes contact with the floor. As a result,
the ball is likely to overshoot the contact point, which results in the ball
penetrating the floor.
Simulink uses zero crossings to ensure that time steps occur exactly (within
machine precision) at the time state events occur. Because time steps occur at
the exact time of contact, the simulation produces no overshoot and the
transition from negative to positive velocity is extremely sharp (that is, there
is no rounding of corners at the discontinuity). To see a bouncing ball demo,
type bounce at the MATLAB prompt.
Integration of Discontinuous Signals
Numerical integration routines are formulated on the assumption that the
signals they are integrating are continuous and have continuous derivatives. If
a discontinuity (state event) is encountered during an integration step,
Simulink uses zero crossing detection to find the time at which the
discontinuity occurs. An integration step is then taken up to the left edge of the
9-3
9
Additional Topics
discontinuity. Finally, Simulink steps over the discontinuity and begins a new
integration step on the next piece-wise continuous portion of the signal.
Implementation Details
An example of a Simulink block that uses zero crossings is the Saturation
block. Zero crossings detect these state events in the Saturation block:
• The input signal reaches the upper limit
• The input signal leaves the upper limit
• The input signal reaches the lower limit
• The input signal leaves the lower limit
Simulink blocks that define their own state events are considered to have
intrinsic zero crossings. If you need explicit notification of a zero crossing event,
use the Hit Crossing block. See “Blocks with Zero Crossings” on page 9-6 for a
list of blocks that incorporate zero crossings.
The detection of a state event depends on the construction of an internal zero
crossing signal. This signal is not accessible by the block diagram. For the
Saturation block, the signal that is used to detect zero crossings for the upper
limit is zcSignal = UpperLimit – u, where u is the input signal.
Zero crossing signals have a direction attribute, which can have these values:
• rising – a zero crossing occurs when a signal rises to or through zero, or when
a signal leaves zero and becomes positive.
• falling – a zero crossing occurs when a signal falls to or through zero, or when
a signal leaves zero and becomes negative.
• either – a zero crossing occurs if either a rising or falling condition occurs.
For the Saturation block’s upper limit, the direction of the zero crossing is
either. This enables the entering and leaving saturation events to be detected
using the same zero crossing signal.
If the error tolerances are too large, it is possible for Simulink to fail to detect
a zero crossing. For example, if a zero crossing occurs within a time step, but
the values at the beginning and end of the step do not indicate a sign change,
the solver will step over the crossing without detecting it.
9-4
How Simulink Works
This figure shows a signal that crosses zero. In the first instance, the integrator
“steps over” the event. In the second, the solver detects the event.
not
detected
detected
If you suspect this is happening, tighten the error tolerances to ensure that the
solver takes small enough steps. For more information, see “Error Tolerances”
on page 4–13.
Caveat
It is possible to create models that exhibit high frequency fluctuations about a
discontinuity (chattering). Such systems typically are not physically realizable;
a mass-less spring, for example. Because chattering causes repeated detection
of zero crossings, the step sizes of the simulation become very small, essentially
halting the simulation.
If you suspect that this behavior applies to your model, you can disable zero
crossings by selecting the Disable zero crossing detection check box on the
Diagnostics page of the Simulation Parameters dialog box. Although
disabling zero crossing detection may alleviate the symptoms of this problem,
you no longer benefit from the increased accuracy that zero crossing detection
provides. A better solution is to try to identify the source of the underlying
problem in the model.
9-5
9
Additional Topics
Blocks with Zero Crossings
Table 9-1: Blocks with Intrinsic Zero Crossings
9-6
Block
Description of Zero Crossing
Abs
One: to detect when the input signal crosses zero in either
the rising or falling direction.
Backlash
Two: one to detect when the upper threshold is engaged,
and one to detect when the lower threshold is engaged.
Dead Zone
Two: one to detect when the dead zone is entered (the input
signal minus the lower limit), and one to detect when the
dead zone is exited (the input signal minus the upper
limit).
Hit
Crossing
One: to detect when the input crosses the threshold. These
zero crossings are not affected by the Disable zero
crossing detection check box in the Simulation
Parameters dialog box.
Integrator
If the reset port is present, to detect when a reset occurs. If
the output is limited, there are three zero crossings: one to
detect when the upper saturation limit is reached, one to
detect when the lower saturation limit is reached, and one
to detect when saturation is left.
MinMax
One: for each element of the output vector, to detect when
an input signal is the new minimum or maximum
Relay
One: if the relay is off, to detect the switch on point. If the
relay is on, to detect the switch off point.
Relational
Operator
One: to detect when the output changes.
Saturation
Two: one to detect when the upper limit is reached or left,
and one to detect when the lower limit is reached or left.
Sign
One: to detect when the input crosses through zero.
Step
One: to detect the step time.
How Simulink Works
Table 9-1: Blocks with Intrinsic Zero Crossings (Continued)
Block
Description of Zero Crossing
Subsystem
For conditionally executed subsystems: one for the enable
port if present, and one for the trigger port, if present.
Switch
One: to detect when the switch condition occurs.
Algebraic Loops
Some Simulink blocks have input ports with direct feedthrough. This means
that the output of these blocks cannot be computed without knowing the values
of the signals entering the blocks at these input ports. Some examples of blocks
with direct feedthrough inputs are:
• The Elementary Math block
• The Gain block
• The Integrator block’s initial condition ports
• The Product block
• The State-Space block when there is a nonzero D matrix
• The Sum block
• The Transfer Fcn block when the numerator and denominator are of the
same order
• The Zero-Pole block when there are as many zeros as poles
To determine whether a block has direct feedthrough, consult the
Characteristics table that describes the block, in Chapter 8.
An algebraic loop generally occurs when an input port with direct feedthrough
is driven by the output of the same block, either directly, or by a feedback path
through other blocks with direct feedthrough. (See “Non-Algebraic
Direct-Feedthrough Loops” on page 9-9 for an example of an exception to this
general rule.) An example of an algebraic loop is this simple scalar loop:
9-7
9
Additional Topics
Mathematically, this loop implies that the output of the Sum block is an
algebraic state z constrained to equal the first input u minus z (i.e. z = u – z).
The solution of this simple loop is z = u/2, but most algebraic loops cannot be
solved by inspection. It is easy to create vector algebraic loops with multiple
algebraic state variables z1, z2, etc., as shown in this model
The Algebraic Constraint block (see Algebraic Constraint on page 8-12) is a
convenient way to model algebraic equations and specify initial guesses. The
Algebraic Constraint block constrains its input signal F(z) to zero and outputs
an algebraic state z. This block outputs the value necessary to produce a zero
at the input. The output must affect the input through some feedback path.
You can provide an initial guess of the algebraic state value in the block’s dialog
box to improve algebraic loop solver efficiency.
A scalar algebraic loop represents a scalar algebraic equation or constraint of
the form F(z) = 0, where z is the output of one of the blocks in the loop and the
function F consists of the feedback path through the other blocks in the loop to
the input of the block. In the simple one-block example shown on the previous
page, F(z) = z – (u – z). In the vector loop example shown above, the equations
are:
z2 + z1 – 1 = 0
z2 – z1 – 1 = 0
Algebraic loops arise when a model includes an algebraic constraint F(z) = 0.
This constraint may arise as a consequence of the physical interconnectivity of
the system you are modeling, or it may arise because you are specifically trying
to model a differential/algebraic system (DAE).
9-8
How Simulink Works
When a model contains an algebraic loop, Simulink calls a loop solving routine
at each time step. The loop solver performs iterations to determine the solution
to the problem (if it can). As a result, models with algebraic loops run slower
than models without them.
To solve F(z) = 0, the Simulink loop solver uses Newton's method with weak
line search and rank-one updates to a Jacobian matrix of partial derivatives.
Although the method is robust, it is possible to create loops for which the loop
solver will not converge without a good initial guess for the algebraic states z.
You can specify an initial guess for a line in an algebraic loop by placing an IC
block (which is normally used to specify an initial condition for a signal) on that
line. As shown above, another way to specify an initial guess for a line in an
algebraic loop is to use an Algebraic Constraint block.
Whenever possible, use an IC block or an Algebraic Constraint block to specify
an initial guess for the algebraic state variables in a loop.
Non-Algebraic Direct-Feedthrough Loops
There are exceptions to the general rule that all loops comprising
direct-feedthrough blocks are algebraic. The exceptions are:
• Loops involving triggered subsystems
• A loop from the output to the reset port of an integrator
In the case of a triggered subsystem, a solver can safely assume that the
subsystem’s inputs are stable at the time of the trigger. This allows use of the
output from a previous time step to compute the input at the current time step,
thus eliminating the need for an algebraic loop solver.
9-9
9
Additional Topics
Consider, for example, the following system.
This system effectively solves the equation
z = 1 + u
where u is the value of z the last time the subsystem was triggered. The output
of the system is a staircase function as illustrated by the display on the
system’s scope.
9-10
How Simulink Works
Now consider the effect of removing the trigger from the system shown in the
previous example.
In this case, the input at the u2 port of the adder subsystem is equal to the
subsystem’s output at the current time step for every time step. The
mathematical representation of this system
z = z + 1
reveals that it has no mathematically valid solution.
Invariant Constants
Blocks either have explicitly defined sample times or inherit their sample
times from blocks that feed them or are fed by them.
Simulink assigns Constant blocks a sample time of infinity, also referred to as
a constant sample time. Other blocks have constant sample time if they receive
their input from a Constant block and do not inherit the sample time of another
block. This means that the output of these blocks does not change during the
simulation unless the parameters are explicitly modified by the model user.
For example, in this model, both the Constant and Gain blocks have constant
sample time.
9-11
9
Additional Topics
Because Simulink supports the ability to change block parameters during a
simulation, all blocks, even blocks having constant sample time, must generate
their output at the model’s effective sample time.
Because of this feature, all blocks compute their output at each sample time
hit, or, in the case of purely continuous systems, at every simulation step. For
blocks having constant sample time whose parameters do not change during a
simulation, evaluating these blocks during the simulation is inefficient and
slows down the simulation.
You can set the InvariantConstants parameter to remove all blocks having
constant sample times from the simulation “loop.” The effect of this feature is
twofold: first, parameters for these blocks cannot be changed during a
simulation; and second, simulation speed is improved. The speed improvement
depends on model complexity, the number of blocks with constant sample time,
and the effective sampling rate of the simulation.
You can set the parameter for your model by entering this command:
set_param('model_name', 'InvariantConstants', 'on')
You can turn off the feature by issuing the command again, assigning the
parameter the value of 'off'.
You can determine which blocks have constant sample time by selecting
Sample Time Colors from the Format menu. Blocks having constant sample
time are colored magenta.
9-12
Discrete-Time Systems
Discrete-Time Systems
Simulink has the ability to simulate discrete (sampled data) systems. Models
can be multirate; that is, they can contain blocks that are sampled at different
rates. Models can also be hybrid, containing a mixture of discrete and
continuous blocks.
Discrete Blocks
Each of the discrete blocks has a built-in sampler at its input, and a zero-order
hold at its output. When the discrete blocks are mixed with continuous blocks,
the output of the discrete blocks between sample times is held constant. The
outputs of the discrete blocks are updated only at times that correspond to
sample hits.
Sample Time
The Sample time parameter sets the sample time at which a discrete block’s
states are updated. Normally, the sample time is set to a scalar variable;
however, it is possible to specify an offset time (or skew) by specifying a
two-element vector in this field.
For example, specifying the Sample time parameter as the vector [Ts,offset]
sets the sample time to Ts and the offset value to offset. The discrete block is
updated on integer multiples of the sample time and offset values only
t = n * Ts + offset
where n is an integer and offset can be positive or negative, but less than the
sample time. The offset is useful if some discrete blocks must be updated sooner
or later than others.
You cannot change the sample time of a block while a simulation is running. If
you want to change a block’s sample time, you must stop and restart the
simulation for the change to take effect.
Purely Discrete Systems
Purely discrete systems can be simulated using any of the solvers; there is no
difference in the solutions. To generate output points only at the sample hits,
choose one of the discrete solvers.
9-13
9
Additional Topics
Multirate Systems
Multirate systems contain blocks that are sampled at different rates. These
systems can be modeled with discrete blocks or both discrete and continuous
blocks. For example, consider this simple multirate discrete model.
For this example the DTF1 Discrete Transfer Fcn block’s Sample time is set to
[1 0.1], which gives it an offset of 0.1. The DTF2 Discrete Transfer Fcn block’s
Sample time is set to 0.7, with no offset.
Starting the simulation and plotting the outputs using the stairs function
[t,x,y] = sim('multirate', 3);
stairs(t,y)
produces this plot:
y(2)
y(1)
For the DTF1 block, which has an offset of 0.1, there is no output until t = 0.1.
Because the initial conditions of the transfer functions are zero, the output of
DTF1, y(1), is zero before this time.
9-14
Discrete-Time Systems
Sample Time Colors
Simulink identifies different sample rates in a model using the sample time
color feature, which shows sample rates by applying the color scheme shown in
this table.
Table 9-2: Sample Time Colors
Color
Use
Black
Continuous blocks
Magenta
Constant blocks
Yellow
Hybrid (subsystems grouping blocks, or Mux or Demux
blocks grouping signals with varying sample times)
Red
Fastest discrete sample time
Green
Second fastest discrete sample time
Blue
Third fastest discrete sample time
Light Blue
Fourth fastest discrete sample time
Dark Green
Fifth fastest discrete sample time
Cyan
Triggered sample time
Gray
Fixed in minor step
To understand how this feature works, it is important to be familiar with
Simulink’s Sample Time Propagation Engine (STPE). The figure below
illustrates a Discrete Filter block with a sample time of Ts driving a Gain block.
Because the Gain block’s output is simply the input multiplied by a constant,
its output changes at the same rate as the filter. In other words, the Gain block
has an effective sample rate equal to that of the filter’s sample rate. This is the
fundamental mechanism behind the STPE.
9-15
9
Additional Topics
To enable the sample time colors feature, select Sample Time Colors from the
Format menu.
Simulink does not automatically recolor the model with each change you make
to it, so you must select Update Diagram from the Edit menu to explicitly
update the model coloration. To return to your original coloring, disable sample
time coloration by again choosing Sample Time Colors.
When using sample time colors, the color assigned to each block depends on its
sample time with respect to other sample times in the model.
Simulink sets sample times for individual blocks according to these rules:
• Continuous blocks (e.g., Integrator, Derivative, Transfer Fcn, etc.) are, by
definition, continuous.
• Constant blocks (for example, Constant) are, by definition, constant.
• Discrete blocks (e.g., Zero-Order Hold, Unit Delay, Discrete Transfer Fcn,
etc.) have sample times that are explicitly specified by the user on the block
dialog boxes.
• All other blocks have implicitly defined sample times that are based on the
sample times of their inputs. For instance, a Gain block that follows an
Integrator is treated as a continuous block, whereas a Gain block that follows
a Zero-Order Hold is treated as a discrete block having the same sample time
as the Zero-Order Hold block.
For blocks whose inputs have different sample times, if all sample times are
integer multiples of the fastest sample time, the block is assigned the sample
time of the fastest input. If a variable-step solver is being used, the block is
assigned the continuous sample time. If a fixed-step solver is being used and
the greatest common divisor of the sample times (the fundamental sample
time) can be computed, it is used. Otherwise continuous is used.
It is important to note that Mux and Demux blocks are simply grouping
operators – signals passing through them retain their timing information. For
this reason, the lines emanating from a Demux block may have different colors
if they are driven by sources having different sample times. In this case, the
Mux and Demux blocks are color coded as hybrids (yellow) to indicate that they
handle signals with multiple rates.
Similarly, Subsystem blocks that contain blocks with differing sample times
are also colored as hybrids, because there is no single rate associated with
9-16
Discrete-Time Systems
them. If all of the blocks within a subsystem run at a single rate, then the
Subsystem block is colored according to that rate.
Under some circumstances, Simulink also backpropagates sample times to
source blocks if it can do so without affecting the output of a simulation. For
instance, in the model below, Simulink recognizes that the Signal Generator
block is driving a Discrete-Time Integrator block so it assigns the Signal
Generator block and the Gain block the same sample time as the Discrete-Time
Integrator block.
You can verify this by enabling Sample Time Colors and noting that all blocks
are colored red. Because the Discrete-Time Integrator block only looks at its
input at its sample times, this change does not affect the outcome of the
simulation but does result in a performance improvement.
Replacing the Discrete-Time Integrator block with a continuous Integrator
block, as shown below, and recoloring the model by choosing Update Diagram
from the Edit menu cause the Signal Generator and Gain blocks to change to
continuous blocks, as indicated by their being colored black.
Mixed Continuous and Discrete Systems
Mixed continuous and discrete systems are composed of both sampled and
continuous blocks. Such systems can be simulated using any of the integration
methods, although certain methods are more efficient and accurate than
others. For most mixed continuous and discrete systems, the Runge-Kutta
variable step methods, ode23 and ode45, are superior to the other methods in
terms of efficiency and accuracy. Due to discontinuities associated with the
sample and hold of the discrete blocks, the ode15s and ode113 methods are not
recommended for mixed continuous and discrete systems.
9-17
9
Additional Topics
9-18
10
Model Construction
Commands
Introduction . . . . . . . . . . . . . . . . . . . . 10-2
How to Specify Parameters for the Commands . . . . . . . 10-3
How to Specify a Path for a Simulink Object . . . . . . . 10-3
add_block . . . . . . . . . . . . . . . . . . . . . 10-4
add_line . . . . . . . . . . . . . . . . . . . . . . 10-5
bdclose
. . . . . . . . . . . . . . . . . . . . . . 10-6
bdroot . . . . . . . . . . . . . . . . . . . . . . . 10-7
close_system . . . . . . . . . . . . . . . . . . . . 10-8
delete_block . . . . . . . . . . . . . . . . . . . 10-10
delete_line . . . . . . . . . . . . . . . . . . . . 10-11
find_system
. . . . . . . . . . . . . . . . . . . 10-12
gcb . . . . . . . . . . . . . . . . . . . . . . . 10-14
gcbh . . . . . . . . . . . . . . . . . . . . . . . 10-15
gcs
. . . . . . . . . . . . . . . . . . . . . . . 10-16
get_param . . . . . . . . . . . . . . . . . . . . 10-17
new_system
. . . . . . . . . . . . . . . . . . . 10-19
open_system . . . . . . . . . . . . . . . . . . . 10-20
replace_block
. . . . . . . . . . . . . . . . . . 10-21
save_system . . . . . . . . . . . . . . . . . . . 10-23
set_param . . . . . . . . . . . . . . . . . . . . 10-24
simulink . . . . . . . . . . . . . . . . . . . . . 10-26
10
Model Construction Commands
Introduction
This table indicates the tasks performed by the commands described in this
chapter. The reference section of this chapter lists the commands in
alphabetical order.
10-2
Task
Command
Create a new Simulink system.
new_system
Open an existing system.
open_system
Close a system window.
close_system, bdclose
Save a system.
save_system
Find a system, block, line, or annotation.
find_system
Add a new block to a system.
add_block
Delete a block from a system.
delete_block
Replace a block in a system.
replace_block
Add a line to a system.
add_line
Delete a line from a system.
delete_line
Get a parameter value.
get_param
Set parameter values.
set_param
Get the pathname of the current block.
gcb
Get the pathname of the current system.
gcs
Get the handle of the current block.
gcbh
Get the name of the root-level system.
bdroot
Open the Simulink block library.
simulink
Introduction
How to Specify Parameters for the Commands
The commands described in this chapter require that you specify arguments
that describe a system, block, or block parameter. Appendix A provides
comprehensive tables of model and block parameters.
How to Specify a Path for a Simulink Object
Many of the commands described in this chapter require that you identify a
Simulink system or block. Identify systems and blocks by specifying their
paths:
• To identify a system, specify its name, which is the name of the file that
contains the system description, without the mdl extension.
system
• To identify a subsystem, specify the system and the hierarchy of subsystems
in which the subsystem resides.
system/subsystem1/.../subsystem
• To identify a block, specify the path of the system that contains the block and
specify the block name.
system/subsystem1/.../subsystem/block
If the block name includes a newline or carriage return, specify the block name
as a string vector and use sprintf('\n') as the newline character. For
example, these lines assign the newline character to cr, then get the value for
the Signal Generator block’s Amplitude parameter.
cr = sprintf('\n');
get_param(['untitled/Signal',cr,'Generator'],'Amplitude')
ans =
1
If the block name includes a slash character (/), you repeat the slash when you
specify the block name. For example, to get the value of the Location
parameter for the block named Signal/Noise in the mymodel system.
get_param('mymodel/Signal//Noise','Location')
10-3
add_block
Purpose
Add a block to a Simulink system.
Syntax
add_block('src', 'dest')
add_block('src', 'dest', 'parameter1', value1, ...)
Description
add_block('src', 'dest') copies the block with the full pathname 'src' to
a new block with the full path name 'dest'. The block parameters of the new
block are identical to those of the original. The name 'built–in' can be used
as a source system name for all Simulink built-in blocks (blocks available in
Simulink block libraries that are not masked blocks).
add_block('src', 'dest_obj', 'parameter1', value1, ...) creates a copy
as above, in which the named parameters have the specified values. Any
additional arguments must occur in parameter-value pairs.
Examples
This command copies the Scope block from the Sinks subsystem of the
simulink system to a block named Scope1 in the timing subsystem of the
engine system.
add_block('simulink/Sinks/Scope', 'engine/timing/Scope1')
This command creates a new subsystem named controller in the F14 system.
add_block('built-in/SubSystem', 'F14/controller')
This command copies the built-in Gain block to a block named Volume in the
mymodel system and assigns the Gain parameter a value of 4.
add_block('built-in/Gain', 'mymodel/Volume', 'Gain', '4')
See Also
10
10-4
delete_block, set_param
10add_block
add_line
Purpose
10add_line
Add a line to a Simulink system.
Syntax
h = add_line('sys', 'oport', 'iport')
h = add_line('sys', points)
Description
The add_line command adds a line to the specified system and returns a
handle to the new line. The line can be defined in two ways:
• By naming the block ports that are to be connected by the line
• By specifying the location of the points that define the line segments
add_line('sys', 'oport', 'iport') adds a straight line to a system from the
specified block output port 'oport' to the specified block input port 'iport'.
'oport' and 'iport' are strings consisting of a block name and a port
identifier in the form 'block/port'. Most block ports are identified by
numbering the ports from top to bottom or from left to right, such as 'Gain/1'
or 'Sum/2'. Enable, Trigger, and State ports are identified by name, such as
'subsystem_name/Enable', 'subsystem_name/Trigger', or
'Integrator/State'.
add_line(system, points) adds a segmented line to a system. Each row of the
points array specifies the x and y coordinates of a point on a line segment. The
origin is the top left corner of the window. The signal flows from the point
defined in the first row to the point defined in the last row. If the start of the
new line is close to the output of an existing block or line, a connection is made.
Likewise, if the end of the line is close to an existing input, a connection is
made.
Examples
This command adds a line to the mymodel system connecting the output of the
Sine Wave block to the first input of the Mux block.
add_line('mymodel','Sine Wave/1','Mux/1')
This command adds a line to the mymodel system extending from (20,55) to
(40,10) to (60,60).
add_line('mymodel',[20 55; 40 10; 60 60])
See Also
delete_line
10-5
bdclose
10
10bdclose
Purpose
Close any or all Simulink system windows unconditionally.
Syntax
bdclose
bdclose('sys')
bdclose('all')
Description
bdclose with no arguments closes the current system window unconditionally
and without confirmation. Any changes made to the system since it was last
saved are lost.
bdclose('sys') closes the specified system window.
bdclose('all') closes all system windows.
Examples
This command closes the vdp system.
bdclose('vdp')
See Also
10-6
close_system, new_system, open_system, save_system
bdroot
Purpose
10bdroot
Return the name of the top-level Simulink system.
Syntax
bdroot
bdroot('obj')
Description
bdroot with no arguments returns the top-level system name.
bdroot('obj') where 'obj' is a system or block pathname, returns the name
of the top-level system containing the specified object name.
Examples
This command returns the name of the top-level system that contains the
current block.
bdroot(gcb)
See Also
find_system, gcb
10-7
close_system
Purpose
10close_system
Close a Simulink system window or a block dialog box.
Syntax
close_system
close_system('sys')
close_system('sys', saveflag)
close_system('sys', 'newname')
close_system('blk')
Description
close_system with no arguments closes the current system or subsystem
window. If the current system is the top-level system and it has been modified,
then close_system asks if the changed system should be saved to a file before
removing the system from memory. The current system is defined in the
description of the gcs command (see “gcs” on page 10-16).
close_system('sys') closes the specified system or subsystem window.
close_system('sys', saveflag) closes the specified top-level system window
and removes it from memory:
• If saveflag is 0, the system is not saved.
• If saveflag is 1, the system is saved with its current name.
close_system('sys', 'newname') saves the specified top-level system to a file
with the specified new name, then closes the system.
close_system('blk') where 'blk' is a full block pathname, closes the dialog
box associated with the specified block or calls the block’s CloseFcn callback
parameter if one is defined. Any additional arguments are ignored.
Examples
This command closes the current system.
close_system
This command closes the vdp system.
close_system('vdp')
This command saves the engine system with its current name, then closes it.
close_system('engine', 1)
10-8
close_system
This command closes the mymdl12 system with the name testsys, then closes
it.
close_system('mymdl12', 'testsys')
This command closes the dialog box of the Unit Delay block in the Combustion
subsystem of the engine system.
close_system('engine/Combustion/Unit Delay')
See Also
bdclose, gcs, new_system, open_system, save_system
10-9
delete_block
Purpose
10delete_block
Delete a block from a Simulink system.
Syntax
delete_block('blk')
Description
delete_block('blk') where 'blk' is a full block pathname, deletes the
specified block from a system.
Example
This command removes the Out1 block from the vdp system:
delete_block('vdp/Out1')
See Also
10-10
add_block
delete_line
Purpose
10delete_line
Delete a line from a Simulink system.
Syntax
delete_line('sys', 'oport', 'iport')
Description
delete_line('sys', 'oport', 'iport') deletes the line extending from the
specified block output port 'oport' to the specified block input port 'iport'.
'oport' and 'iport' are strings consisting of a block name and a port
identifier in the form 'block/port'. Most block ports are identified by
numbering the ports from top to bottom or from left to right, such as 'Gain/1'
or 'Sum/2'. Enable, Trigger, and State ports are identified by name, such as
'subsystem_name/Enable', 'subsystem_name/Trigger' , or
'Integrator/State'.
delete_line('sys', [x y]) deletes one of the lines in the system that
contains the specified point (x,y), if any such line exists.
Example
This command removes the line from the mymodel system connecting the Sum
block to the second input of the Mux block.
delete_line('mymodel','Sum/1','Mux/2')
See Also
add_line
10-11
find_system
Purpose
10find_system
Find systems, blocks, lines, and annotations.
Syntax
find_system(sys, 'constraint', cv, ‘p1’, v1, ‘p2’, v2,...)
Description
find_system(sys, constraint, cv, ‘p1’, v1, ‘p2’, v2,...) searches the
system(s) or subsystems specified by sys, using the constraint specified by
constraint, and returns handles or paths to the objects having the specified
parameter values v1, v2, etc. sys can be a pathname (or cell array of
pathnames), a handle (or vector of handles), or omitted. If sys is a pathname
or cell array of pathnames , find_system returns a cell array of pathnames of
the objects it finds. If sys is a handle or a vector of handles, find_system
returns a vector of handles to the objects that it finds. If sys is omitted,
find_system searches all open systems.
Case is ignored for parameter names. Value strings are case sensitive. Any
parameters that correspond to dialog box entries have string values. See
Appendix A for a list of model and block parameters.
You can specify any of the following search constraints.
Table 10-1: Search Constraints
10-12
Name
Value Type
Description
'SearchDepth'
scalar
Restricts the search depth to the
specified level (0 for open systems
only, 1 for blocks and subsystems of
the top-level system , 2 for the
top-level system and its children,
etc.) Default is all levels.
'LookUnderMasks'
'on'| 'off'
If 'on', search extends into masked
systems. Default is 'off'.
'FollowLinks'
'on'| 'off'
If 'on', search follows links into
library blocks. Default is 'off'.
'FindAll'
'on'| 'off'
If 'on', search extends to lines and
annotations within systems.
Default is 'off'.
find_system
If 'constraint' is omitted, find_system uses the default constraint values.
Examples
This command returns a cell array containing the names of all open systems
and blocks.
find_system
This command returns the names of all open block diagrams.
open_bd = find_system('Type', 'block_diagram')
This command returns the names of all Goto blocks that are children of the
Unlocked subsystem in the clutch system.
find_system('clutch/Unlocked','SearchDepth',1,'BlockType','Goto')
These commands return the names of all Gain blocks in the vdp system having
a Gain parameter value of 1.
gb = find_system('vdp', 'BlockType', 'Gain')
find_system(gb, 'Gain', '1')
The above commands are equivalent to this command.
find_system('vdp', 'BlockType', 'Gain', 'Gain', '1')
These commands obtain the handles of all lines and annotations in the vdp
system.
sys = get_param(‘vdp’, ‘Handle’);
l = find_system(sys, ‘FindAll', 'on', 'type', 'line');
a = find_system(sys, ‘FindAll’, ‘on’, ‘type’, ‘annotation’);
See Also
get_param, set_param
10-13
gcb
Purpose
10gcb
Get the pathname of the current block.
Syntax
gcb
gcb('sys')
Description
gcb returns the full block path name of the current block in the current system.
gcb('sys') returns the full block path name of the current block in the
specified system.
The current block is one of these:
• During editing, the current block is the block most recently clicked on.
• During simulation of a system that contains S-Function blocks, the current
block is the S-Function block currently executing its corresponding MATLAB
function.
• During callbacks, the current block is the block whose callback routine is
being executed.
• During evaluation of the MaskInitialization string, the current block is
the block whose mask is being evaluated.
Examples
This command returns the path of the most recently selected block.
gcb
ans =
clutch/Locked/Inertia
This command gets the value of the Gain parameter of the current block.
get_param(gcb,'Gain')
ans =
1/(Iv+Ie)
See Also
10-14
gcbh, gcs
gcbh
Purpose
10gcbh
Get the handle of the current block.
Syntax
gcbh
Description
gcbh returns the handle of the current block in the current system.
You can use this command to identify or address blocks that have no parent
system. The command should be most useful to blockset authors.
Examples
This command returns the handle of the most recently selected block.
gcbh
ans =
281.0001
See Also
gcb
10-15
gcs
Purpose
10gcs
Get the pathname of the current system.
Syntax
gcs
Description
gcs returns the full path name of the current system.
The current system is:
• During editing, the current system is the system or subsystem most recently
clicked in.
• During simulation of a system that contains S-Function blocks, the current
system is the system or subsystem containing the S-Function block that is
currently being evaluated.
• During callbacks, the current system is the system containing any block
whose callback routine is being executed.
• During evaluation of the MaskInitialization string, the current system is
the system containing the block whose mask is being evaluated.
Examples
This example returns the path of the system that contains the most recently
selected block.
gcs
ans =
clutch/Locked
See Also
10-16
gcb
get_param
Purpose
10get_param
Get system and block parameter values.
Syntax
get_param('obj', 'parameter')
get_param( { objects }, 'parameter')
get_param(handle, 'parameter')
get_param('obj', ‘ObjectParameters’)
get_param('obj', 'DialogParameters')
Description
get_param('obj', 'parameter'), where 'obj' is a system or block path name, returns
the value of the specified parameter. Case is ignored for parameter names.
get_param( { objects }, 'parameter') accepts a cell array of full path
specifiers, enabling you to get the values of a parameter common to all objects
specified in the cell array.
get_param(handle, 'parameter') returns the specified parameter of the
object whose handle is handle.
get_param('obj', 'ObjectParameters') returns a structure that describes
obj’s parameters. Each field of the returned structure corresponds to a
particular parameter and has the parameter’s name. For example, the Name
field corresponds to the object’s Name parameter. Each parameter field itself
contains three fields, Name, Type, and Attributes, that specify the parameter’s
name (for example, “Gain”), data type (for example, string), and attributes (for
example, read-only), respectively.
get_param('obj', 'DialogParameters') returns a cell array containing the
names of the dialog parameters of the specified block.
Appendix A contains lists of model and block parameters.
Examples
This command returns the value of the Gain parameter for the Inertia block in
the Requisite Friction subsystem of the clutch system.
get_param('clutch/Requisite Friction/Inertia','Gain')
ans =
1/(Iv+Ie)
10-17
get_param
These commands display the block types of all blocks in the mx+b system (the
current system), described in “A Sample Masked Subsystem” on page 6–3:
blks = find_system(gcs, 'Type', 'block');
listblks = get_param(blks, 'BlockType')
listblks =
'SubSystem'
'Inport'
'Constant'
'Gain'
'Sum'
'Outport'
This command returns the name of the currently selected block.
get_param(gcb, 'Name')
The following commands gets the attributes of the currently selected block’s
Name parameter.
p = get_param(gcb, 'ObjectParameters');
a = p.Name.Attributes
ans =
'read-write'
'always-save'
The following command gets the dialog parameters of a Sine Wave block.
p = get_param('untitled/Sine Wave', 'DialogParameters')
p =
'Amplitude'
'Frequency'
'Phase'
'SampleTime'
See Also
10-18
find_system, set_param
new_system
Purpose
10new_system
Create an empty Simulink system.
Syntax
new_system('sys')
Description
new_system('sys') creates a new empty system with the specified name. If 'sys'
specifies a path, the new system will be a subsystem of the system specified in
the path. new_system does not open the system window.
For a list of the default parameter values for the new system, see Appendix A.
Example
This command creates a new system named 'mysys'.
new_system('mysys')
This command creates a new subsystem named 'mysys' in the vdp system.
new_system('vdp/mysys')
See Also
close_system, open_system, save_system
10-19
open_system
Purpose
10open_system
Open a Simulink system window or a block dialog box.
Syntax
open_system('sys')
open_system('blk')
open_system('blk', 'force')
Description
open_system('sys') opens the specified system or subsystem window.
open_system('blk'), where 'blk' is a full block pathname, opens the dialog
box associated with the specified block. If the block’s OpenFcn callback
parameter is defined, the routine is evaluated.
open_system('blk', 'force'), where 'blk' is a full pathname or a masked
system, looks under the mask of the specified system. This command is
equivalent to using the Look Under Mask menu item.
Example
This command opens the controller system in its default screen location.
open_system('controller')
This command opens the block dialog box for the Gain block in the controller
system.
open_system('controller/Gain')
See Also
10-20
close_system, new_system, save_system
replace_block
Purpose
10replace_block
Replace blocks in a Simulink model.
Syntax
replace_block('sys', 'blk1', 'blk2', 'noprompt')
replace_block('sys', 'Parameter', 'value', 'blk', ...)
Description
replace_block('sys', 'blk1', 'blk2') replaces all blocks in 'sys' having
the block or mask type 'blk1' with 'blk2'. If 'blk2' is a Simulink built-in
block, only the block name is necessary. If 'blk' is in another system, its full
block pathname is required. If 'noprompt' is omitted, Simulink displays a
dialog box that asks you to select matching blocks before making the
replacement. Specifying the 'noprompt' argument suppresses the dialog box
from being displayed. If a return variable is specified, the paths of the replaced
blocks are stored in that variable.
replace_block('sys', 'Parameter', 'value', ..., 'blk') replaces all
blocks in 'sys' having the specified values for the specified parameters with
'blk'. You can specify any number of parameter/value pairs.
Note Because it may be difficult to undo the changes this command makes, it
is a good idea to save your system first.
Example
This command replaces all Gain blocks in the f14 system with Integrator
blocks and stores the paths of the replaced blocks in RepNames. Simulink lists
the matching blocks in a dialog box before making the replacement.
RepNames = replace_block('f14','Gain','Integrator')
This command replaces all blocks in the Unlocked subsystem in the clutch
system having a Gain of 'bv' with the Integrator block. Simulink displays a
dialog box listing the matching blocks before making the replacement.
replace_block('clutch/Unlocked','Gain','bv','Integrator')
This command replaces the Gain blocks in the f14 system with Integrator
blocks but does not display the dialog box.
replace_block('f14','Gain','Integrator','noprompt')
10-21
replace_block
See Also
10-22
find_system, set_param
save_system
Purpose
10save_system
Save a Simulink system.
Syntax
save_system
save_system('sys')
save_system('sys', 'newname')
Description
save_system saves the current top-level system to a file with its current name.
save_system('sys') saves the specified top-level system to a file with its
current name. The system must be open.
save_system('sys', 'newname') saves the specified top-level system to a file
with the specified new name. The system must be open.
Example
This command saves the current system.
save_system
This command saves the vdp system:
save_system('vdp')
This command saves the vdp system to a file with the name 'myvdp'.
save_system('vdp', 'myvdp')
See Also
close_system, new_system, open_system
10-23
set_param
Purpose
10set_param
Set Simulink system and block parameters.
Syntax
set_param('obj', 'parameter1', value1, 'parameter2', value2, ...)
Description
set_param('obj', 'parameter1', value1, 'parameter2', value2, ...),
where 'obj' is a system or block path, sets the specified parameters to the
specified values. Case is ignored for parameter names. Value strings are case
sensitive. Any parameters that correspond to dialog box entries have string
values. Model and block parameters are listed in Appendix A.
You can change block parameter values in the workspace during a simulation
and update the block diagram with these changes. To do this, make the
changes in the command window, then make the model window the active
window, then choose Update Diagram from the Edit menu.
Note Most block parameter values must be specified as strings. Two
exceptions are the Position and UserData parameters, common to all blocks.
Examples
This command sets the Solver and StopTime parameters of the vdp system.
set_param('vdp', 'Solver', 'ode15s', 'StopTime', '3000')
This command sets the Gain parameter of block Mu in the vdp system to 1000
(stiff).
set_param('vdp/Mu', 'Gain', '1000')
This command sets the position of the Fcn block in the vdp system.
set_param('vdp/Fcn', 'Position', [50 100 110 120])
This command sets the Zeros and Poles parameters for the Zero-Pole block in
the mymodel system.
set_param('mymodel/Zero-Pole','Zeros','[2 4]','Poles','[1 2 3]')
This command sets the Gain parameter for a block in a masked subsystem. The
variable k is associated with the Gain parameter.
set_param('mymodel/Subsystem', 'k', '10')
10-24
set_param
This command sets the OpenFcn callback parameter of the block named
Compute in system mymodel. The function 'my_open_fcn' executes when the
user double-clicks on the Compute block. For more information, see “Using
Callback Routines” on page 3–53.
set_param('mymodel/Compute', 'OpenFcn', 'my_open_fcn')
See Also
get_param, find_system
10-25
simulink
Purpose
10simulink
Open the Simulink block library.
Syntax
simulink
Description
The simulink command opens the Simulink block library window and creates
and displays a new (empty) model window, except in these cases:
• If a model window is open, Simulink does not create a new model window.
• If the Simulink block library window is already open, issuing this command
makes the Simulink window the active window.
10-26
11
Simulink Debugger
Introduction . . . . . . . . . . . . . . . . . . . . 11-2
Using the Debugger
. . . . . . . . . . . . . . . . 11-3
Running a Simulation Incrementally . . . . . . . . . 11-6
Setting Breakpoints
. . . . . . . . . . . . . . . . 11-9
Displaying Information About the Simulation . . . . 11-13
Displaying Information About the Model . . . . . . 11-17
Debugger Command Reference
. . . . . . . . . . 11-22
11
Simulink Debugger
Introduction
The Simulink debugger is a tool for locating and diagnosing bugs in a Simulink
model. It enables you to pinpoint problems by running simulations step-by-step
and displaying intermediate block states and input and outputs. The following
sections describe how to use the debugger to diagnose problems in Simulink
models.
11-2
Using the Debugger
Using the Debugger
Starting the Debugger
Use the sldebug command or the debug option of the sim command to start a
model under debugger control. (See sim on page 4-30 for information on
specifying sim options.)
For example, either the command
sim('vdp',[0,10],simset('debug','on'))
or the command
sldebug 'vdp’
loads the Simulink demo model, vdp, into memory and pauses at the first block
in the first time step. The debugger highlights the model’s initial block and
associated output signal lines in the model diagram. The next figure shows the
vdp block diagram as it appears on debug mode start-up.
Start block
The debugger also prints the simulation start time and a debug command
prompt in the MATLAB command window. The command prompt displays the
block index (see “About Block Indexes” on page 11-4) and name of the first block
11-3
11
Simulink Debugger
to be executed. For example, the command in the preceding example results in
the following output in the MATLAB command window.
[Tm=0
] **Start** of system 'vdp' outputs
(sldebug @0:0 'vdp/Integrator1'): step
At this point, you can get help, run the simulation step-by-step, examine data,
or perform other debugging tasks by entering debugger and other MATLAB
commands at the debug prompt. The following sections explain how to use the
debugger commands.
Getting Help
You can get a brief description of the debugger commands by typing help at the
debug prompt. For a detailed description of each command, refer to the
debugger command reference at the end of this chapter. The following sections
show how to use these commands to debug a model.
Entering Commands
The debugger accepts abbreviations for debugger commands. You can also
repeat some commands by entering an empty command (i.e., by pressing the
Return key) at the MATLAB command line. See “Debugger Command
Reference” on page 11-22 for a list of command abbreviations and repeatable
commands.
About Block Indexes
Many Simulink debugger commands and messages use block indexes to refer
to blocks. A block index has the form s:b where s is an integer identifying a
system in the model being debugged and b is an integer identifying a block
within that system. For example, the block index 0:1 refers to block 1 in the
model’s 0 system. The slist command shows the block index for each block in
the model being debugged (see slist on page 11-40).
Accessing the MATLAB Workspace
You can type any MATLAB expression at the sldebug prompt. For example,
suppose you are at a breakpoint and you are logging time and output of your
model as tout and yout. Then, the following command
(sldebug ...) plot(tout, yout)
11-4
Using the Debugger
creates a plot. Suppose you would like to access a variable whose name is the
same as the complete or incomplete name of an sldebug command, for
example, s, which is a partial completion for the step command. Typing an s
at the sldebug prompt steps the model However,
(sldebug...) eval(‘s’)
displays the value of the variable s.
11-5
11
Simulink Debugger
Running a Simulation Incrementally
The Simulink debugger lets you run a simulation step by step. You can step
from block to block, time point to time point, or from breakpoint to breakpoint
(see “Setting Breakpoints” on page 11-9). You select the amount to advance the
simulation by entering the appropriate debugger command.
Command
Advances a Simulation...
step
One block
next
One time step
continue
To next breakpoint
run
To end of simulation, ignoring breakpoints
Stepping by Blocks
To advance a simulation one block, enter step at the debugger prompt. The
debugger executes the current block, stops, and highlights the next block in the
model’s block execution order (see “Displaying a Model’s Block Execution
Order” on page 11-17). For example, the following figure shows the vdp block
diagram after execution of the model’s first block.
11-6
Running a Simulation Incrementally
If the next block to be executed occurs in a subsystem block, the debugger opens
the subsystem’s block diagram and highlights the next block.
After executing a block, the debugger prints the block’s inputs (U) and outputs
(Y) and redisplays the debug command prompt in the MATLAB command
window. The debugger prompt shows the next block to be evaluated.
(sldebug @0:0 'vdp/Integrator1'): step
U1 = [0]
Y1 = [2]
(sldebug @0:1 'vdp/Out1'):
Crossing a Time Step Boundary
When you step through the last block in the model’s sorted list, the debugger
advances the simulation to the next time step and halts the simulation at the
beginning of the first block to be executed in the next time step. To signal that
you have crossed a time step boundary, the debugger prints the current time
in the MATLAB command window. For example, stepping through the last
block of the first time step of the vdp model results in the following output in
the MATLAB command window.
(sldebug @0:8 'vdp/Sum'): step
U1 = [2]
U2 = [0]
Y1 = [-2]
[Tm=0.0001004754572603832 ] **Start** of system 'vdp' outputs
Stepping by Minor Time Steps
You can step by blocks within minor time steps, as well as within major steps.
To step by blocks within minor time steps, enter minor at the debugger
command prompt.
Stepping by Time Steps
The next command executes the remaining blocks in the current time step. In
effect, it enables you to advance the simulation to the next time step with a
single command. This is convenient when you know that nothing of interest
happens in the remainder of the current time step. After advancing the
simulation to the next time step, the debugger breaks at the first block in the
model’s sorted list. For example, entering next after starting the vdp model in
11-7
11
Simulink Debugger
debug mode causes the following message to appear in the MATLAB command
window.
[Tm=0.0001004754572603832
] **Start** of system 'vdp' outputs
Stepping by Breakpoints
The continue command advances the simulation from the current breakpoint
to the next breakpoint (see “Setting Breakpoints” on page 11-9) or to the end of
the simulation, whichever comes first.
Running a Simulation Nonstop
The run command lets you run a program from the current point in the
simulation to the end, skipping any intervening breakpoints. At the end of the
simulation, the debugger returns you to the MATLAB command line. To
continue debugging a model, you must restart the debugger (see “Starting the
Debugger” on page 11-3).
11-8
Setting Breakpoints
Setting Breakpoints
The Simulink debugger allows you to define stopping points in a simulation
called breakpoints. You can then run a simulation from breakpoint to
breakpoint, using the debugger’s continue command. The debugger lets you
define two types of breakpoints: unconditional and conditional. An
unconditional breakpoint occurs whenever a simulation reaches a block or time
step that you specified previously. A conditional breakpoint occurs when a
condition that you specified in advance arises in the simulation.
Breakpoints come in handy when you know that a problem occurs at a certain
point in your program or when a certain condition occurs. By defining an
appropriate breakpoint and running the simulation via the continue
command, you can skip immediately to the point in the simulation where the
problem occurs.
You set a particular kind of breakpoint by entering the appropriate breakpoint
command.
Command
Causes Simulation to Stop...
break <gcb | s:b>
At the beginning of a block
bafter <gcb | s:b>
At the end of a block
tbreak [t]
At a simulation time step
nanbreak
At the occurrence of an underflow or overflow
(NaN) or infinite (Inf) value
xbreak
When the simulation reaches the state that
determines the simulation step size.
zcbreak
When a zero-crossing occurs between
simulation time steps.
Breaking at Blocks
The debugger lets you specify a breakpoint at the beginning or end of a block.
11-9
11
Simulink Debugger
Breaking at a Block’s Beginning
The break command lets you set a breakpoint at the beginning of a block.
Setting a breakpoint at the beginning of a block causes the debugger to stop the
simulation when it reaches the block on each time step.
You can specify the block on which to set the breakpoint via a block index or
graphically. To specify the block graphically, select the block in the model’s
block diagram and enter
break gcb
as shown in the following figure.
This command
sets a
breakpoint on
this block.
To specify the block via its index, enter
break s:b
11-10
Setting Breakpoints
where s:b is the block’s index (see “About Block Indexes” on page 11-4).
Note You cannot set a breakpoint on a virtual block. A virtual block is a block
whose function is purely graphical: it indicates a grouping or relationship
among a model’s computational blocks. The debugger warns you if you
attempt to set a breakpoint on a virtual block. You can obtain a listing of a
model’s nonvirtual blocks, using the slist command (see “Displaying a
Model’s Nonvirtual Blocks” on page 11-18).
Breaking at a Block’s End
The bafter command sets a breakpoint at the end of a nonvirtual block. As
with break, you can specify the block graphically or via its block index.
Clearing Breakpoints from Blocks
The clear command clears a breakpoint from the beginning or end of a block.
You can specify the block by entering its block index or by selecting the block
in the model diagram and entering gcb as the argument of the clear command.
Breaking at Time Steps
You can use the tbreak command to set a breakpoint at a particular time step.
The tbreak command takes a time value as its only argument. It causes the
debugger to stop the simulation at the beginning of the first time step that
follows the specified time. For example, starting vdp in debug mode and
entering the commands
tbreak 9
continue
causes the debugger to halt the simulation at the beginning of time step 9.0785
as indicated by the output of the continue command.
[Tm=9.07847133212036
] **Start** of system 'vdp' outputs
Breaking on Nonfinite Values
The nanbreak command stops a simulation when the simulation computes a
value that is infinite or outside the range of values that can be represented by
11-11
11
Simulink Debugger
the machine running the simulation. The nanbreak command is useful for
pinpointing computational errors in a Simulink model.
Breaking on Step-Size Limiting Steps
The xbreak command causes the debugger to stop the simulation when the
model uses a variable-step solver and the solver encounters a state that limits
the size of the steps that it can take. This command is useful in debugging
models that appear to require an excessive number of simulation time steps to
solve.
Breaking at Zero-Crossings
The zcbreak command causes the simulation to halt when Simulink detects a
non-sampled zero crossing in a model that includes blocks where zero-crossings
can arise. After halting, Simulink prints the location in the model, the time,
and the type (rising or falling) of the zero-crossing. For example, setting a
zero-crossing break at the start of execution of the zeroxing demo model
sldebug zeroxing
[Tm=0
] **Start** of system 'zeroxing' outputs
(sldebug @0:0 'zeroxing/Sine Wave'): zcbreak
Break at zero crossing events is enabled.
and continuing the simulation
(sldebug @0:0 'zeroxing/Sine Wave'): continue
results in a rising zero-crossing break at
[Tm=0.34350110879329
] Breaking at block 0:2
[Tm=0.34350110879329
] Rising zero crossing on 3rd zcsignal
in block 0:2 'zeroxing/Saturation'
If a model does not include blocks capable of producing nonsampled
zero-crossings, the command prints a message advising you of this fact.
11-12
Displaying Information About the Simulation
Displaying Information About the Simulation
The Simulink debugger provides a set of commands that allow you to display
block states, block inputs and outputs, and other information while running a
model.
Displaying Block I/O
The debugger provides three commands for displaying block I/O. Each displays
the I/O of a specified block. The main difference among them is when they
display the I/O.
Command
Displays a Block’s I/O...
probe
Immediately
disp
At every breakpoint
trace
Whenever the block is executed
probe Command
The probe command prints the current inputs and outputs of a block that you
specify. The command prints the block’s I/O in the MATLAB command window.
Command
Description
probe
Enter or exit probe mode. In probe mode, the debugger
displays the current inputs and outputs of any block that
you select in the model’s block diagram. Typing any
command causes the debugger to exit probe mode.
probe gcb
Displays I/O of selected block.
probe s:b
Prints the I/O of the block specified by system number s
and block number b.
The probe command comes in handy when you need to examine the I/O of a
block whose I/O is not otherwise displayed. For example, suppose you are using
the step command to run a model block by block. Each time you step the model,
11-13
11
Simulink Debugger
the debugger displays the inputs and outputs of the current block. The probe
command lets you examine the I/O of other blocks as well. Similarly, suppose
you are using the next command to step through a model by time steps. The
next command does not display block I/O. However, if you need to examine a
block’s I/O after entering a next command, you can do so, using the probe
command.
disp Command
The disp command causes the debugger to display a specified block’s inputs
and outputs whenever it halts the simulation. You can specify a block either by
entering its block index or by selecting it in the block diagram and entering gcb
as the disp command argument. You can remove any block from the debugger’s
list of display points, using the undisp command. For example, to remove
block 0:0, either select the block in the model diagram and enter undisp gcb
or simply enter undisp 0:0.
The disp command is useful when you need to monitor the I/O of a specific
block or set of blocks as you step through a simulation. Using the disp
command, you can specify the blocks you want to monitor and the debugger will
then redisplay the I/O of those blocks on every step. Note that the debugger
always displays the I/O of the current block when you step through a model
block by block, using the step command. So, you do not need to use the disp
command if you are interested in watching only the I/O of the current block.
trace Command
The trace command causes the debugger to display a specified block’s I/O
whenever Simulink evaluates the block. It lets you obtain a complete record of
a block’s I/O without having to stop the simulation. As with the other block I/O
display commands, you can specify the block either by entering its block index
or by selecting it in the model diagram. You can remove a block from the
debugger’s list of trace points, using the untrace command.
Displaying Algebraic Loop Information
The atrace command causes the debugger to display information about a
model’s algebraic loops (see “Algebraic Loops” on page 9-7) each time they are
11-14
Displaying Information About the Simulation
solved. The command takes a single argument that specifies the amount of
information to display.
Command
Displays for Each Algebraic Loop ...
atrace 0
No information
atrace 1
The loop variable solution, the number of iterations
required to solve the loop, and the estimated solution error
atrace 2
Same as level 1
atrace 3
Level 2 plus the Jacobian matrix used to solve loop
atrace 4
Level 3 plus intermediate solutions of the loop variable
Displaying System States
The states debug command lists the current values of the system’s states in
the MATLAB command window. For example, the following sequence of
commands shows the states of the Simulink bouncing ball demo (bounce) after
its first and second time-steps.
sldebug bounce
[Tm=0
] **Start** of system 'bounce' outputs
(sldebug @0:0 'bounce/Position'): states
Continuous state vector (value,index,name):
10
0 (0:0 'bounce/Position')
15
1 (0:5 'bounce/Velocity')
(sldebug @0:0 'bounce/Position'): next
[Tm=0.01
] **Start** of system 'bounce' outputs
(sldebug @0:0 'bounce/Position'): states
Continuous state vector (value,index,name):
10.1495095
0 (0:0 'bounce/Position')
14.9019
1 (0:5 'bounce/Velocity')
Displaying Integration Information
The ishow command toggles display of integration information. When enabled,
this option causes the debugger to print a message each time that it takes a
11-15
11
Simulink Debugger
time step or encounters a state that limits the size of a time step. In the first
case, the debugger prints the size of the time step, for example,
[Tm=9.996264188473381
] Step of 0.01 was taken by integrator
In the second case, the debugger displays the state that currently determines
the size of time steps, for example,
[Ts=9.676264188473388
] Integration limited by 1st state of
block 0:0 'bounce/Position'
11-16
Displaying Information About the Model
Displaying Information About the Model
In addition to providing information about a simulation, the debugger can
provide you with information about the model that underlies the simulation.
Displaying a Model’s Block Execution Order
Simulink determines the order in which to execute blocks at the beginning of a
simulation run, during model initialization. During simulation, Simulink
maintains a list of blocks sorted by execution order. This list is called the sorted
list. You can display the sorted list at any time by typing slist at the debugger
command prompt. The slist command lists the model’s blocks in execution
order. The list includes the block index for each command:
---- Sorted list for 'vdp' [12 blocks, 9 nonvirtual blocks,
directFeed=0]
0:0
'vdp/Integrator1' (Integrator)
0:1
'vdp/Out1' (Outport)
0:2
'vdp/Integrator2' (Integrator)
0:3
'vdp/Out2' (Outport)
0:4
'vdp/Fcn' (Fcn)
0:5
'vdp/Product' (Product)
0:6
'vdp/Mu' (Gain)
0:7
'vdp/Scope' (Scope)
0:8
'vdp/Sum' (Sum)
Displaying a Block
To determine which block in a model’s diagram corresponds to a particular
index, type bshow s:b at the command prompt, where s:b is the block index.
The bshow command opens the system containing the block (if necessary) and
selects the block in the system’s window.
11-17
11
Simulink Debugger
Displaying a Model’s Nonvirtual Systems
The systems command prints a list of the nonvirtual systems in the model
being debugged. For example, the Simulink clutch demo ( clutch) contains the
following systems:
sldebug clutch
[Tm=0
] **Start** of system 'clutch' outputs
(sldebug @0:0 'clutch/Clutch Pedal'): systems
0
'clutch'
1
'clutch/Locked'
2
'clutch/Unlocked'
Note The systems command does not list subsystems that are purely
graphical in nature, that is, subsystems that the model diagram represents as
Subsystem blocks but which Simulink solves as part of a parent system. In
Simulink models, the root system and triggered or enabled subsystems are
true systems. All other subsystems are virtual (that is, graphical) and hence
do not appear in the listing produced by the systems command.
Displaying a Model’s Nonvirtual Blocks
The slist command displays a list of the nonvirtual blocks in a model. The
listing groups the blocks by system. For example, the following sequence of
11-18
Displaying Information About the Model
commands produces a list of the nonvirtual blocks in the Van der Pol (vdp)
demo model:
sldebug vdp
[Tm=0
] **Start** of system 'vdp' outputs
(sldebug @0:0 'vdp/Integrator1'): slist
---- Sorted list for 'vdp' [12 blocks, 9 nonvirtual blocks,
directFeed=0]
0:0
'vdp/Integrator1' (Integrator)
0:1
'vdp/Out1' (Outport)
0:2
'vdp/Integrator2' (Integrator)
0:3
'vdp/Out2' (Outport)
0:4
'vdp/Fcn' (Fcn)
0:5
'vdp/Product' (Product)
0:6
'vdp/Mu' (Gain)
0:7
'vdp/Scope' (Scope)
0:8
'vdp/Sum' (Sum)
Note The slist command does not list blocks that are purely graphical in
nature, that is, blocks that indicate relationships or groupings among
computational blocks.
11-19
11
Simulink Debugger
Displaying Blocks with Potential Zero-Crossings
The zclist prints a list of blocks in which nonsampled zero-crossings can occur
during a simulation. For example, zclist prints the following list for the clutch
sample model:
(sldebug
2:3
0:4
0:10
0:11
0:18
0:20
0:24
0:27
@0:0 'clutch/Clutch Pedal'): zclist
'clutch/Unlocked/Sign' (Signum)
'clutch/Lockup Detection/Velocities Match' (HitCross)
'clutch/Lockup Detection/Required Friction
for Lockup/Abs' (Abs)
'clutch/Lockup Detection/Required Friction for
Lockup/ Relational Operator' (RelationalOperator)
'clutch/Break Apart Detection/Abs' (Abs)
'clutch/Break Apart Detection/Relational Operator'
(RelationalOperator)
'clutch/Unlocked' (SubSystem)
'clutch/Locked' (SubSystem)
Displaying Algebraic Loops
The ashow command highlights a specified algebraic loop or the algebraic loop
that contains a specified block. To highlight a specified algebraic loop, type
ashow s#n, where s is the index of the system (see “Displaying a Model’s Block
Execution Order” on page 11-17) that contains the loop and n is the index of the
loop in the system. To display the loop that contains the currently selected
block, enter ashow gcb. To show a loop that contains a specified block, type
ashow s:b, where s:b is the block’s index. To clear algebraic-loop highlighting
from the model diagram, enter ashow clear.
11-20
Displaying Information About the Model
Displaying Debug Settings
The status command displays the settings of various debug options, such as
conditional breakpoints. For example, the following sequence of commands
displays the initial debug settings for the vdp model:
sim('vdp',[0,10],simset('debug','on'))
[Tm=0
] **Start** of system 'vdp' outputs
(sldebug @0:0 'vdp/Integrator1'): status
Current simulation time: 0 (MajorTimeStep)
Last command: ""
Stop in minor times steps is disabled.
Break at zero crossing events is disabled.
Break when step size is limiting by a state is disabled.
Break on non-finite (NaN,Inf) values is disabled.
Display of integration information is disabled.
Algebraic loop tracing level is at 0.
11-21
11
Simulink Debugger
Debugger Command Reference
The following table lists the debugger commands. The table’s Repeat column
specifies whether pressing the Return key at the command line repeats the
command. Detailed descriptions of the commands follow the table.
11-22
Command
Short
Form
Repeat
Description
ashow
as
No
Show an algebraic loop.
atrace
at
No
Set algebraic loop trace level.
bafter
ba
No
Insert a breakpoint after execution of a
block.
break
b
No
Insert a breakpoint before execution of a
block.
bshow
bs
No
Show a specified block.
clear
cl
No
Clear a breakpoint from a block.
continue
c
Yes
Continue the simulation.
disp
d
Yes
Display a block’s I/O when the
simulation stops.
help
? or h
No
Display help for debugger commands.
ishow
i
No
Enable or disable display of integration
information.
minor
m
No
Enable or disable minor step mode.
nanbreak
na
No
Set or clear break on nonfinite value.
next
n
Yes
Go to start of the next time step.
probe
p
No
Display a block’s I/O.
quit
q
No
Abort simulation.
run
r
No
Run the simulation to completion.
Debugger Command Reference
Command
Short
Form
Repeat
Description
slist
sli
No
List a model’s nonvirtual blocks.
states
state
No
Display current state values.
status
stat
No
Display debugging options in effect.
step
s
Yes
Step to next block.
stop
sto
No
Stop the simulation.
systems
sys
No
List a model’s nonvirtual systems.
tbreak
tb
No
Set or clear a time breakpoint.
trace
tr
Yes
Display a block’s I/O each time it
executes.
undisp
und
Yes
Remove a block from the debugger’s list
of display points.
untrace
unt
Yes
Remove a block from the debugger’s list
of trace point.
xbreak
x
No
Break when the debugger encounters a
step-size-limiting state.
zcbreak
zcb
No
Break at nonsampled zero-crossing
events.
zclist
zcl
No
List blocks containing nonsampled zero
crossings.
11-23
ashow
Purpose
Show an algebraic loop.
Syntax
ashow <gcb | s:b | s#n | clear>
Arguments
s:b
The block whose system index is s and block index is b.
gcb
Current block.
s#n
The algebraic loop numbered n in system s.
clear
Switch that clears loop coloring.
Description
ashow gcb or ashow s:b highlights the algebraic loop that contains the
specified block. ashow s#n highlights the nth algebraic loop in system s.
ashow clear removes algebraic loop highlights from the model diagram.
See Also
atrace, slist
11
11ashow
11-24
atrace
Purpose
11atrace
Set algebraic loop trace level.
Syntax
atrace level
Arguments
level
Description
The atrace command sets the algebraic loop trace level for a simulation.
See Also
Trace level (0 = none, 4 = everything).
Command
Displays for Each Algebraic Loop ...
atrace 0
No information
atrace 1
The loop variable solution, the number of iterations
required to solve the loop, and the estimated solution error
atrace 2
Same as level 1
atrace 3
Level 2 plus Jacobian matrix used to solve loop
atrace 4
Level 3 plus intermediate solutions of the loop variable
systems, states
11-25
bafter
Purpose
11bafter
Insert a break point after a block is executed.
Syntax
bafter gcb
bafter s:b
Arguments
s:b
The block whose system index is s and block index is b.
gcb
Current block.
Description
The bafter command inserts a breakpoint after execution of the specified
block.
See Also
break, xbreak, tbreak, nanbreak, zcbreak, slist
11-26
break
Purpose
11break
Insert a break point before a block is executed.
Syntax
break gcb
break s:b
Arguments
s:b
The block whose system index is s and block index is b.
gcb
Current block.
Description
The break command inserts a breakpoint before execution of the specified
block.
See Also
bafter, tbreak, xbreak, nanbreak, zcbreak, slist
11-27
bshow
Purpose
11bshow
Show a specified block.
Syntax
bshow s:b
Arguments
s:b
Description
This command opens the model window containing the specified block and
selects the block.
See Also
slist
11-28
The block whose system index is s and block index is b.
clear
Purpose
11clear
Clear a breakpoint from a block.
Syntax
clear gcb
clear s:b
Arguments
s:b
The block whose system index is s and block index is b.
gcb
Current block.
Description
The clear command clears a breakpoint from the specified block.
See Also
bafter, slist
11-29
continue
Purpose
11continue
Continue the simulation.
Syntax
continue
Description
The continue command continues the simulation from the current breakpoint.
The simulation continues until it reaches another breakpoint or its final time
step.
See Also
run, stop, quit
11-30
disp
Purpose
11disp
Display a block’s I/O when the simulation stops.
Syntax
disp gcb
disp s:b
disp
Arguments
s:b
The block whose system index is s and block index is b.
gcb
Current block.
Description
The disp command registers a block as a display point. The debugger displays
the inputs and outputs of all display points in the MATLAB command window
whenever the simulation halts. Invoking disp without arguments shows a list
of display points. Use undisp to unregister a block.
See Also
undisp, slist, probe, trace
11-31
help
Purpose
11help
Display help for debugger commands.
Syntax
help
Description
The help command displays a list of debugger commands in the command
window. The list includes the syntax and a brief description of each command.
11-32
ishow
Purpose
11ishow
Enable or disable display of integration information.
Syntax
ishow
Description
The ishow command toggles display of integration information during a
simulation.
See Also
atrace
11-33
minor
Purpose
11minor
Enable or disable minor step mode.
Syntax
minor
Description
The minor command causes the debugger to enter or exit minor step mode. In
minor step mode, the step command advances the simulation by blocks within
a minor step. In minor step mode, after executing the last block in the model’s
sorted block list, the step command advances the simulation to the next minor
time step, if any minor time steps remain in the current major time step;
otherwise, the step command advances the simulation to the first minor time
step in the next major time step.
See Also
step
11-34
nanbreak
Purpose
11nanbreak
Set or clear nonfinite value break mode.
Syntax
nanbreak
Description
The nanbreak command causes the debugger to break whenever the simulation
encounters a nonfinite (NaN or Inf) value. If nonfinite break mode is set,
nanbreak clears it.
See Also
break, bafter, xbreak, tbreak, zcbreak
11-35
next
Purpose
11next
Go to start of the next time step.
Syntax
next
Description
The next command evaluates all of the blocks remaining to be evaluated in the
current time step, stopping at the start of the next time step. After executing
the next command, the debugger highlights the first block to be evaluated on
the next time step and displays the time of the next step.
See Also
step
11-36
probe
Purpose
11probe
Display a block’s I/O.
Syntax
probe [<s:b | gcb>]
Arguments
s:b
The block whose system index is s and block index is b.
gcb
Current block.
Description
probe causes the debugger to enter or exit probe mode. In probe mode, the
debugger displays the I/O of any block you select. To exit probe mode, type any
command. probe gcb displays the I/O of the currently selected block. probe
s:b displays the I/O of the block whose index is s:b.
See Also
disp, trace
11-37
quit
Purpose
11quit
Abort simulation.
Syntax
quit
Description
The quit command terminates the current simulation.
See Also
stop
11-38
run
Purpose
11run
Run the simulation to completion.
Syntax
run
Description
The run command runs the simulation from the current breakpoint to its final
time step. It ignores breakpoints and display points.
See Also
continue, stop, quit
11-39
slist
Purpose
11slist
List a model’s nonvirtual blocks.
Syntax
slist
Description
The slist command lists the nonvirtual blocks in the model being debugged.
The list shows the block index and name of each listed block.
See Also
systems
11-40
states
Purpose
11states
Display current state values.
Syntax
states
Description
The states command displays a list of the current states of the model. The
display lists the value, index, and name of each state.
See Also
ishow
11-41
systems
Purpose
11systems
List a model’s nonvirtual systems.
Syntax
systems
Description
The systems command lists a model’s nonvirtual systems in the MATLAB
command window.
See Also
slist
11-42
status
Purpose
11status
Display debugging options in effect.
Syntax
status
Description
The status command displays a list of the debugging options in effect.
11-43
step
Purpose
11step
Step to next block.
Syntax
step
Description
The step command evaluates the next block to be evaluated in the current time
step. After executing the step command, the debugger highlights the next block
to be evaluated and its output signal lines. It also displays the name of the next
block as part of the debugger command-line prompt.
See Also
next
11-44
stop
Purpose
11stop
Stop the simulation.
Syntax
stop
Description
The stop command stops the simulation.
See Also
continue, run, quit
11-45
tbreak
Purpose
11tbreak
Set or clear a time breakpoint.
Syntax
tbreak t
tbreak
Description
The tbreak command sets a breakpoint at the specified time step. If a
breakpoint already exists at the specified time, tbreak clears the breakpoint.
If you do not specify a time, tbreak toggles a breakpoint at the current time
step.
See Also
break, bafter, xbreak, nanbreak, zcbreak
11-46
trace
Purpose
11trace
Display a block’s I/O each time the block executes.
Syntax
trace gcb
trace s:b
Arguments
s:b
The block whose system index is s and block index is b.
gcb
Current block.
Description
The trace command registers a block as a trace point. The debugger displays
the I/O of each registered block each time the block executes.
See Also
disp, probe, untrace, slist
11-47
undisp
Purpose
11undisp
Remove a block from the debugger’s list of display points.
Syntax
undisp gcb
undisp s:b
Arguments
s:b
The block whose system index is s and block index is b.
gcb
Current block.
Description
The undisp command removes the specified block from the debugger’s list of
display points.
See Also
disp, slist
11-48
untrace
Purpose
11untrace
Remove a block from the debugger’s list of trace points.
Syntax
untrace gcb
untrace s:b
Arguments
s:b
The block whose system index is s and block index is b.
gcb
Current block.
Description
The untrace command removes the specified block from the debugger’s list of
trace points.
See Also
trace, slist
11-49
xbreak
Purpose
11xbreak
Break when the debugger encounters a step-size-limiting state.
Syntax
xbreak
Description
The xbreak command pauses execution of the model when the debugger
encounters a state that limits the size of the steps that the solver takes. If
xbreak mode is already on, xbreak turns the mode off.
See Also
break, bafter, zcbreak, tbreak, nanbreak
11-50
zcbreak
Purpose
11zcbreak
Toggle breaking at nonsampled zero-crossing events.
Syntax
zcbreak
Description
The zcbreak command causes the debugger to break when a nonsampled
zero-crossing event occurs. If zero-crossing break mode is already on, zcbreak
turns the mode off.
See Also
break, bafter, xbreak, tbreak, nanbreak, zclist
11-51
zclist
Purpose
11zclist
List blocks containing nonsampled zero crossings.
Syntax
zclist
Description
The zclist command prints a list of blocks in which nonsampled zero crossings
can occur. The command prints the list in the MATLAB command window.
See Also
zcbreak
11-52
A
Model and Block
Parameters
Introduction . . . . . . . . . . . . . . . . . . . . A-2
Model Parameters
. . . . . . . . . . . . . . . . . A-3
Common Block Parameters . . . . . . . . . . . . . A-7
Block-Specific Parameters
. . . . . . . . . . . . . A-10
Mask Parameters . . . . . . . . . . . . . . . . . . A-24
A
Model and Block Parameters
Introduction
This appendix lists model, block, and mask parameters. The tables that list the
parameters provide enough information to enable you to modify models from
the command line, using the set_param command, described in Chapter 10.
A-2
Model Parameters
Model Parameters
This table lists and describes parameters that describe a model. The
parameters appear in the order they are defined in the model file, described in
Appendix B. The table also includes model callback parameters, described in
“Using Callback Routines” on page 3-53. The Description column indicates
where you can set the value on the Simulation Parameters dialog box. Model
parameters that are simulation parameters are described in more detail in
Chapter 4. Examples showing how to change parameters follow the table.
Parameter values must be specified as quoted strings. The string contents
depend on the parameter and can be numeric (scalar, vector, or matrix), a
variable name, a filename, or a particular value. The Values column shows the
type of value required, the possible values (separated with a vertical line), and
the default value, enclosed in braces.
Table A-1: Model Parameters
Parameter
Description
Values
Name
Model name
text
Version
Simulink version used to modify the
model (read-only)
(release)
SimParamPage
Simulation Parameters dialog box page
to display (page last displayed)
{Solver} | WorkspaceI/O |
Diagnostics
SampleTimeColors
Sample Time Colors menu option
on | {off}
InvariantConstants
Invariant constant setting
on | {off}
WideVectorLines
Wide Vector Lines menu option
on | {off}
ShowLineWidths
Show Line Widths menu option
on | {off}
PaperOrientation
Printing paper orientation
portrait | {landscape}
PaperPosition
Position of diagram on paper
[left, bottom, width, height]
PaperPositionMode
Paper position mode
auto | {manual}
PaperSize
Size of PaperType in PaperUnits
[width height] (read only)
A-3
A
Model and Block Parameters
Table A-1: Model Parameters (Continued)
A-4
Parameter
Description
Values
PaperType
Printing paper type
{usletter} | uslegal | a0 |
a1 | a2 | a3 | a4 | a5 | b0 |
b1 | b2 | b3 | b4 | b5 |
arch-A | arch-B | arch-C |
arch-D | arch-E | A | B | C |
D | E | tabloid
PaperUnits
Printing paper size units
normalized | {inches} |
centimeters | points
StartTime
Simulation start time
scalar {0.0}
StopTime
Simulation stop time
scalar {10.0}
Solver
Solver
{ode45} | ode23 | ode113 |
ode15s | ode23s | ode5 | ode4
| ode3 | ode2 | ode1 |
FixedStepDiscrete |
VariableStepDiscrete
RelTol
Relative error tolerance
scalar {1e–3}
AbsTol
Absolute error tolerance
scalar {1e–6}
Refine
Refine factor
scalar {1}
MaxStep
Maximum step size
scalar {auto}
InitialStep
Initial step size
scalar {auto}
FixedStep
Fixed step size
scalar {auto}
MaxOrder
Maximum order for ode15s
1 | 2 | 3 | 4 | {5}
OutputOption
Output option
AdditionalOutputTimes |
{RefineOutputTimes} |
SpecifiedOutputTimes
OutputTimes
Values for chosen OutputOption
vector {[]}
LoadExternalInput
Load input from workspace
on | {off}
ExternalInput
Time and input variable names
scalar or vector [t, u]
Model Parameters
Table A-1: Model Parameters (Continued)
Parameter
Description
Values
SaveTime
Save simulation time
{on} | off
TimeSaveName
Simulation time name
variable {tout}
SaveState
Save states
on | {off}
StateSaveName
State output name
variable {xout}
SaveOutput
Save simulation output
{on} | off
OutputSaveName
Simulation output name
variable {yout}
LoadInitialState
Load initial state
on | {off}
InitialState
Initial state name or values
variable or vector {xInitial}
SaveFinalState
Save final state
on | {off}
FinalStateName
Final state name
variable {xFinal}
LimitMaxRows
Limit output
on | {off}
MaxRows
Maximum number of output rows to save
scalar {1000}
Decimation
Decimation factor
scalar {1}
AlgebraicLoopMsg
Algebraic loop diagnostic
none | {warning} | error
MinStepSizeMsg
Minimum step size diagnostic
{warning} | error
UnconnectedInputMsg
Unconnected input ports diagnostic
none | {warning} | error
UnconnectedOutputMsg
Unconnected output ports diagnostic
none | {warning} | error
UnconnectedLineMsg
Unconnected lines diagnostic
none | {warning} | error
ConsistencyChecking
Consistency checking
on | {off}
ZeroCross
Intrinsic zero crossing detection (see “Zero
Crossings” on page 9-3)
{on} | off
CloseFcn
Close callback
command or variable
PreLoadFcn
Pre-load callback
command or variable
PostLoadFcn
Post-load callback
command or variable
A-5
A
Model and Block Parameters
Table A-1: Model Parameters (Continued)
Parameter
Description
Values
SaveFcn
Save callback
command or variable
StartFcn
Start simulation callback
command or variable
StopFcn
Stop simulation callback
command or variable
BooleanDataType
Enable Boolean mode
on | {off}
BufferReuse
Enable reuse of block I/O buffers
{on} | off
These examples show how to set model parameters for the mymodel system.
This command sets the simulation start and stop times.
set_param('mymodel','StartTime','5','StopTime','100')
This command sets the solver to ode15s and changes the maximum order.
set_param('mymodel','Solver','ode15s','MaxOrder','3')
This command associates a SaveFcn callback.
set_param('mymodel','SaveFcn','my_save_cb')
A-6
Common Block Parameters
Common Block Parameters
This table lists the parameters common to all Simulink blocks, including block
callback parameters, which are described in “Using Callback Routines” on page
3-53. Examples of commands that change these parameters follow this table.
Table A-2: Common Block Parameters
Parameter
Description
Values
Name
Block’s name
string
Type
Simulink object type
(read-only)
'block'
Parent
Name of the system that owns
the block
string
BlockType
Block type
text
BlockDescription
Block description
text
Description
User-specifiable description
text
InputPorts
Array of input port locations
[h1,v1; h2,v2; ...]
OutputPorts
Array of output port locations
[h1,v1; h2,v2; ...]
CompiledPortWidths
Structure of port widths
scalar and vector
Orientation
Where block faces
{right} | left | down | up
ForegroundColor
Block name, icon, outline,
output signals, and signal
label
{black} | white | red | green | blue |
cyan | magenta | yellow | gray |
lightBlue | orange | darkGreen
BackgroundColor
Block icon background
black | {white} | red | green | blue |
cyan | magenta | yellow | gray |
lightBlue | orange | darkGreen
DropShadow
Display drop shadow
{off} | on
NamePlacement
Position of block name
{normal} | alternate
FontName
Font
{Helvetica}
FontSize
Font size
{10}
A-7
A
Model and Block Parameters
Table A-2: Common Block Parameters (Continued)
Parameter
Description
Values
FontWeight
Font weight
(system-dependent) light | {normal} | demi
| bold
FontAngle
Font angle
(system-dependent) {normal} | italic |
oblique
A-8
Position
Position of block in model
window
vector [left top right bottom]
not enclosed in quotes
ShowName
Display block name
{on} | off
Tag
User-defined string
' '
UserData
Any MATLAB data type (not
saved in the mdl file)
[ ]
Selected
Block selected state
on | {off}
CloseFcn
Close callback
MATLAB expression
CopyFcn
Copy callback
MATLAB expression
DeleteFcn
Delete callback
MATLAB expression
InitFcn
Initialization callback
MATLAB expression
LoadFcn
Load callback
MATLAB expression
ModelCloseFcn
Model close callback
MATLAB expression
NameChangeFcn
Block name change callback
MATLAB expression
OpenFcn
Open callback
MATLAB expression
ParentCloseFcn
Parent subsystem close callback
MATLAB expression
PreSaveFcn
Pre-save callback
MATLAB expression
PostSaveFcn
Post-save callback
MATLAB expression
StartFcn
Start simulation callback
MATLAB expression
StopFcn
Termination of simulation
callback
MATLAB expression
Common Block Parameters
Table A-2: Common Block Parameters (Continued)
Parameter
Description
Values
UndoDeleteFcn
Undo block delete callback
MATLAB expression
LinkStatus
Link status of block.
none |resolved | unresolved | implicit
AttributesFormat
String
Specifies parameters to be displayed below block in a block
diagram
string
These examples illustrate how to change these parameters.
This command changes the orientation of the Gain block in the mymodel system
so it faces the opposite direction (right to left).
set_param('mymodel/Gain','Orientation','left')
This command associates an OpenFcn callback with the Gain block in the
mymodel system.
set_param('mymodel/Gain','OpenFcn','my_open_cb')
This command sets the Position parameter of the Gain block in the mymodel
system. The block is 75 pixels wide by 25 pixels high. The position vector is not
enclosed in quotes.
set_param('mymodel/Gain','Position',[50 250 125 275])
A-9
A
Model and Block Parameters
Block-Specific Parameters
These tables list block-specific parameters for all Simulink blocks. When
setting block parameters with the set_param command, you identify the block
by specifying its BlockType parameter. The BlockType appears in parentheses
after the block name.
The table includes detailed information only for built-in blocks, not for masked
blocks, although the table includes the MaskType parameter value for masked
blocks. For more information, see “Mask Parameters” on page A-24.
The Dialog Box Prompt column indicates the text of the prompt for the
parameter on the block’s dialog box. The Values column shows the type of
value required (scalar, vector, variable), the possible values (separated with a
vertical line), and the default value (enclosed in braces).
Table A-3: Sources Library Block Parameters
Block (BlockType)/Parameter
Dialog Box Prompt
Values
Band-Limited White Noise (Continuous White Noise) (masked)
Chirp Signal (chirp) (masked)
Clock (Clock) (no block-specific parameters)
Constant (Constant)
Value
Constant value
scalar or vector {1}
Sample time
scalar (sample period) {1}
or vector [period offset]
Filename
filename {untitled.mat}
Matrix table
matrix {[T,U]}
Digital Clock (DigitalClock)
SampleTime
Digital Pulse Generator
From File (FromFile)
FileName
From Workspace (FromWorkspace)
VariableName
A-10
Block-Specific Parameters
Table A-3: Sources Library Block Parameters (Continued)
Block (BlockType)/Parameter
Dialog Box Prompt
Values
Pulse Generator (Pulse Generator) (masked)
Ramp (Ramp) (masked)
Random Number (RandomNumber)
Seed
Initial seed
scalar or vector {0}
Repeating Sequence (Repeating table) (masked)
Signal Generator (SignalGenerator)
WaveForm
Wave form
{sine} | square | sawtooth |
random
Amplitude
Amplitude
scalar or vector {1}
Frequency
Frequency
scalar or vector {1}
Units
Units
{Hertz} | rad/sec
Amplitude
Amplitude
scalar or vector {1}
Frequency
Frequency
scalar or vector {1}
Phase
Phase
scalar or vector {0}
SampleTime
Sample time
scalar (sample period) {–1}
or vector [period offset]
Time
Step time
scalar or vector {1}
Before
Initial value
scalar or vector {0}
After
Final value
scalar or vector {1}
Sine Wave (Sin)
Step (Step)
Uniform Random Number (Uniform RandomNumber)
Minimum
Minimum
scalar or vector {–1}
Maximum
Maximum
scalar or vector {1}
A-11
A
Model and Block Parameters
Table A-3: Sources Library Block Parameters (Continued)
Block (BlockType)/Parameter
Dialog Box Prompt
Values
Seed
Initial Seed
scalar or vector {0}
SampleTime
Sample Time
scalar or vector {0}
Table A-4: Sinks Library Block Parameters
Block (BlockType)/Parameter
Dialog Box Prompt
Values
Format
Format
{short} | long | short_e | long_e
| bank
Decimation
Decimation
scalar {1}
Floating
Floating display
{off} on
SampleTime
Sample time
scalar (sample period) {–1}
or vector [period offset]
Location
Position of Scope window
on screen
vector {[left top right bottom]}
Open
(If Scope open when the
model is opened. Cannot
set from dialog box)
{off} | on
NumInputPorts
Number of Axes
positive integer > 0
TickLabels
Hide tick labels
{on} | off
ZoomMode
(Zoom button initially
pressed)
{on} | xonly | yonly
AxesTitles
Title (on right click axes)
scalar {auto}
Grid
(for future use)
{on} | off
TimeRange
Time range
scalar {auto}
Display (Display)
Scope (Scope)
A-12
Block-Specific Parameters
Table A-4: Sinks Library Block Parameters (Continued)
Block (BlockType)/Parameter
Dialog Box Prompt
Values
YMin
Y min
scalar {–5}
YMax
Y max
scalar {5}
SaveToWorkspace
Save data to workspace
{off} | on
SaveName
Variable name
variable {ScopeData}
DataFormat
Format
{matrix | structure}
LimitMaxRows
Limit rows to last
{on} | off
MaxRows
(no label)
scalar {5000}
Decimation
(Value if Decimation
selected)
scalar {1}
SampleInput
(Toggles with Decimation)
{off} | on
SampleTime
(SampleInput value)
scalar (sample period) {0}
or vector [period offset]
Stop Simulation (StopSimulation) (no block-specific parameters)
To File (ToFile)
Filename
Filename
filename {untitled.mat}
MatrixName
Variable name
variable {ans}
Decimation
Decimation
scalar {1}
SampleTime
Sample time
scalar (sample period) {–1}
or vector [period offset]
VariableName
Variable name
variable {simout}
Buffer
Maximum number of rows
scalar {inf}
Decimation
Decimation
scalar {1}
To Workspace (ToWorkspace)
A-13
A
Model and Block Parameters
Table A-4: Sinks Library Block Parameters (Continued)
Block (BlockType)/Parameter
SampleTime
Dialog Box Prompt
Values
Sample time
scalar (sample period) {–1}
or vector [period offset]
XY Graph (XY scope.) (masked)
Table A-5: Discrete Library Block Parameters
Block (BlockType)/Parameter
Dialog Box Prompt
Values
Numerator
Numerator
vector {[1]}
Denominator
Denominator
vector {[1 2]}
SampleTime
Sample time
scalar (sample period) {1}
or vector [period offset]
Discrete Filter (DiscreteFilter)
Discrete State-Space (DiscreteStateSpace)
A
A
matrix {1}
B
B
matrix {1}
C
C
matrix {1}
D
D
matrix {1}
X0
Initial conditions
vector {0}
SampleTime
Sample time
scalar (sample period) {1}
or vector [period offset]
Discrete-Time Integrator (DiscreteIntegrator)
A-14
IntegratorMethod
Integrator method
{ForwardEuler} | BackwardEuler |
Trapezoidal
ExternalReset
External reset
{none} | rising | falling | either
InitialConditionSource
Initial condition source
{internal} | external
InitialCondition
Initial condition
scalar or vector {0}
Block-Specific Parameters
Table A-5: Discrete Library Block Parameters (Continued)
Block (BlockType)/Parameter
Dialog Box Prompt
Values
LimitOutput
Limit output
{off} | on
UpperSaturationLimit
Upper saturation limit
scalar or vector {inf}
LowerSaturationLimit
Lower saturation limit
scalar or vector {–inf}
ShowSaturationPort
Show saturation port
{off} | on
ShowStatePort
Show state port
{off} | on
SampleTime
Sample time
scalar (sample period) {1}
or vector [period offset]
Discrete Transfer Fcn (DiscreteTransferFcn)
Numerator
Numerator
vector {[1]}
Denominator
Denominator
vector {[1 0.5]}
SampleTime
Sample time
scalar (sample period) {1}
or vector [period offset]
Discrete Zero-Pole (DiscreteZeroPole)
Zeros
Zeros
vector {[1]}
Poles
Poles
vector [0 0.5]
Gain
Gain
scalar {1}
SampleTime
Sample time
scalar (sample period) {1}
or vector [period offset]
First-Order Hold (First Order Hold) (masked)
Unit Delay (UnitDelay)
X0
Initial condition
scalar or vector {0}
SampleTime
Sample time
scalar (sample period) {1}
or vector [period offset]
Sample time
scalar (sample period) {1}
or vector [period offset]
Zero-Order Hold (ZeroOrderHold)
SampleTime
A-15
A
Model and Block Parameters
Table A-6: Continuous Library Block Parameters
Block (BlockType)/Parameter
Dialog Box Prompt
Values
Derivative (Derivative) (no block-specific parameters)
Integrator (Integrator)
ExternalReset
External reset
{none} | rising | falling | either
InitialConditionSource
Initial condition source
{internal} | external
InitialCondition
Initial condition
scalar or vector {0}
LimitOutput
Limit output
{off} | on
UpperSaturationLimit
Upper saturation limit
scalar or vector {inf}
LowerSaturationLimit
Lower saturation limit
scalar or vector {–inf}
ShowSaturationPort
Show saturation port
{off} | on
ShowStatePort
Show state port
{off} | on
AbsoluteTolerance
Absolute tolerance
scalar {auto}
X0
Initial condition
scalar or vector {0}
InheritSampleTime
Inherit sample time
{off} | on
A
A
matrix {1}
B
B
matrix {1}
C
C
matrix {1}
D
D
matrix {1}
X0
Initial conditions
vector {0}
Numerator
vector or matrix {[1]}
Memory (Memory)
State-Space (StateSpace)
Transfer Fcn (TransferFcn)
Numerator
A-16
Block-Specific Parameters
Table A-6: Continuous Library Block Parameters (Continued)
Block (BlockType)/Parameter
Dialog Box Prompt
Values
Denominator
vector {[1 1]}
DelayTime
Time delay
scalar or vector {1}
InitialInput
Initial input
scalar or vector {0}
BufferSize
Initial buffer size
scalar {1024}
Denominator
Transport Delay (TransportDelay)
Variable Transport Delay (VariableTransportDelay)
MaximumDelay
Maximum delay
scalar or vector {10}
InitialInput
Initial input
scalar or vector {0}
MaximumPoints
Buffer size
scalar {1024}
Zeros
Zeros
vector {[1]}
Poles
Poles
vector {[0 –1]}
Gain
Gain
vector {[1]}
Zero-Pole (ZeroPole)
Table A-7: Math Library Block Parameters
Block (BlockType)/Parameter
Dialog Box Prompt
Values
Abs (Abs) (no block-specific parameters)
Algebraic Constraint (Algebraic Constraint) (masked)
Combinatorial Logic (CombinatorialLogic)
TruthTable
Truth table
matrix {[0 0;0 1;0 1;1 0;
0 1;1 0;1 0;1 1]}
Complex to Magnitude-Angle
Complex to Real-Imag
A-17
A
Model and Block Parameters
Table A-7: Math Library Block Parameters (Continued)
Block (BlockType)/Parameter
Dialog Box Prompt
Values
Gain
scalar or vector {1}
Operator
Operator
{AND} | OR | NAND | NOR | XOR | NOT
Inputs
Number of input ports
scalar {2}
Function
{exp} | log | log10 | square | sqrt
| pow | reciprocal | hypot | rem |
mod
Function
Function
{min} | max
Inputs
Number of input ports
scalar {1}
Number of inputs
scalar {2}
Dot Product (Dot Product) (masked)
Gain (Gain)
Gain
Logical Operator (Logic)
Magnitude-Angle to Complex
Math Function (Math)
Operator
Matrix Gain (Matrix Gain) (masked)
MinMax (MinMax)
Product (Product)
Inputs
Relational Operator (RelationalOperator)
Operator
Operator
== | != | < | {<=} | >= | >
Relational Operator (RelationalOperator)
Operator
Operator
== | != | < | {<=} | >= | >
Function
{floor} | ceil | round | fix
Rounding Function (Rounding)
Operator
Sign (Signum) (no block-specific parameters)
Slider Gain (SliderGain) (masked)
A-18
Block-Specific Parameters
Table A-7: Math Library Block Parameters (Continued)
Block (BlockType)/Parameter
Dialog Box Prompt
Values
List of signs
scalar or list of signs {++}
Sum (Sum)
Inputs
Trigonometric Function (Trigonometry)
Operator
Function
{sin} | cos | tan | asin | acos |
atan | atan2 | sinh | cosh | tanh
Table A-8: Functions and Tables Block Parameters
Block (BlockType)/Parameter
Dialog Box Prompt
Values
Expression
expression
{sin(u(1)*exp(2.3*(–u(2))))}
InputValues
Vector of input values
vector {[–5:5]}
OutputValues
Vector of output values
vector {tanh([–5:5])}
Fcn (Fcn)
Expr
Look-up Table (Lookup)
Look-Up Table (2-D) (Lookup Table (2-D))
RowIndex
Row
vector
ColumnIndex
Column
vector
OutputValues
Table
2-D matrix
MATLABFcn
MATLAB function
MATLAB function {sin}
OutputWidth
Output width
scalar or vector {–1}
FunctionName
S-function name
name {system}
Parameters
S-function parameters
additional parameters if needed
MATLAB Fcn (MATLABFcn)
S-Function (S-Function)
A-19
A
Model and Block Parameters
Table A-9: Nonlinear Library Block Parameters
Block (BlockType)/Parameter
Dialog Box Prompt
Values
BacklashWidth
Deadband width
scalar or vector {1}
InitialOutput
Initial output
scalar or vector {0}
Backlash (Backlash)
Coulomb & Viscous Friction (Coulombic and Viscous Friction) (masked)
Dead Zone (DeadZone)
LowerValue
Start of dead zone
scalar or vector {–0.5}
UpperValue
End of dead zone
scalar or vector {0.5}
Number of inputs
scalar or vector {3}
Quantization interval
scalar or vector {0.5}
RisingSlewLimit
Rising slew rate
scalar or vector {1.}
FallingSlewLimit
Falling slew rate
scalar or vector {–1.}
OnSwitchValue
Switch on point
scalar or vector {eps}
OffSwitchValue
Switch off point
scalar or vector {eps}
OnOutputValue
Output when on
scalar or vector {1}
OffOutputValue
Output when off
scalar or vector {0}
UpperLimit
Upper limit
scalar or vector {0.5}
LowerLimit
Lower limit
scalar or vector {–0.5}
Manual Switch
Multiport Switch (MultiPortSwitch)
Inputs
Quantizer (Quantizer)
QuantizationInterval
Rate Limiter (RateLimiter)
Relay (Relay)
Saturation (Saturate)
S-Function (S-Function)
A-20
Block-Specific Parameters
Table A-9: Nonlinear Library Block Parameters (Continued)
Block (BlockType)/Parameter
Dialog Box Prompt
Values
FunctionName
S-function name
name {system}
Parameters
S-function parameters
additional parameters if needed
Sign (Signum) (no block-specific parameters)
Switch (Switch)
Threshold
Threshold
scalar or vector {0}
Table A-10: Signals & Systems Library Block Parameters
Block (BlockType)/Parameter
Dialog Box Prompt
Values
Choice
Block choice
string
LibraryName
Library name
string
Bus Selector
Configurable Subsystem (SubSystem)
Data Store Memory (DataStoreMemory)
DataStoreName
Data store name
tag {A}
InitialValue
Initial value
vector {0}
DataStoreName
Data store name
tag {A}
SampleTime
Sample time
scalar (sample period) {–1}
or vector [period offset]
DataStoreName
Data store name
tag {A}
SampleTime
Sample time
scalar (sample period) {–1}
or vector [period offset]
Data Store Read (DataStoreRead)
Data Store Write (DataStoreWrite)
Data Type Conversion
A-21
A
Model and Block Parameters
Table A-10: Signals & Systems Library Block Parameters (Continued)
Block (BlockType)/Parameter
Dialog Box Prompt
Values
Number of outputs
scalar or vector {3}
StatesWhenEnabling
States when enabling
{held} | reset
ShowOutputPort
Show output port
{off} | on
Goto tag
tag {A}
GotoTag
Tag
tag {A}
TagVisibility
Tag visibility
{local} | scoped | global
Demux (Demux)
Outputs
Enable (EnablePort)
From (From)
GotoTag
Goto (Goto)
Goto Tag Visibility (GotoTagVisibility)
GotoTag
Goto tag
tag {A}
Ground (Ground) (no block-specific parameters)
Hit Crossing (HitCross)
HitCrossingOffset
Hit crossing offset
scalar or vector {0}
HitCrossingDirection
Hit crossing direction
rising | falling | {either}
ShowOutputPort
Show output port
{on} | off
Initial value
scalar or vector {1}
Port
Port number
scalar {1}
PortWidth
Port width
scalar {–1}
SampleTime
Sample time
scalar (sample period) {–1}
or vector [period offset]
IC (InitialCondition)
Value
In (Inport)
A-22
Block-Specific Parameters
Table A-10: Signals & Systems Library Block Parameters (Continued)
Block (BlockType)/Parameter
Dialog Box Prompt
Values
Number of inputs
scalar or vector {3}
Port
Port number
scalar {1}
OutputWhenDisabled
Output when disabled
{held} | reset
InitialOutput
Initial output
scalar or vector {0}
ProbeWidth
Probe width
{on} | off
ProbeSampleTime
Probe sample time
{on} | off
ProbeCompexSignal
Probe complex signal
{on} | off
Show/Hide Port Labels
Format menu item
{on} | off
Merge
Model Info
Mux (Mux)
Inputs
Out (Outport)
Probe (Probe)
Subsystem (SubSystem)
ShowPortLabels
Terminator (Terminator) (no block-specific parameters)
Trigger (TriggerPort)
TriggerType
Trigger type
{rising} | falling | either |
function-call
ShowOutputPort
Show output port
{off} | on
Width (Width) (no block-specific parameters)
A-23
A
Model and Block Parameters
Mask Parameters
This section lists parameters that describe masked blocks. This table lists
masking parameters, which correspond to Mask Editor dialog box parameters.
Table A-11: Mask Parameters
Parameter
Dialog Box Parameter
Values
MaskType
Mask type
string
MaskDescription
Block description
string
MaskHelp
Block help
string
MaskPrompts
Prompt (see below)
cell array of strings
MaskPromptString
Prompt (see below)
delimited string
MaskStyles
Control type (see below)
cell array {Edit} | Checkbox | Popup
MaskStyleString
Control type (see below)
{Edit} | Checkbox | Popup
MaskVariables
Variable (see below)
string
MaskInitialization
Initialization commands
MATLAB command
MaskDisplay
Drawing commands
display commands
MaskIconFrame
Icon frame (Visible is on, Invisible is
off)
{on} | off
MaskIconOpaque
Icon transparency (Opaque is on,
Transparent is off)
{on} | off
MaskIconRotate
Icon rotation (Rotates is on, Fixed is
off)
on | {off}
MaskIconUnits
Drawing coordinates
Pixel | {Autoscale} | Normalized
MaskValues
Block parameter values (see below)
cell array of strings
MaskValueString
Block parameter values (see below)
delimited string
MaskTunableValues
Tunable parameter attributes
cell array of strings
MaskTunableValue
Tunable parameter attributes
delimited string
String
A-24
Mask Parameters
When you use the Mask Editor to create a dialog box parameter for a masked
block, you provide this information:
• The prompt, which you enter in the Prompt field
• The variable that holds the parameter value, which you enter in the
Variable field
• The type of field created, which you specify by selecting a Control type
• Whether the value entered in the field is to be evaluated or stored as a literal,
which you specify by selecting an Assignment type
The mask parameters, listed in the table on the previous page, store the values
specified for the dialog box parameters in these ways:
• The Prompt field values for all dialog box parameters are stored in the
MaskPromptString parameter as a string, with individual values separated
by a vertical bar (|), as shown in this example.
"Slope:|Intercept:"
• The Variable field values for all dialog box parameters are stored in the
MaskVariables parameter as a string, with individual assignments
separated by a semi-colon. A sequence number indicates which prompt is
associated with a variable. A special character preceding the sequence
number indicates the Assignment type: @ indicates Evaluate, & indicates
Literal.
For example, "[email protected];b=&2;" indicates that the value entered in the first
parameter field is assigned to variable a and is evaluated in MATLAB before
assignment, and the value entered in the second field is assigned to variable
b and is stored as a literal, which means that its value is the string entered
in the dialog box.
• The Control type field values for all dialog box parameters are stored in the
MaskStyleString parameter as a string, with individual values separated by
a comma. The Popup strings values appear after the popup type, as shown
in this example:
"edit,checkbox,popup(red|blue|green)"
• The parameter values are stored in the MaskValueString mask parameter
as a string, with individual values separated by a vertical bar. The order of
the values is the same as the order the parameters appear on the dialog box.
A-25
A
Model and Block Parameters
For example, these statements define values for the parameter field prompts
and the values for those parameters.
MaskPromptString
MaskValueString
A-26
"Slope:|Intercept:"
"2|5"
B
Model File Format
Model File Contents . .
Model Section . . . . . .
BlockDefaults Section . . .
AnnotationDefaults Section
System Section . . . . .
A Sample Model File
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B-2
B-3
B-3
B-3
B-3
. . . . . . . . . . . . . . . . B-4
B
Model File Format
Model File Contents
A model file is a structured ASCII file that contains keywords and
parameter-value pairs that describe the model. The file describes model
components in hierarchical order.
The structure of the model file is as follows.
Model {
<Model Parameter Name> <Model Parameter Value>
...
BlockDefaults {
<Block Parameter Name> <Block Parameter Value>
...
}
AnnotationDefaults {
<Annotation Parameter Name> <Annotation Parameter Value>
...
}
System {
<System Parameter Name> <System Parameter Value>
...
Block {
<Block Parameter Name> <Block Parameter Value>
...
}
Line {
<Line Parameter Name> <Line Parameter Value>
...
Branch {
<Branch Parameter Name> <Branch Parameter Value>
...
}
}
Annotation {
<Annotation Parameter Name> <Annotation Parameter Value>
...
}
}
}
B-2
Model File Contents
The model file consists of sections that describe different model components:
• The Model section defines model parameters.
• The BlockDefaults section contains default settings for blocks in the model.
• The AnnotationDefaults section contains default settings for annotations in
the model.
• The System section contains parameters that describe each system
(including the top-level system and each subsystem) in the model. Each
System section contains block, line, and annotation descriptions.
All model and block parameters are described in Appendix A.
Model Section
The Model section, located at the top of the model file, defines the values for
model-level parameters. These parameters include the model name, the
version of Simulink used to last modify the model, and simulation parameters.
BlockDefaults Section
The BlockDefaults section appears after the simulation parameters and
defines the default values for block parameters within this model. These values
can be overridden by individual block parameters, defined in the Block
sections.
AnnotationDefaults Section
The AnnotationDefaults section appears after the BlockDefaults section.
This section defines the default parameters for all annotations in the model.
These parameter values cannot be modified using the set_param command.
System Section
The top-level system and each subsystem in the model are described in a
separate System section. Each System section defines system-level parameters
and includes Block, Line, and Annotation sections for each block, line, and
annotation in the system. Each Line that contains a branch point includes a
Branch section that defines the branch line.
B-3
B
Model File Format
A Sample Model File
This model file describes the sample system that illustrates masking, described
in Chapter 6. The model and subsystem look like this.
The mx + b subsystem
B-4
A Sample Model File
The model file, mask_example.mdl, follows.
Model {
Name
"slopeintercept"
Version 3.00
SimParamPage "Solver"
SampleTimeColors off
InvariantConstants off
WideVectorLines off
ShowLineWidths off
ShowPortDataTypes off
StartTime "0.0"
StopTime "10.0"
SolverMode "Auto"
Solver "ode45"
RelTol "1e-3"
AbsTol "auto"
Refine "1"
MaxStep "auto"
InitialStep "auto"
FixedStep "auto"
MaxOrder 5
OutputOption "RefineOutputTimes"
OutputTimes "[]"
LoadExternalInput off
ExternalInput "[t, u]"
SaveTime on
TimeSaveName "tout"
SaveState off
StateSaveName "xout"
SaveOutput on
OutputSaveName "yout"
LoadInitialState off
InitialState "xInitial"
SaveFinalState off
FinalStateName "xFinal"
SaveFormat "Matrix"
LimitMaxRows off
MaxRows "1000"
Decimation "1"
B-5
B
Model File Format
AlgebraicLoopMsg "warning"
MinStepSizeMsg "warning"
UnconnectedInputMsg "warning"
UnconnectedOutputMsg "warning"
UnconnectedLineMsg "warning"
InheritedTsInSrcMsg "warning"
IntegerOverflowMsg "none"
UnnecessaryDatatypeConvMsg "none"
Int32ToFloatConvMsg "warning"
SignalLabelMismatchMsg "none"
ConsistencyChecking "off"
ZeroCross on
SimulationMode "normal"
BlockDataTips on
BlockParametersDataTip on
BlockAttributesDataTip off
BlockPortWidthsDataTip off
BlockDescriptionStringDataTipoff
BlockMaskParametersDataTip off
ToolBar on
StatusBar on
BrowserShowLibraryLinks off
BrowserLookUnderMasks off
OptimizeBlockIOStorage on
BufferReuse on
BooleanDataType off
RTWSystemTargetFile "grt.tlc"
RTWInlineParameters off
RTWRetainRTWFile off
RTWTemplateMakefile "grt_default_tmf"
RTWMakeCommand "make_rtw"
RTWGenerateCodeOnly off
ExtModeMexFile "ext_comm"
ExtModeBatchMode off
ExtModeTrigType "manual"
ExtModeTrigMode "oneshot"
ExtModeTrigPort "1"
ExtModeTrigElement "any"
ExtModeTrigDuration 1000
ExtModeTrigHoldOff 0
B-6
A Sample Model File
ExtModeTrigDelay 0
ExtModeTrigDirection "rising"
ExtModeTrigLevel 0
ExtModeArchiveMode "off"
ExtModeAutoIncOneShot off
ExtModeIncDirWhenArm off
ExtModeAddSuffixToVar off
ExtModeWriteAllDataToWs off
ExtModeArmWhenConnect off
Created "Tue Jul 28 15:18:08 1998"
Creator "JoeSchmo"
UpdateHistory "UpdateHistoryNever"
ModifiedByFormat "%<Auto>"
LastModifiedBy "MoeSchmo"
ModifiedDateFormat "%<Auto>"
LastModifiedDate "Fri Oct 30 15:17:59 1998"
ModelVersionFormat "1.%<AutoIncrement:4>"
ConfigurationManager "none"
BlockDefaults {
Orientation
"right"
ForegroundColor
"black"
BackgroundColor
"white"
DropShadow
off
NamePlacement
"normal"
FontName
"Helvetica"
FontSize
10
FontWeight
"normal"
FontAngle
"normal"
ShowName
on
}
AnnotationDefaults {
HorizontalAlignment
"center"
VerticalAlignment
"middle"
ForegroundColor
"black"
BackgroundColor
"white"
DropShadow
off
FontName
"Helvetica"
FontSize
10
FontWeight
"normal"
FontAngle
"normal"
B-7
B
Model File Format
}
LineDefaults {
FontName
"Helvetica"
FontSize
9
FontWeight
"normal"
FontAngle
"normal"
}
System {
Name
"slopeintercept"
Location
[629, 86, 984, 341]
Open
on
ModelBrowserVisibility off
ModelBrowserWidth
200
ScreenColor
"automatic"
PaperOrientation
"landscape"
PaperPositionMode
"auto"
PaperType
"usletter"
PaperUnits
"inches"
ZoomFactor
"100"
AutoZoom
on
ReportName
"simulink-default.rpt"
Block {
BlockType
Scope
Name
"Scope"
Ports
[1, 0, 0, 0, 0]
Position
[205, 79, 235, 111]
Floating
off
Location
[188, 365, 512, 604]
Open
off
NumInputPorts
"1"
TickLabels
"OneTimeTick"
ZoomMode
"on"
List {
ListTypeAxesTitles
axes1
"%<SignalLabel>"
}
Grid
"on"
TimeRange
"auto"
YMin
"-5"
YMax
"5"
B-8
A Sample Model File
SaveToWorkspace
off
SaveName
"ScopeData"
DataFormat
"StructureWithTime"
LimitMaxRows
on
MaxRows
"5000"
Decimation
"1"
SampleInput
off
SampleTime
"0"
}
Block {
BlockType
Sin
Name
"Sine Wave"
Position
[35, 80, 65, 110]
Amplitude
"1"
Frequency
"1"
Phase
"0"
SampleTime
"0"
}
Block {
BlockType
ToWorkspace
Name
"To Workspace"
Position
[200, 150, 260, 180]
VariableName
"simout"
Buffer
"inf"
Decimation
"1"
SampleTime
"-1"
SaveFormat
"Structure"
}
Block {
BlockType
SubSystem
Name
"mx + b"
Ports
[1, 1, 0, 0, 0]
Position
[105, 80, 135, 110]
ShowPortLabels
on
MaskType
"SampleMaskedBlock"
MaskDescription
"Models the equation for a line, y =
mx + b.\nTh"
"e slope and intercept are mask block parameters."
MaskHelp
"Enter the slope (m) and intercept (b) in the
bl"
B-9
B
Model File Format
"ock dialog parameter fields.\nThe block generates y for a given
input x."
MaskPromptString
"Slope:|Intercept:"
MaskStyleString
"edit,edit"
MaskTunableValueString "on,on"
MaskCallbackString
"|"
MaskEnableString
"on,on"
MaskVisibilityString
"on,on"
MaskVariables
"[email protected];[email protected];"
MaskDisplay
"plot([0 1],[0 m] + (m<0))"
MaskIconFrame
on
MaskIconOpaque
on
MaskIconRotate
"none"
MaskIconUnits
"normalized"
MaskValueString
" 4|2"
System {
Name
"mx + b"
Location[175, 110, 504, 342]
Open
off
ModelBrowserVisibilityoff
ModelBrowserWidth200
ScreenColor"white"
PaperOrientation"landscape"
PaperPositionMode"auto"
PaperType"usletter"
PaperUnits"inches"
ZoomFactor"100"
AutoZoomon
Block {
BlockType Inport
Name
"x"
Position [15, 68, 45, 82]
Port
"1"
PortWidth "-1"
SampleTime "-1"
DataType "auto"
SignalType "auto"
Interpolate on
}
Block {
B-10
A Sample Model File
BlockType Constant
Name
"Intercept"
Position [145, 130, 175, 160]
Orientation "up"
Value
"b"
}
Block {
BlockType Gain
Name
"Slope"
Position [80, 60, 110, 90]
Gain
"m"
SaturateOnIntegerOverflow on
}
Block {
BlockType Sum
Name
"Sum"
Ports
[2, 1, 0, 0, 0]
Position [145, 60, 175, 90]
NamePlacement "alternate"
IconShape "round"
Inputs "|++"
SaturateOnIntegerOverflow on
}
Block {
BlockType Outport
Name
"y"
Position [225, 68, 255, 82]
Port
"1"
OutputWhenDisabled "held"
InitialOutput "[]"
}
Line {
SrcBlock "Intercept"
SrcPort 1
DstBlock "Sum"
DstPort 2
}
Line {
SrcBlock "Sum"
SrcPort 1
B-11
B
Model File Format
DstBlock "y"
DstPort 1
}
Line {
SrcBlock "x"
SrcPort 1
DstBlock "Slope"
DstPort 1
}
Line {
SrcBlock "Slope"
SrcPort 1
DstBlock "Sum"
DstPort 1
}
}
}
Line {
SrcBlock
"Sine Wave"
SrcPort
1
DstBlock
"mx + b"
DstPort
1
}
Line {
SrcBlock
"mx + b"
SrcPort
1
Points
[25, 0]
Branch {
DstBlock"Scope"
DstPort
1
}
Branch {
Points
[0, 70]
DstBlock"To Workspace"
DstPort
1
}
}
Annotation {
Position
[135, 27]
Text
"Sample Masked Subsystem"
B-12
A Sample Model File
}
}
}
B-13
B
Model File Format
B-14
Index
A
Abs block 8-11
zero crossings 9-6
absolute tolerance 4-13, 4-32, 8-105
simulation accuracy 4-28
absolute value, generating 8-11
accuracy of derivative 8-49
accuracy of simulation 4-28
Ada Extension to Real-Time Workshop 1-12
Adams-Bashforth-Moulton PECE solver 4-11
add_block command 10-4
add_line command 10-5
adding
block inputs 8-191
blocks 10-4
lines 10-5
Algebraic Constraint block 8-12
algebraic equations, specifying 8-12
algebraic loops 9-7
detection 9-2
integrator block reset or IC port 8-60
simulation speed 4-28
alignment of blocks 3-11
analysis functions, perturbing model 8-100
AnnotationDefaults section of mdl file B-3
annotations
annotation block, see Model Info block 8-131
changing font 3-37
creating 3-37
definition 3-37
deleting 3-37
editing 3-37
manipulating with mouse and keyboard 3-49
moving 3-37
using to document models 3-57
Apply button on Mask Editor 6-9
ashow debug command 11-24
Assignment mask parameter 6-10
atrace debug command 11-25
attributes format string 3-18
AttributesFormatString block parameter 3-14,
3-17
Autoscale icon drawing coordinates 6-25
auto-scaling Scope axes 8-166
B
Backlash block 8-14
zero crossings 9-6
backpropagating sample time 9-17
Backspace key 3-14, 3-33, 3-37
Backward Euler method 8-59
Backward Rectangular method 8-59
bad link 3-22
bafter debug command 11-26
Band-Limited White Noise block 8-18, 8-150,
8-212
simulation speed 4-28
bdclose command 10-6
bdroot command 10-7
Block data tips 3-9
block descriptions
creating 6-6
entering 6-26
block diagrams, printing 3-62
block dialog boxes
closing 10-8
opening 3-13, 10-20
block icons
drawing coordinates 6-24
font 3-16
icon frame property 6-23
icon rotation property 6-24
I-1
Index
icon transparency property 6-24
properties 6-23
question marks in 6-21, 6-23
transfer functions on 6-21
block indexes 11-4
block libraries
Blocksets and Toolboxes 8-3
Demos 8-3
Discrete 8-5
Extras 8-3
Linear 8-5, 8-6
Nonlinear 8-7, 8-8
Sinks 8-4
Sources 8-3
block names
changing location 3-17
copied blocks 3-11
editing 3-16
flipping location 3-17
font 3-16
hiding and showing 3-17
location 3-16
newline character in 10-3
rules 3-16
sequence numbers 3-11, 3-12
slash character in 10-3
block parameters A-7, A-10-A-11
changing during simulation 10-24
Continuous library A-16
copying 3-11, 3-12
Discrete library A-14
displaying beneath a block icon 3-17
evaluating 9-2
Functions and Tables library A-19
Math library A-17
modifying 4-2
Nonlinear library A-20
I-2
prompts 6-10
scalar expansion 3-18, 3-19
Signals and Systems library A-21
Sinks library A-12
Sources library A-10
block priorities
assigning 3-19
block type of masked block 6-26
BlockDefaults section of mdl file B-3
blocks 3-9-3-20
adding to model 10-4
alignment 3-11
callback parameters 3-55
callback routines 3-53
connecting 2-10, 3-27
connections, checking 9-2
copying 3-26
copying from block library 3-22
copying into models 3-10
copying to other applications 3-12
current 10-14
deleting 3-14, 10-10
disconnecting 3-18
discrete 9-13
drop shadows 3-20
duplicating 3-12
grouping to create subsystem 3-52
handle of current 10-15
library 3-21
moving between windows 3-12
moving in a model 2-9, 3-12
orientation 3-15
path 10-3
reference 3-21, 3-22
replacing 10-21
resizing 3-15
reversing signal flow through 3-59
Index
signal flow through 3-15
under mask 6-9
updating 9-2
updating from library 3-23
vectorization 3-18
blocksets
DSP Blockset 1-14
Fixed-Point Blockset 1-14
Nonlinear Control Design Blockset 1-16
Power System Blockset 1-16
Blocksets and Toolboxes library 8-3
bode function 5-11
Bogacki-Shampine formula 4-11, 4-12
Boolean expressions, modeling 8-25
boolean type checking 4-26
bounding box
grouping blocks for subsystem 3-52
selecting objects 3-7
branch lines 3-28, 3-59
break debug command 11-27
Break Library Link menu item 3-24
breaking link to library block 3-23
breakpoints
clearing from blocks 11-11
setting 11-9
setting at beginning of a block 11-10
setting at end of block 11-11
setting at timesteps 11-11
setting on nonfinite values 11-11
setting on step-size limiting steps 11-12
setting on zero crossings 11-12
Browser 3-66
bshow debug command 11-28
building models
exercise 2-6
tips 3-57
C
callback parameters
block 3-55
model 3-54
callback routines 3-53
canceling a command 3-7
capping unconnected blocks 8-196
changing
annotations, font 3-37
block icons, font 3-16
block names, font 3-16
block names, location 3-17
block size 3-15
sample time during simulation 9-13
signal labels, font 3-33
check box control type 6-13
Chirp Signal block 8-22
clear debug command 11-29
Clear menu item 3-14
Clock block 8-24
example 5-3
Close Browser menu item 3-67
Close button on Mask Editor 6-9
Close menu item 2-3
Close Model menu item 3-67
close_system command 10-8
CloseFcn block callback parameter 3-55
CloseFcn model callback parameter 3-54
closing
block dialog boxes 10-8
model windows 10-6
system windows 10-8
clutch demo 8-96
colors for sample times 9-15
Combinatorial Logic block 8-25
combining input lines into vector line 8-136
Communications Toolbox 1-5
I-3
Index
Complex to Magnitude-Angle block 8-28
Complex to Real-Imag block 8-29
conditionally executed subsystems 7-2
Configurable Subsystem block 8-30
configuration manager 3-73
connecting blocks 2-10, 3-27
connecting lines to input ports 2-11
consistency checking 4-24
Constant block 8-34
constant sample time 9-11
constant value, generating 8-34
continue debug command 11-30
Continue menu item 4-5
Continuous block library
block parameters A-16
control input 7-2
control signal 7-2
Control System Toolbox 1-6
linearization 5-5
control type 6-12
check box 6-13
edit 6-12
pop-up 6-13
Copy menu item 3-11, 3-12
copy, definition 3-21
CopyFcn block callback parameter 3-55
copying
block parameters 3-11, 3-12
blocks 3-10
library block into a model 3-22
signal labels 3-33
Coulomb and Viscous Friction block 8-35
Create Mask menu item 6-9
Create Subsystem menu item 3-52, 8-190
Created model parameter 3-77
creating
annotations 3-37
I-4
block libraries 3-21
first mask prompt 6-11
masked block descriptions 6-6
masked block icons 6-6
models 3-3, 10-19
signal labels 3-33
subsystems 3-51-3-56
Creator model parameter 3-77
current block 10-14
handle 10-15
current system 10-16
Cut menu item 3-12, 3-14
D
Data Store Memory block 8-36
Data Store Read block 8-38
Data Store Write block 8-39
Data Type Conversion block 8-41
data types 3-38-3-45
displaying 3-43
propagation 3-43
specifying 3-43
dbstop if error command 6-17
dbstop if warning command 6-17
Dead Zone block 8-43
zero crossings 9-6
deadband 8-14
debug commands
ashow 11-24
atrace 11-25
bafter 11-26
break 11-27
bshow 11-28
clear 11-29
continue 11-30
disp 11-31
Index
help 11-32
ishow 11-33
minor 11-34
nanbreak 11-35
next 11-36
probe 11-37
quit 11-38
run 11-39
slist 11-40
states 11-41
status 11-43
step 11-44
stop 11-45
systems 11-42
tbreak 11-46
trace 11-47
undisp 11-48
untrace 11-49
xbreak 11-50
zcbreak 11-51
zclist 11-52
debugger
getting command help 11-4
starting 11-3
debugging initialization commands 6-17
decimation factor 4-32
saving simulation output 4-21
decision tables, modeling 8-25
default
solvers 4-10
defining
mask type 6-6, 6-26
masked block descriptions 6-26
masked block help text 6-6
delaying
and holding input signals 8-214
input by specified sample time 8-221
input by variable amount 8-216
Delete key 3-14, 3-33, 3-37
delete_block command 10-10
delete_line command 10-11
DeleteFcn block callback parameter 3-55
deleting
annotations 3-37
blocks 3-14, 10-10
lines 10-11
mask prompts 6-12
signal labels 3-33
demo model, running 2-2
Demos library 8-3
Demux block 8-45
Derivative block 8-49
linearization 5-5
derivatives
calculating 8-49, 9-3
limiting 8-152
Description model parameter 3-78
description of masked blocks 6-26
Diagnostics page of Simulation Parameter dialog
box 4-24
diagonal line segments 3-28
diagonal lines 3-27
dialogs
creating for masked blocks 6-28-6-30
Digital Clock block 8-51
direct feedthrough 9-2
disabled subsystem, output 7-4
disabling zero crossing detection 4-25, 9-5
disconnecting blocks 3-18
discontinuities
detecting 5-11
zero crossings 9-3
Discrete block library 8-5
block parameters A-14
I-5
Index
discrete blocks 9-13
in enabled subsystem 7-5
in triggered systems 7-10
Discrete Filter block 8-52
Discrete Pulse Generator block 8-54
discrete solver 4-10, 4-11, 4-12
Discrete State-Space block 8-56
discrete state-space model 5-10
Discrete Transfer Fcn block 8-65, 8-214
Discrete Zero-Pole block 8-67
Discrete-Time Integrator block 8-58
sample time colors 9-17
discrete-time systems 9-13
linearization 5-10
disp command 6-18
disp debug command 11-31
Display Alphabetical List menu item 3-67
Display block 8-69
Display Hierarchical List menu item 3-67
displaying
line widths 3-31
output trajectories 5-2
output values 8-69
signals graphically 8-163
transfer functions on masked block icons 6-21
vector signals 8-164
X-Y plot of signals 8-219
dlinmod function 5-4, 5-9, 5-10
dlinmod2 function 5-9
documentation page of Mask Editor 6-9
Dormand-Prince
formula 4-12
pair 4-11
Dot Product block 8-72
dpoly command 6-22
drawing coordinates 6-24
Autoscale 6-25
I-6
normalized 6-7, 6-25
Pixel 6-25
droots command 6-23
drop shadows 3-20
DSP Blockset 1-14
duplicating blocks 3-12
E
edit control type 6-12
editing
annotations 3-37
block names 3-16
mask prompts 6-11
models 3-3
signal labels 3-33
eigenvalues of linearized matrix 5-10
either trigger type 7-9
Elementary Math block
algebraic loops 9-7
Enable block 8-74
creating enabled subsystems 7-3
outputting enable signal 7-5
states when enabling 7-4
enabled subsystems 7-2, 7-3, 8-74
setting states 7-4
ending Simulink session 3-79
equations, modeling 3-58
equilibrium point determination 5-7
error tolerance 4-13
simulation accuracy 4-28
simulation speed 4-27
Euler’s method 4-12
eval command and masked block help 6-27
Evaluate Assignment type 6-10
examples
Clock block 5-3
Index
continuous system 3-59
converting Celsius to Fahrenheit 3-58
equilibrium point determination 5-7
linearization 5-4
masking 6-3
multirate discrete model 9-14
return variables 5-2
Scope block 5-2
To Workspace block 5-3
Transfer Function block 3-60
Exit MATLAB menu item 2-13, 3-79
Expand All menu item 3-67
Expand Library Links menu item 3-67
expressions, applying to block inputs 8-76, 8-121
external inputs 4-31
from workspace 8-100
extracting linear models 5-4, 5-9
Extras block library 8-3
F
falling trigger 7-9
Fcn block 8-76
compared to Math Function block 8-119
compared to Rounding Function block 8-161
compared to Trigonometric Function block
8-210
simulation speed 4-27
file
reading from 8-82
writing to 4-5, 8-197
final states, saving 4-21
Financial Toolbox 1-6
find_system command 10-12
finding library block 3-24
finding objects 10-12
Finite Impulse Response filter 8-52
finite-state machines, implementing 8-25
First-Order Hold block 8-78
compared to Zero-Order Hold block 8-78, 8-88
fixed icon rotation 6-24
fixed step size 4-13, 4-33
Fixed-Point Blockset 1-14
fixed-step solvers 4-9, 4-12
Flip Block menu item 3-15, 3-59
Flip Name menu item 3-17
flip-flops, implementing 8-25
floating Display block 4-2, 8-69
floating Scope block 4-2, 8-170
fohdemo demo 8-78, 8-88
font
annotations 3-37
block icons 3-16
block names 3-16
signal labels 3-33
Font menu item 3-16, 3-33
Forward Euler method 8-58
Forward Rectangular method 8-58
fprintf command 6-19
Frequency-Domain System Identification Toolbox
1-6
From block 8-80
From File block 8-82
From Workspace block 8-85
Function-Call Generator block 8-88
Functions and Tables block library
block parameters A-19
fundamental sample time 4-10
Fuzzy Logic Toolbox 1-6
G
Gain block 8-89
and algebraic loops 9-7
I-7
Index
gain, varying during simulation 8-183
Gaussian number generator 8-150
gcb command 10-14
gcbh command 10-15
gcs command 10-16
get_param command 10-17
checking simulation status 4-29
global Goto tag visibility 8-80, 8-91
Go To Library Link menu item 3-24
Goto block 8-91
Goto Tag Visibility block 8-94
Ground block 8-95
grouping blocks 3-51
H
handle of current block 10-15
handles on selected object 3-7
hardstop demo 8-96
held output of enabled subsystem 7-4
held states of enabled subsystem 7-5
Help button on Mask Editor 6-9
help debug command 11-32
help text for masked blocks 6-6, 6-27
Heun’s method 4-12
Hide Name menu item 3-17, 3-53, 8-140
Hide Port Labels menu item 3-53
hiding block names 3-17
hierarchy of model 3-57, 9-2
Higher-Order Spectral Analysis Toolbox 1-6
Hit Crossing block 8-96
zero crossing detection 4-25
zero crossings 9-4, 9-6
hybrid systems
integrating 9-17
linearization 5-10
simulating 9-13
I-8
I
IC block 8-98
icon frame mask property 6-23
icon page of Mask Editor 6-9
icon rotation mask property 6-24
icon transparency mask property 6-24
icons
creating for masked blocks 6-6, 6-18
displaying graphics on 6-20
displaying images on 6-21
displaying text on 6-18
transfer functions on 6-21
Image Processing Toolbox 1-6
improved Euler formula 4-12
inf values in mask plotting commands 6-21
Infinite Impulse Response filter 8-52
InitFcn block callback parameter 3-55
InitFcn model callback parameter 3-54
initial conditions
determining 4-22
setting 8-98
specifying 4-21
initial states 4-33
initial step size 4-12, 4-13, 4-33
simulation accuracy 4-28
initialization commands 6-15
debugging 6-17
initialization page of Mask Editor 6-9
Inport block 8-99
in subsystem 3-51, 3-52, 8-190
linearization 5-4
linmod function 5-9
supplying input to model 4-17
input ports, unconnected 8-95
inputs
adding 8-191
applying expressions to 8-76
Index
applying MATLAB function to 8-76, 8-121
choosing between 8-134
combining into vector line 8-136
constraining 8-12
delaying and holding 8-214
delaying by specified time 8-221
delaying by variable amount 8-216
external 4-31
from outside system 8-99
from previous time step 8-124
from workspace 8-100
generating step between two levels 8-187
loading from base workspace 4-17
logical operations on 8-108
mixing vector and scalar 3-18
multiplying 8-89
outputting minimum or maximum 8-129
passing through stair-step function 8-148
piecewise linear mapping 8-110, 8-113
plotting 8-219
reading from file 8-82
scalar expansion 3-18
sign of 8-177
vector or scalar 3-18
width of 8-218
inserting mask prompts 6-11
integration
block input 8-103
discrete-time 8-58
Integrator block 8-103
algebraic loops 9-7
example 3-59
sample time colors 9-17
simulation speed 4-28
zero crossings 9-6
invariant constants 9-11
invisible icon frame 6-23
ishow debug command 11-33
J
Jacobian matrices 4-12
Jacobians 5-9
K
keyboard actions, summary 3-48
keyboard command 6-17
L
labeling signals 3-32
labeling subsystem ports 3-53
LastModificationDate model parameter 3-78
left-hand approximation 8-58
libinfo command 3-24
libraries 3-21-3-26
creating 3-21
modifying 3-22
searching 3-25
library block
definition 3-21
finding 3-24
library blocks, getting information about 3-24
Library Browser 3-25
library, definition 3-21
limit rows to last check box 4-21
limiting
derivative of signal 8-152
integral 8-104
signals 8-162
line segments 3-28
creating 3-29
diagonal 3-28
I-9
Index
moving 3-29
line vertices, moving 3-31
Line Widths menu item 3-31
Linear block library 8-5, 8-6
linear models, extracting 5-4, 5-9
linearization 5-4, 5-9
discrete-time systems 5-10
linearized matrix, eigenvalues 5-10
lines 3-27-3-32
adding 10-5
branch 3-28, 3-59
carrying the same signal 2-11
connecting to input ports 2-11
deleting 10-11
diagonal 3-27
dividing into segments 3-29
manipulating with mouse and keyboard 3-48
signals carried on 4-2
widths, displaying 3-31
link
breaking 3-23
definition 3-21
to library block 3-22
unresolved 3-22
LinkStatus block parameter 3-23
linmod function 5-4, 5-9, 8-100
Transport Delay block 8-206
linmod2 function 5-11
Literal Assignment type 6-10
LMI Control Toolbox 1-7
load initial check box 4-22
LoadFcn block callback parameter 3-55
loading from base workspace 4-17
loading initial states 4-22
local Goto tag visibility 8-80, 8-91
location of block names 3-16, 3-17
logic circuits, modeling 8-25
I-10
Logical Operator block 8-108
Look Into System menu item 3-67
Look Under Mask Dialog menu item 3-67
Look Under Mask menu item 6-9
Look-Up Table (2-D) block 8-113
Look-Up Table block 8-110
loops, algebraic 9-7
lorenzs demo 8-219
M
Magnitude-Angle to Complex block 8-116
Manual Switch block 8-118
manual, organization 1-3
Mask Editor 6-9
mask help text 6-6
Mask Subsystem menu item 6-4, 6-9
mask type 6-6, 6-26
mask workspace 6-5, 6-15
masked blocks
block descriptions 6-6
control types 6-12
description 6-26
dialogs
creating dynamic 6-28-6-30
setting parameters for 6-28
documentation 6-26
help text 6-27
icons
creating 6-6, 6-18
displaying a transfer function on 6-22
displaying graphics on 6-20
displaying images on 6-21
displaying text on 6-18
setting properties of 6-23
initialization commands 6-15
looking under 6-9
Index
parameters 6-3, A-24
assigning values to 6-10
default values 6-14
predefined 6-29
prompts for 6-10
tunable 6-14
undefined 6-23
ports
displaying labels of 6-20
question marks in icon 6-21, 6-23
type 6-26
unmasking 6-9
Math block library
block parameters A-17
Math Function block 8-119
mathematical functions, performing 8-119, 8-161,
8-210
MATLAB Fcn block 8-121
simulation speed 4-27
MATLAB function, applying to block input 8-76,
8-121
Matrix Gain block 8-123
matrix, writing to 8-199
maximum number of output rows 4-33
maximum order of ode15s solver 4-14, 4-33
maximum step size 4-12, 4-13, 4-33
maximum step size parameter 4-13
mdl file 3-61, B-2
Memory block 8-124
simulation speed 4-27
memory issues 3-57
memory region, shared 8-36, 8-38, 8-39
menus 3-3
Merge block 8-126
MEX-file models, simulating 4-3
M-file models, simulating 4-3
M-file S-functions
simulation speed 4-27
M-files, running simulation from 4-3
MinMax block 8-129
zero crossings 9-6
minor debug command 11-34
mixed continuous and discrete systems 9-17
Model Browser 3-66
model files 3-61, B-2
names 3-61
Model Info block 8-131
model parameters for version control 3-77
Model Predictive Control Toolbox 1-7
ModelCloseFcn block callback parameter 3-55
modeling
equations 3-58
strategies 3-57
models
building 2-6
callback parameters 3-54
callback routines 3-53
closing 10-6
creating 3-3, 10-19
creating change histories for 3-76
editing 3-3
name, getting 10-7
organizing and documenting 3-57
parameters A-3
printing 3-62
properties of 3-72
saving 2-13, 3-61
selecting entire 3-8
simulating 4-30
tips for building 3-57
tracking versions of 3-70
version control properties of 3-77
ModelVersion model parameter 3-78
ModelVersionFormat model parameter 3-78
I-11
Index
ModifiedBy model parameter 3-77
ModifiedByFormat model parameter 3-77
ModifiedComment model parameter 3-78
ModifiedDate model parameter 3-78
ModifiedDateFormat model parameter 3-78
ModifiedHistory> model parameter 3-78
modifying libraries 3-22
Monte Carlo analysis 4-29
mouse actions, summary 3-48
MoveFcn block callback parameter 3-55
moving
annotations 3-37
blocks and lines 3-12
blocks between windows 3-12
blocks in a model 2-9, 3-12
line segments 3-29
line vertices 3-31
mask prompts 6-12
signal labels 3-33
Mu-Analysis and Synthesis Toolbox 1-7
multiplying block inputs
by constant, variable, or expression 8-89
by matrix 8-123
during simulation 8-183
together 8-143
Multiport Switch block 8-134
multirate systems 9-13, 9-14
linearization 5-10
Mux block 8-136
changing number of input ports 2-10
N
NAG Foundation Toolbox 1-7
NameChangeFcn block callback parameter 3-55
names
blocks 3-16
I-12
copied blocks 3-11
model files 3-61
Nan values in mask plotting commands 6-21
nanbreak debug command 11-35
Neural Network Toolbox 1-7
New Library menu item 3-21
New menu item 3-3
new_system command 3-21, 10-19
newline in block name 10-3
next debug command 11-36
Nonlinear block library 8-7, 8-8
block parameters A-20
Nonlinear Control Design Blockset 1-16
nonlinear systems, spectral analysis of 8-22
normalized icon drawing coordinates 6-7, 6-25
normally distributed random numbers 8-150
numerical differentiation formula 4-11
numerical integration 9-3
O
objects
finding 10-12
path 10-3
selecting more than one 3-7
selecting one 3-7
ode1 solver 4-12
ode113 solver 4-11
hybrid systems 9-17
Memory block 4-27, 8-124
ode15s solver 4-10, 4-11, 4-27
hybrid systems 9-17
maximum order 4-14, 4-33
Memory block 4-27, 8-124
unstable simulation results 4-28
ode2 solver 4-12
ode23 solver 4-11
Index
hybrid systems 9-17
ode23s solver 4-11, 4-14, 4-28
ode3 solver 4-12
ode4 solver 4-12
ode45 solver 4-10, 4-11
hybrid systems 9-17
ode5 solver 4-12
offset to sample time 9-13
opaque icon 6-24
Open menu item 3-3
Open System menu item 3-67
open_system command 10-20
OpenFcn block callback parameter 3-56, 3-68
OpenFcn model callback parameter 3-69
opening
block dialog boxes 3-13, 10-20
Simulink block library 10-26
Subsystem block 3-52
system windows 10-20
operating point 5-9
Optimization Toolbox 1-7
options structure
getting values 4-36
setting values 4-32
ordering of states 4-22
organization of manual 1-3
orientation of blocks 3-15
Outport block 8-139
example 5-2
in subsystem 3-51, 3-52, 8-190
linearization 5-4
linmod function 5-9
output
additional 4-16
between trigger events 7-10
disabled subsystem 7-4
displaying values of 8-69
enable signal 7-5
maximum rows 4-33
options 4-15
outside system 8-139
refine factor 4-34
saving to workspace 4-20
selected elements of input vector 8-173
smoother 4-16
specifying for simulation 4-16
specifying points 4-34
switching between inputs 8-194
switching between values 8-158
trajectories, viewing 5-2
trigger signal 7-10
variables 4-34
vector or scalar 3-18
writing to file 4-5, 8-197
writing to workspace 4-5, 4-20, 8-199
zero within range 8-43
output ports
capping unconnected 8-196
Enable block 7-5
Trigger block 7-10
P
PaperOrientation model parameter 3-64
PaperPosition model parameter 3-64
PaperPositionMode model parameter 3-64
PaperType model parameter 3-64
parameters
blocks A-7, A-10-A-11
getting values of 10-17
masked blocks A-24
model A-3
setting values of 10-24
Parameters menu item 2-12, 4-4, 4-8
I-13
Index
ParentCloseFcn block callback parameter 3-56
Partial Differential Equation Toolbox 1-8
Paste menu item 3-11, 3-12
path, specifying 10-3
Pause menu item 4-5
perturbation
factor 5-9
levels 5-12
phase-shifted wave 8-178
piecewise linear mapping 8-110, 8-113
Pixel icon drawing coordinates 6-25
plot command and masked block icon 6-20
plotting input signals 8-163, 8-219
pop-up control type 6-13
port labels 8-140, 8-190
displaying 6-20
ports
block orientation 3-15
labeling in subsystem 3-53
PostLoadFcn model callback parameter 3-54
PostSaveFcn block callback parameter 3-56
PostSaveFcn model callback parameter 3-54
PostScript file, printing to 3-64
Power System Blockset 1-16
PreLoadFcn model callback parameter 3-54
PreSaveFcn block callback parameter 3-56
PreSaveFcn model callback parameter 3-54
Print (Browser) menu item 3-67
print command 3-62
Print menu item 3-62
printing
block diagrams 3-62
to PostScript file 3-64
Priority block parameter 3-19
probe debug command 11-37
proceeding with suspended simulation 4-5
produce additional output option 4-16
I-14
produce specified output only option 4-16
Product block 8-143, 8-145
algebraic loops 9-7
programmable logic arrays, modeling 8-25
prompts
control types 6-12
creating 6-11
deleting 6-12
editing 6-11
inserting 6-11
masked block parameters 6-10
moving 6-12
propagation of signal labels 3-33
properties of Scope block 8-169
Pulse Generator block 8-146
purely discrete systems 9-13
Q
QFT Control Design Toolbox 1-8
Quantizer block 8-148
modeling A/D converter 8-221
question marks in masked block icon 6-21, 6-23
quit debug command 11-38
Quit MATLAB menu item 2-13, 3-79
R
randn function 8-150
random noise, generating 8-178
Random Number block 8-150
and Band-Limited White Noise block 8-18
simulation speed 4-28
random numbers, generating normally distributed
8-18
Rate Limiter block 8-152
reading data
Index
from data store 8-38
from file 8-82
from workspace 8-85
Real-Imag to Complex block 8-154
Real-Time Workshop 1-10
Real-Time Workshop Ada Extension 1-12
Redo menu item 3-5
reference block 3-22
definition 3-21
refine factor 4-16, 4-34
region of zero output 8-43
Relational Operator block 8-156
zero crossings 9-6
relative tolerance 4-13, 4-34
simulation accuracy 4-28
Relay block 8-158
zero crossings 9-6
Repeating Sequence block 8-160
replace_block command 10-21
replacing blocks in model 10-21
reset
output of enabled subsystem 7-4
states of enabled subsystem 7-5
resetting state 8-105
resizing blocks 3-15
return variables, example 5-2
reversing direction of signal flow 3-59
Revert button on Mask Editor 6-9
right-hand approximation 8-59
rising trigger 7-8, 7-9
Robust Control Toolbox 1-8
Rosenbrock formula 4-11
Rotate Block menu item 3-15
rotates icon rotation 6-24
Rounding Function block 8-161
run debug command 11-39
Runge-Kutta (2,3) pair 4-11
Runge-Kutta (4,5) formula 4-11
Runge-Kutta fourth-order formula 4-12
running the simulation 2-12
S
sample model 2-6
sample time 9-13
backpropagating 9-17
changing during simulation 9-13
colors 9-15
constant 9-11
fundamental 4-10
offset 9-13
parameter 9-13
simulation speed 4-27
Sample Time Colors menu item 9-12, 9-16
sample-and-hold, applying to block input 8-124
sample-and-hold, implementing 8-221
sampled data systems 9-13
sampling interval, generating simulation time
8-51
Saturation block 8-162
zero crossings 9-4, 9-6
Save As menu item 3-61
Save menu item 2-13, 3-61
save options area 4-20
save to workspace area 4-20
save_system command 3-24, 10-23
saving
axes settings on Scope 8-168
final states 4-21, 4-22
models 2-13, 3-61
output to workspace 4-20
systems 10-23
sawtooth wave, generating 8-178
scalar expansion 3-18
I-15
Index
Scope block 8-163
example 3-60, 5-2
properties 8-169
scoped Goto tag visibility 8-80, 8-91
Select All menu item 3-8
selecting
model 3-8
more than one object 3-7
one object 3-7
Selector block 8-173
separating vector signal 8-45
sequence numbers on block names 3-11, 3-12
sequence of signals 8-54, 8-146, 8-160
sequential circuits, implementing 8-27
Set Font dialog box 3-16
set_param command 3-24, 10-24
running a simulation 4-29
setting breakpoints 11-9
setting parameter values 10-24
S-Function block 8-175
Shampine, L. F. 4-12
shared data store 8-36, 8-38, 8-39
Show Browser menu item 3-67
Show Name menu item 3-17
show output port
Enable block 7-5
Trigger block 7-10
showing block names 3-17
Sign block 8-177
zero crossings 9-6
signal flow through blocks 3-15
Signal Generator block 8-178
signal labels
changing font 3-33
copying 3-33
creating 3-33
deleting 3-33
I-16
editing 3-33
moving 3-33
propagation 3-33
using to document models 3-57
Signal Processing Toolbox 1-8
signal properties
setting 3-34
Signal Properties Dialog 3-35
signals 3-27
delaying and holding 8-214
displaying vector 8-164
labeling 3-32
limiting 8-162
limiting derivative of 8-152
passed from Goto block 8-80
passing to From block 8-91
plotting 8-163, 8-219
pulses 8-54, 8-146
repeating 8-160
vector 3-18
Signals and Systems block library
block parameters A-21
sim command 4-29, 4-30
simget command 4-36
simset command 4-32
simulating models 4-30
simulation
accuracy 4-28
command line 4-29
Index
displaying information about
algebraic loops 11-13, 11-14, 11-20
block execution order 11-17
block I/O 11-13
debug settings 11-21
integration 11-15
nonvirtual blocks 11-18
nonvirtual systems 11-18
system states 11-15
zero crossings 11-20
menu 4-4
proceeding with suspended 4-5
running 2-12
running incrementally 11-6
speed 4-27
starting 4-4
stepping by blocks 11-6
stepping by breakpoints 11-8
stepping by time steps 11-7
stopping 2-13, 4-5, 8-189
suspending 4-5
Simulation Diagnostics Dialog Box 4-6
simulation parameters 4-8
setting 4-4
specifying 2-12, 4-4
specifying using simset command 4-32
Simulation Parameters dialog box 2-12, 4-4,
4-8-4-25, A-3
simulation time
compared to clock time 4-9
generating at sampling interval 8-51
outputting 8-24
writing to workspace 4-20
Simulink
ending session 3-79
icon 3-2
menus 3-3
Real-Time Workshop 1-10
starting 3-2
windows and screen resolution 3-5
Simulink block library 3-2
opening 10-26
simulink command 3-2, 10-26
sine wave
generating 8-178, 8-180
generating with increasing frequency 8-22
Sine Wave block 8-180
Sinks block library 8-4
block parameters A-12
size of block, changing 3-15
sizes vector 4-22
slash in block name 10-3
sldebug command 11-3
Slider Gain block 8-183
slist debug command 11-40
Solver page of Simulation Parameters dialog box
4-8
solver properties, specifying 4-32
solvers 4-9-4-12
changing during simulation 4-2
choosing 4-4
default 4-10
discrete 4-10, 4-11, 4-12
fixed-step 4-9, 4-12
ode1 4-12
ode113 4-11, 4-27
ode15s 4-10, 4-11, 4-14, 4-27, 4-28
ode2 4-12
ode23 4-11
ode23s 4-11, 4-14, 4-28
ode3 4-12
ode4 4-12
ode45 4-10, 4-11
ode5 4-12
I-17
Index
specifying using simset command 4-34
variable-step 4-9, 4-11
Sources block library 8-3
block parameters A-10
spectral analysis of nonlinear systems 8-22
speed of simulation 4-27
Spline Toolbox 1-8
square wave, generating 8-178
ss2tf function 5-12
ss2zp function 5-12
stairs function 9-14
stair-step function, passing signal through
8-148
Start menu item 2-2, 2-12, 3-59, 4-4
start time 4-9
StartFcn block callback parameter 3-56
StartFcn model callback parameter 3-54
starting Simulink 3-2
state derivatives, setting to zero 5-13
state events 9-3
state space in discrete system 8-56
states
absolute tolerance for 8-105
between trigger events 7-10
determining 9-3
initial 4-22, 4-33
loading initial 4-22
ordering of 4-22
outputting 4-34
resetting 8-105
saving at end of simulation 4-33
saving final 4-21, 4-22
updating 9-13
when enabling 7-4
writing to workspace 4-20
states debug command 11-41
State-Space block 8-185
I-18
algebraic loops 9-7
Statistics Toolbox 1-9
Status bar 3-5
status debug command 11-43
Step block 8-187
zero crossings 9-6
step debug command 11-44
step size 4-12
accuracy of derivative 8-49
simulation speed 4-27
stiff problems 4-12
stiff systems and simulation time 4-27
stop debug command 11-45
Stop menu item 2-3, 2-13, 4-5
Stop Simulation block 8-189
stop time 4-9
Stop Time parameter 2-13
StopFcn block callback parameter 3-56
StopFcn model callback parameter 3-54
stopping simulation 8-189
Subsystem block 8-190
adding to create subsystem 3-51
opening 3-52
zero crossings 9-7
subsystems
and Inport blocks 8-99
creating 3-51-3-56
labeling ports 3-53
model hierarchy 3-57
path 10-3
underlying blocks 3-52
Sum block 8-191
algebraic loops 9-7
summary of mouse and keyboard actions 3-48
suspending simulation 4-5
Switch block 8-194
zero crossings 9-7
Index
switching output between inputs 8-118, 8-194
switching output between values 8-158
Symbolic Math Toolbox 1-9
System Identification Toolbox 1-9
System section of mdl file B-3
systems
current 10-16
path 10-3
systems debug command 11-42
T
tbreak debug command 11-46
terminating MATLAB 2-13
terminating Simulink 2-13
terminating Simulink session 3-79
Terminator block 8-196
text command 6-18
tf2ss utility 8-203
time delay, simulating 8-206
time interval and simulation speed 4-27
tips for building models 3-57
To File block 8-197
To Workspace block 8-199
example 5-3
toolboxes 1-5
Communications Toolbox 1-5
Control System Toolbox 1-6
Financial Toolbox 1-6
Frequency-Domain System Identification Toolbox 1-6
Fuzzy Logic Toolbox 1-6
Higher-Order Spectral Analysis Toolbox 1-6
Image Processing Toolbox 1-6
LMI Control Toolbox 1-7
Model Predictive Control Toolbox 1-7
Mu-Analysis and Synthesis Toolbox 1-7
NAG Foundation Toolbox 1-7
Neural Network Toolbox 1-7
Optimization Toolbox 1-7
Partial Differential Equation Toolbox 1-8
QFT Control Design Toolbox 1-8
Robust Control Toolbox 1-8
Signal Processing Toolbox 1-8
Spline Toolbox 1-8
Statistics Toolbox 1-9
Symbolic Math Toolbox 1-9
System Identification Toolbox 1-9
Wavelet Toolbox 1-9
trace debug command 11-47
tracing facilities 4-34
Transfer Fcn block 8-203
algebraic loops 9-7
example 3-60
linearization 5-5
transfer function form, converting to 5-12
transfer functions
discrete 8-65
linear 8-203
masked block icons 6-21
poles and zeros 8-222
poles and zeros, discrete 8-67
transparent icon 6-24
Transport Delay block 8-206
linearization 5-5
Trapezoidal method 8-59
trigger
control signal, outputting 7-10
events 7-2, 7-8
falling 7-9
input 7-8
rising 7-8, 7-9
type parameter 7-9
Trigger block 8-208
I-19
Index
creating triggered subsystem 7-9
outputting trigger signal 7-10
showing output port 7-10
trigger type
either 7-9
triggered and enabled subsystems 7-2, 7-11
triggered subsystems 7-2, 7-8, 8-208
Trigonometric Function block 8-210
trim function 5-7, 5-13, 8-100
truth tables, implementing 8-25
tunable parameters 6-14
U
unconnected input ports 8-95
unconnected output ports, capping 8-196
undisp debug command 11-48
Undo menu item 3-7
UndoDeleteFcn block callback parameter 3-56
Uniform Random Number block 8-212
uniformly distributed random numbers 8-212
Unit Delay block 8-214
compared to Transport Delay block 8-206
Unmask button on Mask Editor 6-9
unresolved link 3-22
unstable simulation results 4-28
untrace debug command 11-49
Update Diagram menu item 3-18, 3-23, 3-34,
9-16, 10-24
updating linked blocks 3-23
updating states 9-13
URL specification in block help 6-27
user
specifying current 3-70
I-20
V
variable time delay 8-216
Variable Transport Delay block 8-216
variable-step solvers 4-9, 4-11
vdp model
initial conditions 4-23
using Scope block 8-165
vector length, checking 9-2
vector signals
displaying 8-164
generating from inputs 8-136
separating 8-45
vectorization of blocks 3-18
version control model parameters 3-77
vertices, moving 3-31
viewing output trajectories 5-2
virtual blocks 3-9
viscous friction 8-35
visibility of Goto tag 8-94
visible icon frame 6-23
W
Wavelet Toolbox 1-9
web command and masked block help 6-27
white noise, generating 8-18
Wide Vector Lines menu item 3-18
Width block 8-218
workspace
destination 4-33
loading from 4-17
mask 6-5, 6-15
reading data from 8-85
saving to 4-20
source 4-34
writing output to 8-199
writing to 4-5
Index
Workspace I/O page of Simulation Parameters dialog box 4-17
writing
data to data store 8-39
output to file 8-197
output to workspace 8-199
X
xbreak debug command 11-50
XY Graph block 8-219
Z
zcbreak debug command 11-51
zclist debug command 11-52
zero crossings 9-3-9-7
detecting 4-35, 8-96
disabling detection of 4-25
zero output in region, generating 8-43
zero-crossing slope method 7-3
Zero-Order Hold block 8-214, 8-221
compared to First-Order Hold block 8-78, 8-88
Zero-Pole block 8-222
algebraic loops 9-7
zero-pole form, converting to 5-12
Zooming block diagrams 3-6
zooming in on displayed data 8-166
I-21
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