User`s guide | Simscape User`s Guide

Simscape™
User's Guide
R2015a
How to Contact MathWorks
Latest news:
www.mathworks.com
Sales and services:
www.mathworks.com/sales_and_services
User community:
www.mathworks.com/matlabcentral
Technical support:
www.mathworks.com/support/contact_us
Phone:
508-647-7000
The MathWorks, Inc.
3 Apple Hill Drive
Natick, MA 01760-2098
Simscape™ User's Guide
© COPYRIGHT 2007–2015 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.
FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program and Documentation
by, for, or through the federal government of the United States. By accepting delivery of the Program
or Documentation, the government hereby agrees that this software or documentation qualifies as
commercial computer software or commercial computer software documentation as such terms are used
or defined in FAR 12.212, DFARS Part 227.72, and DFARS 252.227-7014. Accordingly, the terms and
conditions of this Agreement and only those rights specified in this Agreement, shall pertain to and
govern the use, modification, reproduction, release, performance, display, and disclosure of the Program
and Documentation by the federal government (or other entity acquiring for or through the federal
government) and shall supersede any conflicting contractual terms or conditions. If this License fails
to meet the government's needs or is inconsistent in any respect with federal procurement law, the
government agrees to return the Program and Documentation, unused, to The MathWorks, Inc.
Trademarks
MATLAB and Simulink are registered trademarks of The MathWorks, Inc. See
www.mathworks.com/trademarks for a list of additional trademarks. Other product or brand
names may be trademarks or registered trademarks of their respective holders.
Patents
MathWorks products are protected by one or more U.S. patents. Please see
www.mathworks.com/patents for more information.
Revision History
March 2007
September 2007
March 2008
October 2008
March 2009
September 2009
March 2010
September 2010
April 2011
September 2011
March 2012
September 2012
March 2013
September 2013
March 2014
October 2014
March 2015
Online only
Online only
Online only
Online only
Online only
Online only
Online only
Online only
Online only
Online only
Online only
Online only
Online only
Online only
Online only
Online only
Online only
New for Version 1.0 (Release 2007a)
Revised for Version 2.0 (Release 2007b)
Revised for Version 2.1 (Release 2008a)
Revised for Version 3.0 (Release 2008b)
Revised for Version 3.1 (Release 2009a)
Revised for Version 3.2 (Release 2009b)
Revised for Version 3.3 (Release 2010a)
Revised for Version 3.4 (Release 2010b)
Revised for Version 3.5 (Release 2011a)
Revised for Version 3.6 (Release 2011b)
Revised for Version 3.7 (Release 2012a)
Revised for Version 3.8 (Release 2012b)
Revised for Version 3.9 (Release 2013a)
Revised for Version 3.10 (Release 2013b)
Revised for Version 3.11 (Release 2014a)
Revised for Version 3.12 (Release 2014b)
Revised for Version 3.13 (Release 2015a)
Contents
1
Model Construction
Basic Principles of Modeling Physical Networks . . . . . . . . .
Overview of the Physical Network Approach to Modeling
Physical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Variable Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Building the Mathematical Model . . . . . . . . . . . . . . . . . . . . .
Direction of Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Connector Ports and Connection Lines . . . . . . . . . . . . . . . . .
Connecting Simscape Diagrams to Simulink Sources and
Scopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1-2
1-2
1-4
1-5
1-6
1-8
1-9
Simscape Block Libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Library Structure Overview . . . . . . . . . . . . . . . . . . . . . . . .
Using the Simulink Library Browser to Access the Block
Libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Using the Command Prompt to Access the Block Libraries .
1-12
1-13
Essential Physical Modeling Techniques . . . . . . . . . . . . . . .
Building Your Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Using the Conserving Ports . . . . . . . . . . . . . . . . . . . . . . . . .
Using the Physical Signal Ports . . . . . . . . . . . . . . . . . . . . .
1-15
1-15
1-16
1-16
Creating and Simulating a Simple Model . . . . . . . . . . . . . . .
Building a Simscape Diagram . . . . . . . . . . . . . . . . . . . . . . .
Modifying Initial Settings . . . . . . . . . . . . . . . . . . . . . . . . . .
Running the Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . .
Adjusting the Parameters . . . . . . . . . . . . . . . . . . . . . . . . . .
1-18
1-18
1-26
1-28
1-30
Modeling Best Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Grounding Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Avoiding Numerical Simulation Issues . . . . . . . . . . . . . . . .
1-36
1-36
1-40
Domain-Specific Line Styles . . . . . . . . . . . . . . . . . . . . . . . . . .
1-43
1-11
1-11
v
Modeling Pneumatic Systems . . . . . . . . . . . . . . . . . . . . . . . .
Intended Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Assumptions and Limitations . . . . . . . . . . . . . . . . . . . . . . .
Fundamental Equations . . . . . . . . . . . . . . . . . . . . . . . . . . .
Network Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Connection Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
vi
Contents
1-45
1-45
1-45
1-46
1-47
1-47
1-48
Thermal Liquid Models
Modeling Thermal Liquid Systems . . . . . . . . . . . . . . . . . . . . .
When to Use Thermal Liquid Blocks . . . . . . . . . . . . . . . . . . .
Modeling Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Establish Model Requirements . . . . . . . . . . . . . . . . . . . . . . .
Model Physical Components . . . . . . . . . . . . . . . . . . . . . . . . .
Prepare Model for Analysis . . . . . . . . . . . . . . . . . . . . . . . . . .
Run Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-2
2-2
2-3
2-3
2-4
2-5
2-5
Thermal Liquid Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Why Use Thermal Liquid Blocks? . . . . . . . . . . . . . . . . . . . . .
Representing Thermal Liquid Components . . . . . . . . . . . . . .
Specifying Thermal Liquid Medium . . . . . . . . . . . . . . . . . . .
Modeling Multidomain Systems . . . . . . . . . . . . . . . . . . . . . .
2-6
2-6
2-6
2-8
2-8
Thermal Liquid Modeling Framework . . . . . . . . . . . . . . . . .
How Blocks Represent Components . . . . . . . . . . . . . . . . . .
How Ports Represent Interfaces . . . . . . . . . . . . . . . . . . . . .
Full Flux Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-10
2-10
2-11
2-12
Heat Transfer in Insulated Oil Pipeline . . . . . . . . . . . . . . . .
Oil Pipelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Modeling Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simscape Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Run Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Run Optimization Script . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-14
2-14
2-15
2-17
2-18
2-25
3
Model Simulation
How Simscape Models Represent Physical Systems . . . . . . .
Representations of Physical Systems . . . . . . . . . . . . . . . . . . .
Differential, Differential-Algebraic, and Algebraic Systems . .
Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Events and Zero Crossings . . . . . . . . . . . . . . . . . . . . . . . . . .
Working with Simscape Representation . . . . . . . . . . . . . . . .
3-2
3-2
3-2
3-3
3-3
3-3
How Simscape Simulation Works . . . . . . . . . . . . . . . . . . . . . .
Simscape Simulation Phases . . . . . . . . . . . . . . . . . . . . . . . . .
Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Network Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Equation Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Initial Conditions Computation . . . . . . . . . . . . . . . . . . . . . . .
Transient Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Transient Solve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-5
3-5
3-7
3-7
3-8
3-8
3-9
3-10
Setting Up Solvers for Physical Models . . . . . . . . . . . . . . . .
About Simulink and Simscape Solvers . . . . . . . . . . . . . . . .
Choosing Simulink and Simscape Solvers . . . . . . . . . . . . . .
Harmonizing Simulink and Simscape Solvers . . . . . . . . . . .
3-11
3-11
3-11
3-13
Customizing Solvers for Physical Models . . . . . . . . . . . . . . .
Important Concepts and Choices in Physical Simulation . . .
Making Optimal Solver Choices for Physical Simulation . . .
3-17
3-17
3-20
Troubleshooting Simulation Errors . . . . . . . . . . . . . . . . . . .
Troubleshooting Tips and Techniques . . . . . . . . . . . . . . . . .
System Configuration Errors . . . . . . . . . . . . . . . . . . . . . . . .
Numerical Simulation Issues . . . . . . . . . . . . . . . . . . . . . . .
Initial Conditions Solve Failure . . . . . . . . . . . . . . . . . . . . .
Transient Simulation Issues . . . . . . . . . . . . . . . . . . . . . . . .
3-25
3-25
3-26
3-28
3-29
3-29
Code Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
About Code Generation from Simscape Models . . . . . . . . . .
Reasons for Generating Code . . . . . . . . . . . . . . . . . . . . . . .
Using Code-Related Products and Features . . . . . . . . . . . . .
How Simscape Code Generation Differs from Simulink . . . .
3-31
3-31
3-31
3-32
3-32
vii
viii
Contents
Real-Time Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
What Is Real-Time Simulation? . . . . . . . . . . . . . . . . . . . . .
Requirements for Real-Time Simulation . . . . . . . . . . . . . . .
Simulating Physical Models in Real Time . . . . . . . . . . . . . .
Preparing a Model for Real-Time Simulation . . . . . . . . . . .
Troubleshooting Real-Time Simulation Problems . . . . . . . .
3-34
3-34
3-35
3-36
3-37
3-40
Finding an Operating Point . . . . . . . . . . . . . . . . . . . . . . . . . .
What Is an Operating Point? . . . . . . . . . . . . . . . . . . . . . . . .
Finding Operating Points in Physical Models . . . . . . . . . . .
3-43
3-43
3-44
Linearizing at an Operating Point . . . . . . . . . . . . . . . . . . . .
What Is Linearization? . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Linearizing a Physical Model . . . . . . . . . . . . . . . . . . . . . . .
3-48
3-48
3-50
Linearize an Electronic Circuit . . . . . . . . . . . . . . . . . . . . . . .
Explore the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Linearize with Steady-State Solver and linmod Function . . .
Linearize with Simulink Control Design Software . . . . . . . .
Use Control System Toolbox Software for Bode Analysis . . .
3-54
3-54
3-58
3-60
3-61
Linearize a Plant Model for Use in Feedback Control
Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Explore the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Trim Using the Controller and Linearize with Simulink linmod
Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Linearize with Simulink Control Design Software . . . . . . . .
3-66
3-68
Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sample Time and Solver Restrictions . . . . . . . . . . . . . . . . .
Algebraic Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Restricted Simulink Tools . . . . . . . . . . . . . . . . . . . . . . . . . .
Unsupported Simulink Tools . . . . . . . . . . . . . . . . . . . . . . . .
Simulink Tools Not Compatible with Simscape Blocks . . . . .
Code Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-70
3-70
3-70
3-71
3-73
3-73
3-73
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-75
3-64
3-64
4
5
Variable Initialization and State Viewer
About Variable Initialization . . . . . . . . . . . . . . . . . . . . . . . . . .
Initializing Block Variables for Model Simulation . . . . . . . . .
Variable Initialization Priority . . . . . . . . . . . . . . . . . . . . . . .
Suggested Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-2
4-2
4-3
4-4
Set Priority and Initial Target for Block Variables . . . . . . . .
4-5
Initialize Variables for a Mass-Spring-Damper System . . . .
4-8
Variable Viewer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
About Variable Viewer . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Advanced Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . .
Switching Between Tree View and Flat View . . . . . . . . . . .
Useful Filtering Techniques . . . . . . . . . . . . . . . . . . . . . . . .
Link to Block Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Interaction with Model Updates and Simulation . . . . . . . . .
4-22
4-22
4-24
4-26
4-28
4-28
4-30
Data Logging
About Simulation Data Logging . . . . . . . . . . . . . . . . . . . . . . .
Suggested Workflows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-2
5-2
5-3
Enable Data Logging for the Whole Model . . . . . . . . . . . . . . .
5-4
Log Data for Selected Blocks Only . . . . . . . . . . . . . . . . . . . . .
5-5
Data Logging Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-6
Log and Plot Simulation Data . . . . . . . . . . . . . . . . . . . . . . . . .
5-8
Log Simulation Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-13
Log and View Simulation Data for Selected Blocks . . . . . .
5-17
ix
6
7
Log, Navigate, and Plot Simulation Data . . . . . . . . . . . . . . .
5-22
About the Simscape Results Explorer . . . . . . . . . . . . . . . . . .
5-27
View Sparkline Plots of Simulation Data . . . . . . . . . . . . . . .
5-28
Model Statistics
Simscape Model Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6-2
1-D Physical System Statistics . . . . . . . . . . . . . . . . . . . . . . . . .
6-4
3-D Multibody System Statistics . . . . . . . . . . . . . . . . . . . . . . .
6-7
1-D/3-D Interface Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . .
6-10
View Model Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6-11
Access Block Variables Using Statistics Viewer . . . . . . . . .
6-16
Physical Units
How to Work with Physical Units . . . . . . . . . . . . . . . . . . . . . .
7-2
Unit Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7-4
How to Specify Units in Block Dialogs . . . . . . . . . . . . . . . . . .
7-9
Thermal Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . .
About Affine Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
When to Apply Affine Conversion . . . . . . . . . . . . . . . . . . . .
How to Apply Affine Conversion . . . . . . . . . . . . . . . . . . . . .
x
Contents
7-11
7-11
7-11
7-12
8
Angular Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7-15
7-15
Units for Angular Velocity and Frequency . . . . . . . . . . . . . .
7-16
Add-On Product License Management
About the Simscape Editing Mode . . . . . . . . . . . . . . . . . . . . .
Suggested Workflows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
What You Can Do in Restricted Mode . . . . . . . . . . . . . . . . . .
What You Can Do in Full Mode . . . . . . . . . . . . . . . . . . . . . .
Switching Between Modes . . . . . . . . . . . . . . . . . . . . . . . . . . .
Working with Block Libraries . . . . . . . . . . . . . . . . . . . . . . . .
8-2
8-2
8-3
8-4
8-4
8-7
Working with Restricted and Full Modes . . . . . . . . . . . . . . . .
Set the Model Loading Preference . . . . . . . . . . . . . . . . . . . . .
Save a Model in Restricted Mode . . . . . . . . . . . . . . . . . . . .
Work with a Model in Restricted Mode . . . . . . . . . . . . . . . .
Switch from Restricted to Full Mode . . . . . . . . . . . . . . . . . .
8-9
8-9
8-10
8-13
8-22
Editing Mode Information . . . . . . . . . . . . . . . . . . . . . . . . . . .
What Is the Current Mode? . . . . . . . . . . . . . . . . . . . . . . . . .
Which Licenses Are Checked Out? . . . . . . . . . . . . . . . . . . .
8-24
8-24
8-24
xi
1
Model Construction
• “Basic Principles of Modeling Physical Networks” on page 1-2
• “Simscape Block Libraries” on page 1-11
• “Essential Physical Modeling Techniques” on page 1-15
• “Creating and Simulating a Simple Model” on page 1-18
• “Modeling Best Practices” on page 1-36
• “Domain-Specific Line Styles” on page 1-43
• “Modeling Pneumatic Systems” on page 1-45
1
Model Construction
Basic Principles of Modeling Physical Networks
In this section...
“Overview of the Physical Network Approach to Modeling Physical Systems” on page
1-2
“Variable Types” on page 1-4
“Building the Mathematical Model” on page 1-5
“Direction of Variables ” on page 1-6
“Connector Ports and Connection Lines” on page 1-8
“Connecting Simscape Diagrams to Simulink Sources and Scopes” on page 1-9
Overview of the Physical Network Approach to Modeling Physical
Systems
Simscape™ software is a set of block libraries and special simulation features for
modeling physical systems in the Simulink® environment. It employs the Physical
Network approach, which differs from the standard Simulink modeling approach and is
particularly suited to simulating systems that consist of real physical components.
Simulink blocks represent basic mathematical operations. When you connect Simulink
blocks together, the resulting diagram is equivalent to the mathematical model, or
representation, of the system under design. Simscape technology lets you create a
network representation of the system under design, based on the Physical Network
approach. According to this approach, each system is represented as consisting of
functional elements that interact with each other by exchanging energy through their
ports.
These connection ports are nondirectional. They mimic physical connections between
elements. Connecting Simscape blocks together is analogous to connecting real
components, such as pumps, valves, and so on. In other words, Simscape diagrams mimic
the physical system layout. If physical components can be connected, their models can
be connected, too. You do not have to specify flow directions and information flow when
connecting Simscape blocks, just as you do not have to specify this information when you
connect real physical components. The Physical Network approach, with its Through and
Across variables and nondirectional physical connections, automatically resolves all the
traditional issues with variables, directionality, and so on.
1-2
Basic Principles of Modeling Physical Networks
The number of connection ports for each element is determined by the number of energy
flows it exchanges with other elements in the system, and depends on the level of
idealization. For example, a fixed-displacement hydraulic pump in its simplest form can
be represented as a two-port element, with one energy flow associated with the inlet
(suction) and the other with the outlet. In this representation, the angular velocity of
the driving shaft is assumed constant, making it possible to neglect the energy exchange
between the pump and the shaft. To account for a variable driving torque, you need a
third port associated with the driving shaft.
An energy flow is characterized by its variables. Each energy flow is associated with
two variables, one Through and one Across (see “Variable Types” on page 1-4 for
more information). Usually, these are the variables whose product is the energy flow in
watts. They are called the basic, or conjugate, variables. For example, the basic variables
for mechanical translational systems are force and velocity, for mechanical rotational
systems—torque and angular velocity, for hydraulic systems—flow rate and pressure, for
electrical systems—current and voltage.
The following example illustrates a Physical Network representation of a double-acting
hydraulic cylinder.
The element is represented with three energy flows: two flows of hydraulic energy
through the inlet and outlet of the cylinder and a flow of mechanical energy associated
with the rod motion. It therefore has the following three connector ports:
• A — Hydraulic conserving port associated with pressure p1 (an Across variable) and
flow rate q1 (a Through variable)
• B — Hydraulic conserving port associated with pressure p2 (an Across variable) and
flow rate q2 (a Through variable)
1-3
1
Model Construction
• R — Mechanical translational conserving port associated with rod velocity v3 (an
Across variable) and force F3 (a Through variable)
See “Connector Ports and Connection Lines” on page 1-8 for more information on
connector port types.
Variable Types
Physical Network approach supports two types of variables:
• Through — Variables that are measured with a gauge connected in series to an
element.
• Across — Variables that are measured with a gauge connected in parallel to an
element.
The following table lists the Through and Across variables associated with each type of
physical domain in Simscape software:
Physical Domain
Across Variable
Through Variable
Electrical
Voltage
Current
Hydraulic
Pressure
Flow rate
Magnetic
Magnetomotive force (mmf) Flux
Mechanical rotational
Angular velocity
Torque
Mechanical translational
Translational velocity
Force
Pneumatic
Pressure and temperature
Mass flow rate and heat flow
Thermal
Temperature
Heat flow
Thermal liquid
Pressure and temperature
Mass flow rate and thermal
flux
Note Generally, the product of each pair of Across and Through variables associated with
a domain is power (energy flow in watts). The exceptions are pneumatic domain, where
the product of pressure and mass flow rate is not power, magnetic domain, where the
product of mmf and flux is not power, but energy, and the thermal liquid domain, where
products of both variable pairs are not power. These result in a pseudo-bond graph.
1-4
Basic Principles of Modeling Physical Networks
Building the Mathematical Model
Through and Across variables associated with all the energy flows form the basis of the
mathematical model of the block.
For example, the model of a double-acting hydraulic cylinder shown in the previous
illustration can be described with a simple set of equations:
F3 = p1 i A1 - p2 i A2
q1 = A1 iv3
q2 = A2 iv3
where
q1,q2
Flow rates through ports A and B, respectively (Through variables)
p1,p2
Gauge pressures at ports A and B, respectively (Across variables)
A1,A2
Piston effective areas
F3
Rod force (Through variable)
v3
Rod velocity (Across variable)
The model could be considerably more complex, for example, it could account for friction,
fluid compressibility, inertia of the moving parts, and so on. For all these different
1-5
1
Model Construction
mathematical models, however, the element configuration (that is, the number and
type of ports and the associated Through and Across variables) would remain the same,
meaning that the Physical Network approach lets you substitute models of different
levels of complexity without introducing any changes to the schematic. For example, you
can start developing your system by using the Resistive Tube block from the Foundation
library, which accounts only for friction losses. At a later stage in development, you
may want to account for fluid compressibility. You can then replace it with a Hydraulic
Pipeline block, available with SimHydraulics® block libraries, or, depending on your
application, even with a Segmented Pipeline block if you also need to account for fluid
inertia. This modeling principle is called incremental modeling.
Direction of Variables
Each variable is characterized by its magnitude and sign. The sign is the result of
measurement orientation. The same variable can be positive or negative, depending on
the polarity of a measurement gauge.
Elements with only two ports are characterized with one pair of variables, a Through
variable and an Across variable. Since these variables are closely related, their
orientation is defined with one direction. For example, if an element is oriented from port
A to port B, it implies that the Through variable (TV) is positive if it “flows” from A to B,
and the Across variable is determined as AV = AVA – AVB, where AVA and AVB are the
element node potentials or, in other words, the values of this Across variable at ports A
and B, respectively.
This approach to the direction of variables has the following benefits:
1-6
Basic Principles of Modeling Physical Networks
• Provides a simple and consistent way to determine whether an element is active or
passive. Energy is one of the most important characteristics to be determined during
simulation. If the variables direction, or sign, is determined as described above,
their product (that is, the energy) is positive if the element consumes energy, and
is negative if it provides energy to a system. This rule is followed throughout the
Simscape software.
• Simplifies the model description. Symbol A → B is enough to specify variable polarity
for both the Across and the Through variables.
• Lets you apply the oriented graph theory to network analysis and design.
As an example of variables direction rules, let us consider the Ideal Force Source block.
In this block, as in many other mechanical blocks, port C is associated with the source
reference point (case), and port R is associated with the rod.
The block positive direction is from port C to port R. This means that the force is positive
if it acts in the direction from C to R, and causes bodies connected to port R to accelerate
in the positive direction. The relative velocity is determined as v = vC – vR, where vR, vC
are the absolute velocities at ports R and C, respectively, and it is negative if velocity
at port R is greater than that at port C. The power generated by the source is computed
as the product of force and velocity, and is negative if the source provides energy to the
system.
Definition of positive direction is different for different blocks. Check the block source or
the block reference page if in doubt about the block orientation and direction of variables.
All the elements in a network are divided into active and passive elements, depending
on whether they deliver energy to the system or dissipate (or store) it. Active elements
1-7
1
Model Construction
(force and velocity sources, flow rate and pressure sources, etc.) must be oriented strictly
in accordance with the line of action or function that they are expected to perform in
the system, while passive elements (dampers, resistors, springs, pipelines, etc.) can be
oriented either way.
Connector Ports and Connection Lines
Simscape blocks may have the following types of ports:
• Physical conserving ports — Nondirectional ports (for example, hydraulic or
mechanical) that represent physical connections and relate physical variables based
on the Physical Network approach.
• Physical signal ports — Unidirectional ports transferring signals that use an internal
Simscape engine for computations.
Each of these ports and connections between them are described in greater detail below.
Physical Conserving Ports
Simscape blocks have special conserving ports . You connect conserving ports with
physical connection lines, distinct from normal Simulink lines. Physical connection lines
have no inherent directionality and represent the exchange of energy flows, according to
the Physical Network approach.
• You can connect conserving ports only to other conserving ports of the same type.
• The physical connection lines that connect conserving ports together are
nondirectional lines that carry physical variables (Across and Through variables, as
described above) rather than signals. You cannot connect physical lines to Simulink
ports or to physical signal ports.
• Two directly connected conserving ports must have the same values for all their
Across variables (such as pressure or angular velocity).
• You can branch physical connection lines. When you do so, components directly
connected with one another continue to share the same Across variables. Any
Through variable (such as flow rate or torque) transferred along the physical
connection line is divided among the multiple components connected by the branches.
How the Through variable is divided is determined by the system dynamics.
For each Through variable, the sum of all its values flowing into a branch point equals
the sum of all its values flowing out.
1-8
Basic Principles of Modeling Physical Networks
Each type of physical conserving ports used in Simscape blocks uniquely represents a
physical modeling domain. For a list of port types, along with the Through and Across
variables associated with each type, see the table in “Variable Types” on page 1-4.
For improved readability of block diagrams, each Simscape domain uses a distinct
default color and line style for the connection lines. For more information, see “DomainSpecific Line Styles” on page 1-43.
Physical Signal Ports
Physical signal ports carry signals between Simscape blocks. You connect them with
regular connection lines, similar to Simulink signal connections. Physical signal ports
are used in Simscape block diagrams instead of Simulink input and output ports to
increase computation speed and avoid issues with algebraic loops. Unlike Simulink
signals, which are essentially unitless, physical signals can have units associated with
them. You specify the units along with the parameter values in the block dialogs, and
Simscape software performs the necessary unit conversion operations when solving a
physical network.
Simscape Foundation library contains, among other sublibraries, a Physical Signals
block library. These blocks perform math operations and other functions on physical
signals, and allow you to graphically implement equations inside the Physical Network.
Physical signal lines also have a distinct style and color in block diagrams, similar to
physical connection lines. For more information, see “Domain-Specific Line Styles” on
page 1-43.
Connecting Simscape Diagrams to Simulink Sources and Scopes
Simscape block diagrams use physical signals instead of regular Simulink signals.
Therefore, you need converter blocks to connect Simscape diagrams to Simulink sources
and scopes.
Use the Simulink-PS Converter block to connect Simulink sources or other Simulink
blocks to the inputs of a Physical Network diagram. You can also use it to specify the
input signal units. For more information, see the Simulink-PS Converter block reference
page.
Use the PS-Simulink Converter block to connect outputs of a Physical Network diagram
to Simulink scopes or other Simulink blocks. You can also use it to specify the desired
1-9
1
Model Construction
output signal units. For more information, see the PS-Simulink Converter block
reference page.
For an example of using converter blocks to connect Simscape diagrams to Simulink
sources and scopes, see “Creating and Simulating a Simple Model” on page 1-18.
1-10
Simscape Block Libraries
Simscape Block Libraries
In this section...
“Library Structure Overview” on page 1-11
“Using the Simulink Library Browser to Access the Block Libraries” on page 1-12
“Using the Command Prompt to Access the Block Libraries” on page 1-13
Library Structure Overview
Simscape block library contains two libraries that belong to the Simscape product:
• Foundation library — Contains basic hydraulic, pneumatic, mechanical, electrical,
magnetic, thermal, thermal liquid, and physical signal blocks, organized into
sublibraries according to technical discipline and function performed
• Utilities library — Contains essential environment blocks for creating Physical
Networks models
In addition, if you have installed any of the add-on products of the Physical Modeling
family, you will see the corresponding libraries under the main Simscape library.
Simscape Foundation libraries contain a comprehensive set of basic elements and
building blocks, such as:
• Mechanical building blocks for representing one-dimensional translational and
rotational motion
• Electrical building blocks for representing electrical components and circuits
• Magnetic building blocks that represent electromagnetic components
• Hydraulic building blocks that model fundamental hydraulic effects and can be
combined to create more complex hydraulic components
• Pneumatic building blocks that model fundamental pneumatic effects based on the
ideal gas law
• Thermal building blocks that model fundamental thermal effects
• Thermal liquid building blocks that model fundamental thermodynamic effects in
liquids
• Physical Signals block library that lets you perform math operations on physical
signals, and graphically enter equations inside the physical network
1-11
1
Model Construction
Using the elements contained in these Foundation libraries, you can create more complex
components that span different physical domains. You can then group this assembly of
blocks into a subsystem and parameterize it to reuse and share these components.
In addition to Foundation libraries, there is also a Simscape Utilities library, which
contains utility blocks, such as:
• Solver Configuration block, which contains parameters relevant to numerical
algorithms for Simscape simulations. Each Simscape diagram (or each topologically
distinct physical network in a diagram) must contain a Solver Configuration block.
• Simulink-PS Converter block and PS-Simulink Converter block, to connect Simscape
and Simulink blocks. Use the Simulink-PS Converter block to connect Simulink
outports to Physical Signal inports. Use the PS-Simulink Converter block to connect
Physical Signal outports to Simulink inports.
For examples of using these blocks in a Simscape model, see the tutorial “Creating and
Simulating a Simple Model” on page 1-18.
You can combine all these blocks in your Simscape diagrams to model physical systems.
You can also use the basic Simulink blocks in your diagrams, such as sources or scopes.
See “Connecting Simscape Diagrams to Simulink Sources and Scopes” on page 1-9 for
more information on how to do this.
Simscape block libraries contain a comprehensive selection of blocks that represent
engineering components such as valves, resistors, springs, and so on. These prebuilt
blocks, however, may not be sufficient to address your particular engineering needs.
When you need to extend the existing block libraries, use the Simscape language to
define customized components, or even new physical domains, as textual files. Then
convert your textual components into libraries of additional Simscape blocks that you
can use in your model diagrams. For more information on how to do this, see “Typical
Simscape Language Tasks”.
Using the Simulink Library Browser to Access the Block Libraries
You can access the blocks through the Simulink Library Browser. To display the Library
Browser, click the Simulink Library button in the toolbar of the MATLAB® desktop.
Alternatively, you can type simulink in the MATLAB Command Window. Then expand
the Simscape entry in the contents tree.
1-12
Simscape Block Libraries
Using the Command Prompt to Access the Block Libraries
To access individual block libraries by using the command prompt:
• To open the Simscape library, type simscape in the MATLAB Command Window.
• To open the main Simulink library (to access generic Simulink blocks), type
simulink in the MATLAB Command Window.
The Simscape library consists of two top-level libraries, Foundation and Utilities. In
addition, if you have installed any of the add-on products of the Physical Modeling
family, you will see the corresponding libraries under Simscape library, as shown in
the following illustration. Some of these libraries contain second-level and third-level
sublibraries. You can expand each library by double-clicking its icon.
1-13
1
Model Construction
1-14
Essential Physical Modeling Techniques
Essential Physical Modeling Techniques
Building Your Model
The rules that you must follow when building a physical model with Simscape software
are described in “Basic Principles of Modeling Physical Networks” on page 1-2. This
section briefly reviews these rules.
• Build your physical model by using a combination of blocks from the Simscape
Foundation and Utilities libraries. Simscape software lets you create a network
representation of the system under design, based on the Physical Network approach.
According to this approach, each system is represented as consisting of functional
elements that interact with each other by exchanging energy through their ports.
• Each Simscape diagram (or each topologically distinct physical network in a diagram)
must contain a Solver Configuration block from the Simscape Utilities library.
• If you have hydraulic elements in your model, the working fluid used in the hydraulic
circuit defines their global parameters, such as fluid density, fluid kinematic
viscosity, fluid bulk modulus, and so on. To specify the working fluid, attach a Custom
Hydraulic Fluid block (or a Hydraulic Fluid block, available with SimHydraulics block
libraries) to each topologically distinct hydraulic circuit. If no Hydraulic Fluid block
or Custom Hydraulic Fluid block is attached to a circuit, the hydraulic blocks use the
default fluid, which is equivalent to fluid defined by a Custom Hydraulic Fluid block
with the default parameter values.
• If you have pneumatic elements in your model, default gas properties are for dry air
and ambient conditions of 101325 Pa and 20 degrees Celsius. Attach a Gas Properties
block to each topologically distinct pneumatic circuit to change gas properties and
ambient conditions.
• To connect regular Simulink blocks (such as sources or scopes) to your physical
network diagram, use the converter blocks, as described in “Using the Physical Signal
Ports” on page 1-16.
• Use the incremental modeling approach. Start with a simple model, run and
troubleshoot it, then add the desired special effects. For example, you can start
developing your system by using the Resistive Tube block from the Foundation
library, which accounts only for friction losses. At a later stage in development,
you may want to account for fluid compressibility. You can then replace it with
a Hydraulic Pipeline block, available with SimHydraulics block libraries, or,
depending on your application, even with a Segmented Pipeline block if you also
need to account for fluid inertia. For all these different mathematical models, the
1-15
1
Model Construction
element configuration (that is, the number and type of ports and the associated
Through and Across variables) would remain the same, meaning that the Physical
Network approach lets you substitute models of different levels of complexity without
introducing any changes to the schematic.
Simscape blocks, in general, feature both Conserving ports
and outports .
and Physical Signal inports
Using the Conserving Ports
The following rules apply to Conserving ports:
• There are different types of Physical Conserving ports used in Simscape block
diagrams, such as hydraulic, pneumatic, electrical, magnetic, thermal, mechanical
translational, and mechanical rotational. Each type has specific Through and Across
variables associated with it. For more information, see “Variable Types” on page 1-4.
• You can connect Conserving ports only to other Conserving ports of the same type.
• The Physical connection lines that connect Conserving ports together are
nondirectional lines that carry physical variables (Across and Through variables, as
described above) rather than signals. You cannot connect Physical lines to Simulink
ports or to Physical Signal ports.
• Two directly connected Conserving ports must have the same values for all their
Across variables (such as voltage or angular velocity).
• You can branch Physical connection lines. When you do so, components directly
connected with one another continue to share the same Across variables. Any
Through variable (such as current or torque) transferred along the Physical
connection line is divided among the multiple components connected by the branches.
How the Through variable is divided is determined by the system dynamics.
For each Through variable, the sum of all its values flowing into a branch point equals
the sum of all its values flowing out.
Using the Physical Signal Ports
The following rules apply to Physical Signal ports:
• You can connect Physical Signal ports to other Physical Signal ports with regular
connection lines, similar to Simulink signal connections. These connection lines carry
physical signals between Simscape blocks.
1-16
Essential Physical Modeling Techniques
• You can connect Physical Signal ports to Simulink ports through special converter
blocks. Use the Simulink-PS Converter block to connect Simulink outports to Physical
Signal inports. Use the PS-Simulink Converter block to connect Physical Signal
outports to Simulink inports.
• Unlike Simulink signals, which are essentially unitless, Physical Signals can have
units associated with them. Simscape block dialogs let you specify the units along
with the parameter values, where appropriate. Use the converter blocks to associate
units with an input signal and to specify the desired output signal units.
For examples of applying these rules when creating an actual physical model, see the
tutorial “Creating and Simulating a Simple Model” on page 1-18.
1-17
1
Model Construction
Creating and Simulating a Simple Model
In this section...
“Building a Simscape Diagram” on page 1-18
“Modifying Initial Settings” on page 1-26
“Running the Simulation” on page 1-28
“Adjusting the Parameters” on page 1-30
Building a Simscape Diagram
In this example, you are going to model a simple mechanical system and observe its
behavior under various conditions. This tutorial illustrates the essential steps to building
a physical model and makes you familiar with using the basic Simscape blocks.
The following schematic represents a simple model of a car suspension. It consists of a
spring and damper connected to a body (represented as a mass), which is agitated by a
force. You can vary the model parameters, such as the stiffness of the spring, the mass of
the body, or the force profile, and view the resulting changes to the velocity and position
of the body.
1-18
Creating and Simulating a Simple Model
To create an equivalent Simscape diagram, follow these steps:
1
Open the Simulink Library Browser, as described in “Simscape Block Libraries” on
page 1-11.
2
Create a new model. To do this, from the top menu bar of the Library Browser, select
File > New > Model. The software creates an empty model in memory and displays
it in a new model editor window.
Note Alternately, you can type ssc_new at the MATLAB Command prompt, to
create a new model prepopulated with certain required and commonly-used blocks.
For more information, see “Creating a New Simscape Model”.
3
Open the Simscape > Foundation Library > Mechanical > Translational Elements
library.
4
Drag the Mass, Translational Spring, Translational Damper, and two Mechanical
Translational Reference blocks into the model window.
5
Orient the blocks as shown in the following illustration. To rotate a block, select it
and press Ctrl+R.
1-19
1
Model Construction
6
1-20
Connect the Translational Spring, Translational Damper, and Mass blocks to one of
the Mechanical Translational Reference blocks as shown in the next illustration.
Creating and Simulating a Simple Model
7
To add the representation of the force acting on the mass, open the Simscape >
Foundation Library > Mechanical > Mechanical Sources library and add the Ideal
Force Source block to your diagram.
To reflect the correct direction of the force shown in the original schematic, flip the
block by selecting Diagram > Rotate & Flip > Flip Block > Up-Down from the
top menu bar of the model window. Connect the block's port C (for “case”) to the
second Mechanical Translational Reference block, and its port R (for “rod”) to the
Mass block, as shown below.
1-21
1
Model Construction
8
1-22
Add the sensor to measure speed and position of the mass. Place the Ideal
Translational Motion Sensor block from the Mechanical Sensors library into your
diagram and connect it as shown below.
Creating and Simulating a Simple Model
9
Now you need to add the sources and scopes. They are found in the regular Simulink
libraries. Open the Simulink > Sources library and copy the Signal Builder block
into the model. Then open the Simulink > Sinks library and copy two Scope blocks.
Rename one of the Scope blocks to Velocity and the other to Position.
1-23
1
Model Construction
10 Every time you connect a Simulink source or scope to a Simscape diagram, you have
to use an appropriate converter block, to convert Simulink signals into physical
signals and vice versa. Open the Simscape > Utilities library and copy a Simulink-PS
Converter block and two PS-Simulink Converter blocks into the model. Connect the
blocks as shown below.
1-24
Creating and Simulating a Simple Model
11 Each topologically distinct physical network in a diagram requires exactly one Solver
Configuration block, found in the Simscape > Utilities library. Copy this block into
your model and connect it to the circuit by creating a branching point and connecting
it to the only port of the Solver Configuration block. Your diagram now should look
like this.
1-25
1
Model Construction
12 Your block diagram is now complete. Save it as mech_simple.
Modifying Initial Settings
After you have put together a block diagram of your model, as described in the previous
section, you need to select a solver and provide the correct values for configuration
parameters.
To prepare for simulating the model, follow these steps:
1-26
Creating and Simulating a Simple Model
1
Select a Simulink solver. On the top menu bar of the model window, select
Simulation > Model Configuration Parameters. The Configuration Parameters
dialog box opens, showing the Solver node.
Under Solver options, set Solver to ode23t (mod.stiff/Trapezoidal) and
Max step size to 0.2.
Also note that Simulation time is specified to be between 0 and 10 seconds. You can
adjust this setting later, if needed.
Click OK to close the Configuration Parameters dialog box.
2
Save the model.
1-27
1
Model Construction
Running the Simulation
After you've put together a block diagram and specified the initial settings for your
model, you can run the simulation.
1
The input signal for the force is provided by the Signal Builder block. The signal
profile is shown in the illustration below. It starts with a value of 0, then at 4
seconds there is a step change to 1, and then it changes back to 0 at 6 seconds. This
is the default profile.
The Velocity scope outputs the mass velocity, and the Position scope outputs the
mass displacement as a function of time. Double-click both scopes to open them.
2
1-28
To run the simulation, click
in the model window toolbar. The Simscape solver
evaluates the model, calculates the initial conditions, and runs the simulation.
Creating and Simulating a Simple Model
For a detailed description of this process, see “How Simscape Simulation Works”.
Completion of this step may take a few seconds. The message in the bottom-left
corner of the model window provides the status update.
3
Once the simulation starts running, the Velocity and Position scope windows display
the simulation results, as shown in the next illustration.
1-29
1
Model Construction
In the beginning, the mass is at rest. Then at 4 seconds, as the input signal changes
abruptly, the mass velocity spikes in the positive direction and gradually returns
to zero. The mass position at the same time changes more gradually, on account
of inertia and damping, and stays at the new value as long as the force is acting
upon it. At 6 seconds, when the input signal changes back to zero, the velocity gets a
mirror spike, and the mass gradually returns to its initial position.
You can now adjust various inputs and block parameters and see their effect on the mass
velocity and displacement.
Adjusting the Parameters
After running the initial simulation, you can experiment with adjusting various inputs
and block parameters.
Try the following adjustments:
1
Change the force profile.
2
Change the model parameters.
3
Change the mass position output units.
Changing the Force Profile
This example shows how a change in the input signal affects the force profile, and
therefore the mass displacement.
1-30
1
Double-click the Signal Builder block to open it.
2
Click the first vertical segment of the signal profile and drag it from 4 to 2 seconds,
as shown below. Close the block dialog.
Creating and Simulating a Simple Model
3
Run the simulation. The simulation results are shown in the following illustration.
1-31
1
Model Construction
Changing the Model Parameters
In our model, the force acts on a mass against a translational spring and damper,
connected in parallel. This example shows how changes in the spring stiffness and
damper viscosity affect the mass displacement.
1
1-32
Double-click the Translational Spring block. Set its Spring rate to 2000 N/m.
Creating and Simulating a Simple Model
2
Run the simulation. The increase in spring stiffness results in smaller amplitude of
mass displacement, as shown in the following illustration.
3
Next, double-click the Translational Damper block. Set its Damping coefficient to
500 N/(m/s).
4
Run the simulation. Because of the increase in viscosity, the mass is slower both
in reaching its maximum displacement and in returning to the initial position, as
shown in the following illustration.
1-33
1
Model Construction
Changing the Mass Position Output Units
In our model, we have used the PS-Simulink Converter block in its default parameter
configuration, which does not specify units. Therefore, the Position scope outputs the
mass displacement in the default length units, that is, in meters. This example shows
how to change the output units for the mass displacement to millimeters.
1-34
1
Double-click the PS-Simulink Converter1 block. Type mm in the Output signal unit
combo box and click OK.
2
Run the simulation. In the Position scope window, click
to autoscale the scope
axes. The mass displacement is now output in millimeters, as shown in the following
illustration.
Creating and Simulating a Simple Model
1-35
1
Model Construction
Modeling Best Practices
In this section...
“Grounding Rules” on page 1-36
“Avoiding Numerical Simulation Issues” on page 1-40
Grounding Rules
This section contains guidelines for using domain-specific reference blocks (such as
Electrical Reference, Mechanical Translational Reference, and so on) in Simscape
diagrams, along with examples of correct and incorrect configurations.
Add reference blocks to your models according to the following rules:
• “Each Domain Requires at Least One Reference Block” on page 1-36
• “Each Circuit Requires at Least One Reference Block” on page 1-37
• “Multiple Connections to the Domain Reference Are Allowed Within a Circuit” on
page 1-39
Each Domain Requires at Least One Reference Block
Within a physical network, each domain must contain at least one reference block of
the appropriate type. For example, the electromechanical model shown in the following
diagram has both Electrical Reference and Rotational Reference blocks attached to the
appropriate circuits.
1-36
Modeling Best Practices
Each Circuit Requires at Least One Reference Block
Each topologically distinct circuit within a domain must contain at least one reference
block. Some blocks, such as an Ideal Transformer, interface two parts of the network
but do not convey information about signal levels relative to the reference block. In the
following diagram, there are two separate electrical circuits, and the Electrical Reference
blocks are required on both sides of the Ideal Transformer block.
1-37
1
Model Construction
The next diagram would produce an error because it is lacking an electrical reference in
the circuit of the secondary winding.
The following diagram, however, will not produce an error because the resistor defines
the output voltage relative to the ground reference.
1-38
Modeling Best Practices
Multiple Connections to the Domain Reference Are Allowed Within a Circuit
More that one reference block may be used within a circuit to define multiple connections
to the domain reference:
• Electrical conserving ports of all the blocks that are directly connected to ground must
be connected to an Electrical Reference block.
• All translational ports that are rigidly clamped to the frame (ground) must be
connected to a Mechanical Translational Reference block.
• All rotational ports that are rigidly clamped to the frame (ground) must be connected
to a Mechanical Rotational Reference block.
• Hydraulic conserving ports of all the blocks that are referenced to atmosphere (for
example, suction ports of hydraulic pumps, or return ports of valves, cylinders,
pipelines, if they are considered directly connected to atmosphere) must be connected
to a Hydraulic Reference block.
For example, the following diagram correctly indicates two separate connections to an
electrical ground.
1-39
1
Model Construction
Avoiding Numerical Simulation Issues
Certain configurations of physical modeling blocks can cause numerical difficulties or
slow down your simulation. When this happens, Simscape solver issues a warning in the
MATLAB workspace and, if it fails to initialize, a Simscape error.
In electrical circuits, common examples that can cause this behavior include voltage
sources connected in parallel with capacitors, inductors connected in series with current
sources, voltage sources connected in parallel, and current sources connected in series.
Often, the cause of the numerical difficulty is immediately apparent. For example, two
voltage sources in parallel must have identical voltage values; otherwise, the ports
connecting them would not be physical conserving ports. In practical circuits, topologies
such as parallel voltage sources are possible, and small difference in their instantaneous
voltages is possible due to parasitic series resistance.
Note Mathematically, these topologies result in Index-2 differential algebraic equations
(DAEs). Their solution requires two differentiations of the constraint equations and, as
such, it is numerically better to avoid these component topologies where possible.
1-40
Modeling Best Practices
There are two approaches to resolving these difficulties. The first is to change the circuit
to an equivalent simpler one. In the example of two parallel voltage sources, one source
can be simply deleted. The same applies to two series current sources, the deleted one
being replaced by a short circuit. For some circuit topologies, however, it is not possible
to find an equivalent simpler one that resolves the problem, and the second approach is
needed.
The second approach is to include small parasitic resistances in the component. In
the Simscape Foundation library, the Capacitor and Inductor blocks include such
parasitic terms, so that you can connect capacitances in parallel with voltage sources and
inductors in series with current sources. If your circuit does not have any such topologies,
then you can change the default parasitic terms to zero. Note that other blocks do not
contain these parasitic terms, for example, the Mutual Inductor block. Therefore, if you
wanted to connect a mutual inductor primary in series with a current source, you would
need to introduce your own parasitic conductance across the primary winding.
Example of Using a Parasitic Resistance to Avoid Numerical Simulation Issues
The following diagram models a differentiator that might be used as part of a
Proportional-Integral-Derivative (PID) controller. You can open this model by typing
ssc_differentiator in the MATLAB Command Window.
Simulate the model, and you will see that the output is minus the derivative of the input
sinusoid.
1-41
1
Model Construction
Now open the capacitor C block dialog, and set the series resistance to zero. The model
now issues an initialization error.
The cause of the error is that the circuit effectively connects the voltage source in parallel
with the capacitor. This is because an ideal op-amp satisfies V+ = V- , where V+ and Vare the noninverting and inverting inputs, respectively. This is an example where it is
not possible to replace the circuit with an equivalent simpler one, and a parasitic small
resistance has to be introduced.
1-42
Domain-Specific Line Styles
Domain-Specific Line Styles
For improved readability of block diagrams, each Simscape domain uses a distinct
default color and line style for the connection lines. Physical signal lines also have a
distinct style and color.
To view the line styles assigned to each domain, in a model window, from the top menu
bar, select Display > Simscape > Legend. The Simscape Line Styles Legend window
opens, listing the line color assigned to each registered domain, the domain name, and
the domain path. If you click a domain path link, the Simscape file for the corresponding
domain opens in MATLAB Editor. For more information on domain paths and files, see
“Foundation Domains”.
To turn off domain-specific line styles for a particular model, in the model window, from
the top menu bar, select Display > Simscape > Domain Line Styles. This action clears
the check mark next to the Domain Line Styles menu option, and the block diagram
display changes to black connection lines, with physical ports visible at connection points.
Repeatedly selecting the Domain Line Styles menu option toggles the domain-specific
line styles for this model on or off, as indicated by the check mark.
1-43
1
Model Construction
To turn off domain-specific line styles for all models, on the MATLAB Toolstrip, click
Preferences. In the left pane of the Preferences dialog box, select Simscape, then clear
the Enable domain line styles for all models check box.
1-44
Modeling Pneumatic Systems
Modeling Pneumatic Systems
In this section...
“Intended Applications” on page 1-45
“Assumptions and Limitations” on page 1-45
“Fundamental Equations” on page 1-46
“Network Variables” on page 1-47
“Connection Constraints” on page 1-47
“References” on page 1-48
Intended Applications
The Foundation library contains basic pneumatic elements, such as orifices, chambers,
and pneumatic-mechanical converters, as well as pneumatic sensors and sources. Use
these blocks to model pneumatic systems, for applications such as:
• Factory automation — basic pneumatic linear/rotational actuators, valves (variable
orifices), and air supply
• Robotics — robotic arms and haptic interfaces
• Gaseous transportation systems and pipelines
You can also use these blocks to model dry air and low-pressure flows, for example, for
HVAC applications.
Assumptions and Limitations
Pneumatic block models are based on the following assumptions:
• Working fluid is an ideal gas satisfying the ideal gas law.
• Specific heats at constant pressure and constant volume, cp and cv, are constant.
• Processes are adiabatic, that is, there is no heat transfer between components and the
environment (except for components with a separate thermal port).
• Gravitational effects can be neglected, that is, underlying equations contain no head
pressures due to gravity.
1-45
1
Model Construction
Fundamental Equations
The energy balance for a control volume [1] is
dEcv
= Qcv - Wcv +
dt
Ê
Ê
Ë
Ë
 ÁÁ mi ÁÁ hi +
i
ˆˆ
vi2
+ gzi ˜ ˜ ˜˜
2
¯¯
Ê
Ê
Ë
Ë
 ÁÁ mo ÁÁ ho +
o
ˆˆ
vo2
+ gzo ˜ ˜
˜˜
2
¯¯
where
Ecv
Control volume total energy
Qcv
Heat energy per second added to the gas through the boundary
Wcv
Mechanical work per second performed by the gas
hi, ho
Inlet and outlet enthalpies
vi, vo
Gas inlet and outlet velocities
g
Acceleration due to gravity
zi, zo
Elevations at inlet and outlet ports
mi, mo
Mass flow rates in and out of the control volume
The equation is an accounting balance for the energy of the control volume. It states
that the rate of energy increase or decrease within the control volume equals the
difference between the rates of energy transfer in and out across the boundary. The
mechanisms of energy transfer are heat and work, as for closed systems, and the energy
that accompanies the mass entering and exiting.
Pneumatic block models make several simplifying assumptions, as described previously.
The ideal gas law relates pressure, density, and temperature:
p = rRT
where
1-46
p
Absolute pressure
ρ
Gas density
R
Specific gas constant
Modeling Pneumatic Systems
T
Absolute gas temperature
Also, the specific enthalpies for an ideal gas at temperature T and constant pressure and
constant volume are given by:
h = cp T
h = cv T
The pneumatic components also use the mass continuity equation:
dr 1
= ( mi - mo )
dt V
where ρ is the density of the gas within the component. For components with no internal
mass of gas, the equation simplifies to:
G = mi = mo
where G is the mass flow rate through the component.
For specific equations used in each block, see the block reference pages.
Network Variables
The Across variables are pressure and temperature, and the Through variables are mass
flow rate and heat flow. Note that these choices result in a pseudo-bond graph, because
the product of pressure and mass flow rate is not power.
Connection Constraints
Every node in a pneumatic network must have a defined temperature as well as
pressure. This rule places some constraints on how you connect the pneumatic elements.
In effect, every node should have a volume of fluid associated with it. When the ideal gas
law is applied, this volume of fluid determines the relationship between temperature
and pressure. Some elements already have a volume of fluid associated with them,
and therefore having just one of these components connected to a node satisfies this
1-47
1
Model Construction
condition. Such blocks include Constant Volume Pneumatic Chamber, Pneumatic Piston
Chamber, Rotary Pneumatic Piston Chamber, and Pneumatic Atmospheric Reference.
An exception to the above rule (that every node must have a volume of fluid associated
with it) occurs when two nodes are connected by a component for which the heat equation
says that the temperatures are equal. In this case, just one of the nodes needs to be
connected to a component with associated volume of fluid. Such components include the
pressure and flow rate sources.
For models that represent an actual pneumatic network, these constraints should
have no impact. For example, connecting two orifices in series makes no physical sense
because the underlying assumption of the orifice equation is that gas is discharged into a
volume of fluid. Therefore, modeling actual physical systems should automatically satisfy
these constraints.
References
[1] Moran M.J. and Shapiro H.N. Fundamentals of Engineering Thermodynamics. Second
edition. New York: John Wiley & Sons, 1992.
1-48
2
Thermal Liquid Models
• “Modeling Thermal Liquid Systems” on page 2-2
• “Thermal Liquid Library” on page 2-6
• “Thermal Liquid Modeling Framework” on page 2-10
• “Heat Transfer in Insulated Oil Pipeline” on page 2-14
2
Thermal Liquid Models
Modeling Thermal Liquid Systems
In this section...
“When to Use Thermal Liquid Blocks” on page 2-2
“Modeling Workflow” on page 2-3
“Establish Model Requirements” on page 2-3
“Model Physical Components” on page 2-4
“Prepare Model for Analysis” on page 2-5
“Run Simulation” on page 2-5
When to Use Thermal Liquid Blocks
The Thermal Liquid library expands the fluid modeling capability of Simscape. With
this library, you can account for thermal effects in a fluid system. For example, you can
model the warming effect of viscous dissipation in a pipe. You can also account for the
temperature dependence of fluid properties, e.g., density and viscosity.
To decide whether Thermal Liquid blocks fit your modeling needs, consider the fluid
system you are trying to represent. Other Simscape blocks—e.g. Hydraulic or Pneumatic
—may better suit your application. Assess the following:
• Number of phases
Is the fluid medium single phase or multiphase?
• Relevant phases
Is the fluid medium a gas, a liquid, or a multiphase mixture?
• Thermal effects
Does temperature change significantly in the time scale of the simulation? Are
thermal effects important for analysis? Are the temperature dependences of the liquid
properties important?
As a rule, use Thermal Liquid blocks for fluid systems in which a single-phase liquid
experiences significant temperature changes. For gaseous systems, use Pneumatic blocks
instead. For isothermal liquid systems, use Hydraulic blocks.
2-2
Modeling Thermal Liquid Systems
Modeling Workflow
The suggested workflow for Thermal Liquid models includes four steps:
1
Establish model requirements — Define the purpose and scope of the model. Then,
identify the relevant components and interactions in the model. Use this information
as a guide when building the model.
2
Model physical components — Determine the appropriate blocks for modeling the
relevant components and interactions. Then, add the blocks to the model canvas
and connect them according to the Simscape connection rules. Specify the block
parameters.
3
Prepare model for analysis — Add sensors to the model. Alternatively, configure the
model for Simscape data logging. Check the physical units of each sensed variable.
4
Run simulation — Configure the solver settings. Then, run the simulation. If
necessary, refine the model until you achieve the desired fidelity level.
Establish Model Requirements
The foundation of a good model is a clear understanding of its purpose and requirements.
What are you trying to accomplish with the model? What are the relevant components,
processes, and states? Determine what is essential and what is not. Start simple, using
a rough approximation of the physical system as a guide. Then, iteratively add detail to
reach the appropriate model fidelity for your application.
An insulated oil pipeline buried underground provides an example. As oil flows
through the pipeline, it experiences conductive heat losses due to the cooler pipeline
surroundings. Heat flows across three material layers—pipe wall, insulant, and soil—
causing oil temperature to drop. However, only conduction across soil and insulant layers
matter. A typical pipe wall is thin and conductive, and its effect on conductive heat loss is
minimal at best. Omitting this process simplifies the model and speeds up simulation.
You also must determine the dimensions and properties of each component. During
modeling, you specify these parameters in the Simscape blocks for the components.
Obtain the physical properties of the liquid medium. Manufacturer data sheets typically
provide this data. You can also use analytical expressions to define the physical property
lookup tables.
When modeling pipes, consider the impact that dynamic compressibility and flow
inertia have on the transient system behavior. If the time scale of an effect exceeds
the simulation run time, the impact is usually negligible. During modeling, turn off
2-3
2
Thermal Liquid Models
negligible effects to improve simulation speed. Characteristic time scales for dynamic
compressibility and flow inertia are approximately L/c and L/v, respectively, where:
• L is the length of the pipe.
• v is the mean flow velocity through the pipe.
• c is the speed of sound in the liquid medium.
If you are unsure whether an effect is relevant to your model, simulate the model with
and without that effect. Then, compare the two simulation results. If the difference is
substantial, leave that effect in place. The result is greater model fidelity at small time
scales, e.g., during transients associated with flow reversal in a pipe.
Model Physical Components
Start by adding a Thermal Liquid Settings (TL) block to the model canvas. Use this
block to provide the physical properties of the liquid medium. This block is not strictly
required, but without it the liquid properties are reset to their default values, given
for water. In the block dialog box, enter the physical property lookup tables that you
acquired during the planning stage.
Identify the appropriate blocks for representing the physical components and their
interactions. Components can be simple, requiring a single block, or custom, requiring
multiple blocks typically within a Subsystem block. Add the blocks to the model canvas
and connect them according to the Simscape connection rules.
The ssc_tl_hydraulic_fluid_warming example shows simple and custom
components. The Mass Flow Rate Source (TL) represents an ideal power source. It
is a simple component. The Double-acting cylinder subsystem block represents the
mechanical part of a hydraulic actuator. It contains two Translational Mechanical
Converter (TL) blocks and is a custom component.
Once you have connected the blocks, specify the relevant parameters. These include
dimensions, physical states, empirical correlation coefficients, and initial conditions.
In Pipe (TL), Rotational Mechanical Converter (TL), and Translational Mechanical
Converter (TL) blocks, select the appropriate setting for effects such as dynamic
compressibility and flow inertia.
Note: For accurate simulation results, always replace the default parameter values with
data appropriate for your model.
2-4
Modeling Thermal Liquid Systems
Prepare Model for Analysis
To analyze a model, you must set up that model for data collection. The simplest
approach is to add sensor blocks to the model. The Thermal Liquid library provides two
sensor block types: one for Through variables (mass flow rate and heat flux), the other for
Across variables (pressure and temperature). By using the PS-Simulink Converter block,
you can specify the physical units of the sensed variable.
An alternative approach is to use Simscape data logging. This approach, which uses
MATLAB commands instead of blocks, provides access to a broader range of model
variables and parameters. One example is the kinematic viscosity of the liquid medium
inside a pipeline segment. You can analyze this parameter using Simscape data logging
but not sensor blocks.
For an overview of Simscape data logging, see “About Simulation Data Logging”. For an
example of how to plot logged data, see “Log and Plot Simulation Data”.
Run Simulation
The final step in the modeling workflow is to simulate the model. Before running
simulation, check that the numerical solver is appropriate for your model. To do this, use
the Model Configuration Parameters dialog box.
For physical models, variable-step solvers such as ode15s typically perform best. Reduce
step sizes and tolerances for greater simulation accuracy. Increase them instead for
faster simulation.
Run the simulation. Plot simulation data from sensors and Simscape data logging,
or process it for further analysis. If necessary, refine the model. For example, correct
simulation issues or to improve model fidelity.
Related Examples
•
“Heat Transfer in Insulated Oil Pipeline” on page 2-14
More About
•
“Thermal Liquid Library” on page 2-6
•
“Thermal Liquid Modeling Framework” on page 2-10
2-5
2
Thermal Liquid Models
Thermal Liquid Library
In this section...
“Why Use Thermal Liquid Blocks?” on page 2-6
“Representing Thermal Liquid Components” on page 2-6
“Specifying Thermal Liquid Medium” on page 2-8
“Modeling Multidomain Systems” on page 2-8
Why Use Thermal Liquid Blocks?
The thermal behavior of liquid systems is of interest in many engineering applications.
Liquids can store energy and release it back to their surroundings, often doing work in
the process. Oil flow through an underground pipeline and hydraulic fluid flow in an
aircraft actuator are two examples.
When temperature fluctuations are negligible, liquids behave as isothermal fluids, which
simplifies the modeling process. However, when detailed thermal analysis is a goal, or
when temperature fluctuations are significant, this assumption is no longer suitable.
The Thermal Liquid library provides a modeling tool that you can use to analyze the
thermal behavior of thermal liquid systems. Three featured examples show some
applications well-suited for Thermal Liquid modeling:
• ssc_tl_oil_pipeline — Model oil temperature along an insulated underground
pipeline.
• ssc_tl_hydraulic_fluid_warming — Model hydraulic fluid warming due to
viscous dissipation inside a hydraulic actuator.
• ssc_tl_water_hammer — Model the water hammer effect due to a fast-turning
hydraulic valve.
Representing Thermal Liquid Components
Thermal liquid systems can range in complexity from basic to highly specialized. To
model a basic system, simple components often suffice. These are components such as
chambers, pipes, pumps, and the liquid medium itself. Simple components are often
2-6
Thermal Liquid Library
industry independent and can be modeled using a single Thermal Liquid block. For
example, you can model a pipeline segment using a single Pipe (TL) block.
To model a specialized system, generally you use custom components. These are
components that you cannot represent by a single Thermal Liquid block. The five-way
directional control valve in the ssc_tl_hydraulic_fluid_warming example is one
such component. Custom components are often industry specific and must be modeled by
grouping Thermal Liquid blocks into more complex subsystems.
The Thermal Liquid library shares the structure of other Simscape Foundation libraries.
Four sublibraries supply the Thermal Liquid blocks: Elements, Sources, Sensors, and
Utilities. With these sublibraries you can represent the most common components of a
thermal liquid system. The table summarizes these components.
Component Type
Description
Thermal Liquid Blocks
Liquid storage
Store liquid in chambers or
reservoirs.
Constant Volume Chamber
(TL), Reservoir (TL),
Controlled Reservoir (TL)
Liquid transport
Transport thermal liquid
through closed conduits
such as pipes.
Pipe (TL)
Flow restriction
Restrict thermal liquid
flow, e.g., due to valves or
fittings.
Local Restriction (TL),
Variable Local Restriction
(TL)
Mechanical interfaces
Interface thermal liquid and Translational Mechanical
mechanical systems, e.g., to Converter (TL), Rotational
convert liquid mechanical
Mechanical Converter (TL)
energy into useful work.
Power sources
Provide a power source to
the thermal liquid system,
e.g. , pressure difference or
mass flow rate.
Mass Flow Rate Source
(TL), Pressure Source (TL),
Controlled Mass Flow Rate
Source (TL), Controlled
Pressure Source (TL)
Sensors
Collect measurement data
for analysis of parameters,
such as mass flow rate,
thermal flux, pressure, and
temperature.
Pressure & Temperature
Sensor (TL), Mass Flow Rate
& Thermal Flux Sensor (TL)
2-7
2
Thermal Liquid Models
Component Type
Description
Thermal Liquid Blocks
Thermal liquid
Specify thermodynamic
Thermal Liquid Settings
properties and pressure(TL)
temperature validity region
of thermal liquid medium.
Specifying Thermal Liquid Medium
The Thermal Liquid Settings (TL) block specifies the thermodynamic properties of
the liquid medium. These properties are assumed functions of both pressure and
temperature. This assumption boosts model fidelity, especially in models in which
pressure, temperature, or both, vary widely.
The block accepts two-way lookup tables as input. These tables provide the different
thermodynamic property values at discrete pressures and temperatures. You can
populate these tables using empirical data from product data sheets or values calculated
from analytical expressions.
Modeling Multidomain Systems
Thermal Liquid blocks can contain different types of conserving ports. These ports
include not only Thermal Liquid conserving ports but also thermal and mechanical
conserving ports. By using these ports, you can interface a Thermal Liquid subsystem
with thermal and mechanical subsystems.
For instance, you can use the thermal conserving port of a Pipe (TL) block to model
conductive heat transfer through a pipe wall. Oil pipeline modeling is one application.
The example ssc_tl_oil_pipeline shows this approach.
Similarly, you can use the translational mechanical conserving ports of a Translational
Mechanical Converter (TL) block to convert hydraulic pressure in a thermal liquid
system into a mechanical actuation force. Hydraulic actuator modeling is one application.
The example ssc_tl_hydraulic_fluid_warming shows this approach.
The table lists the Thermal Liquid blocks that have thermal or mechanical conserving
ports. You can use these blocks to create a multidomain model containing thermal liquid,
thermal, and mechanical subsystems.
2-8
Thermal Liquid Library
Thermal Liquid Block
Thermal Conserving Port
Mechanical Conserving Port
Constant Volume Chamber
(TL)
✓
✗
Pipe (TL)
✓
✗
Rotational Mechanical
Converter (TL)
✓
✓
Translational Mechanical
Converter (TL)
✓
✓
Related Examples
•
“Heat Transfer in Insulated Oil Pipeline” on page 2-14
More About
•
“Modeling Thermal Liquid Systems” on page 2-2
•
“Thermal Liquid Modeling Framework” on page 2-10
2-9
2
Thermal Liquid Models
Thermal Liquid Modeling Framework
In this section...
“How Blocks Represent Components” on page 2-10
“How Ports Represent Interfaces” on page 2-11
“Full Flux Scheme” on page 2-12
How Blocks Represent Components
Thermal Liquid models are based on the finite volume method. This method discretizes a
thermal liquid system into multiple control volumes that interact via shared interfaces.
An oil pipeline system is one example: you can model this system as a set of pipeline
segments that connect serially along the pipeline length.
Discretization of Pipeline System
A control volume can represent a thermal liquid component, such as an oil pipeline, or
a part of a component, such as a pipeline segment. You can discretize a thermal liquid
system and its components as finely as you need, for example to increase simulation
accuracy. However, the finer the discretization, the greater the model complexity—and
the slower the simulation.
Thermal Liquid blocks represent the control volume of a component using an internal
node. This node provides the liquid pressure and temperature inside the component. The
node is not visible, but you can access its parameters and variables using Simscape data
logging. For more information, see “About Simulation Data Logging”.
2-10
Thermal Liquid Modeling Framework
Simscape Nodes in Pipe (TL) Block
Two physical principles govern the dynamic evolution of liquid pressure and temperature
at the internal node of a control volume: mass conservation and energy conservation.
Pressure and temperature computation is carried out for the control volume surrounding
the internal node. This control volume is the total volume of the thermal liquid
component the block represents.
A second set of nodes represents the interfaces through which a finite volume can
interact with its neighbors. These nodes are visible as Simscape conserving ports,
of which Thermal Liquid conserving ports are the most important. By allowing the
exchange of mass, momentum, and energy between adjacent liquid volumes, Thermal
Liquid conserving ports govern the dynamic evolution of the finite volume as it tends to a
steady state.
How Ports Represent Interfaces
Thermal Liquid conserving ports provide the liquid pressure and temperature at the
interfaces they represent. They also provide the flow rates of mass and heat, which
govern the interactions between thermal liquid components. Pressure and temperature
are the Across variables of the Thermal Liquid domain, while the flow rates are the
Through variables.
Two physical principles govern the mass and heat flow rates through a Thermal Liquid
conserving port: momentum conservation and energy conservation. The mass flow rate
at a port is computed from the momentum conservation principle. The heat flow rate at a
port is computed from the thermal energy conservation principle.
2-11
2
Thermal Liquid Models
The flow rate computations are carried out for half the control volume of a thermal liquid
component. The half control volume is bounded on one end by the interface the port
represents, and on another end by a parallel surface passing through the control volume
centroid.
The figure shows the half control volume for flow rate computations at interface A of a
pipeline segment. Interface A corresponds to Thermal Liquid conserving port A of a Pipe
(TL) block. Node C corresponds to the internal node of the block, which is coincident with
the control volume centroid.
Half Control Volume for Flow Rate Calculations
Full Flux Scheme
Blocks in the Thermal Liquid library implement a full flux scheme. Using this scheme,
the net heat flux through a Thermal Liquid conserving port contains both convective
and conductive flux contributions. By including thermal conduction in the flow direction,
Thermal Liquid blocks provide more realistic simulation of the physical system they
represent.
Other advantages of the full flux scheme include enhanced simulation robustness of
thermal liquid models. This robustness becomes relevant in models where the conductive
flux contribution can be dominant. Examples include instances of low mass flow rates
and flow reversal, during which the convective flux becomes negligible or vanishes
altogether.
Related Examples
•
2-12
“Heat Transfer in Insulated Oil Pipeline” on page 2-14
Thermal Liquid Modeling Framework
More About
•
“Modeling Thermal Liquid Systems” on page 2-2
•
“Thermal Liquid Library” on page 2-6
2-13
2
Thermal Liquid Models
Heat Transfer in Insulated Oil Pipeline
In this section...
“Oil Pipelines” on page 2-14
“Modeling Considerations” on page 2-15
“Simscape Model” on page 2-17
“Run Simulation” on page 2-18
“Run Optimization Script” on page 2-25
Oil Pipelines
Temperature plays an important role in oil pipeline design. Below the so-called cloud
point, paraffin waxes precipitate from crude oil and start to accumulate along the pipe
wall interior. The waxy deposits restrict oil flow, increasing the power requirements of
the pipeline. At still-lower temperatures—below the pour point of oil—these crystals
become so numerous that, if allowed to quiesce, oil becomes semisolid.
In cold climates, conductive heat losses through the pipe wall can be significant. To
keep oil in its favorable temperature range, pipelines include some temperature control
measures. Heating stations placed at intervals along the pipeline help to warm the oil.
An insulant liner covering the pipe wall interior helps to retard the cooling rate of the oil.
Viscous dissipation provides an additional heat source. As adjacent parcels of oil flow
against each other, they experience energy losses that appear in the form of heat. The
warming effect is small, but sufficient to at least partially offset the conductive heat
losses that occur through the insulant liner.
2-14
Heat Transfer in Insulated Oil Pipeline
At a certain insulation thickness, viscous dissipation exactly balances the conductive
heat loss. Oil stays at its ideal temperature throughout the pipeline length and the need
for heating stations is reduced. From a design standpoint, this insulation thickness is
optimal.
In this example, you simulate an insulated oil pipeline segment. You then run an
optimization script to determine the optimal insulation thickness. This example is based
on Simscape model ssc_tl_oil_pipeline.
Modeling Considerations
The physical system in this example is an oil pipeline segment. Insulation lines the pipe
wall interior, while soil covers the pipe wall exterior, retarding conductive heat loss. The
simplifying assumption is made that the physical system is symmetric about the pipe
center line.
Flow through the pipeline segment is assumed fully developed: the velocity profile of
the flowing oil remains constant along the pipeline length. In addition, oil is assumed
Newtonian and compressible: shear stress is proportional to the shear strain, and mass
density varies with both temperature and pressure.
Oil enters the pipeline segment at a fixed temperature, TUpstream, with a fixed mass
flow rate, Vdot * rho0, where:
• Vdot is the volumetric flow rate of oil through the pipe.
2-15
2
Thermal Liquid Models
• rho0 is the mass density of oil entering the pipeline segment.
Inside the pipeline segment, viscous dissipation heats the flowing oil, while thermal
conduction through the pipe wall cools it. The balance between the two processes governs
the temperature of oil exiting the pipeline segment.
The amount of heat gained through viscous dissipation depends partly on oil viscosity
and mass flow rate. The greater these quantities are, the greater the viscous heat gain
is—and the warmer the oil tends to get. The amount of heat lost via thermal conduction
depends partly on the thermal resistances of the insulation, pipe wall, and soil layer.
The smaller the thermal resistances are, the greater the conductive heat loss is—and the
cooler the oil tends to get.
Using an electrical circuit analogy, the combined thermal resistance of three material
layers arranged in series equals the sum of the individual thermal resistances:
Rcombined = Rwall + Rins. + Rsoil
Assuming the pipe wall is thin and its material a good thermal conductor, you can safely
ignore the thermal resistance of the pipe wall. The combined thermal resistance is then
simply the sum of the insulation and soil contributions, Rins. and Rsoil.
The thermal resistance of the insulation layer is directly proportional to its thickness,
(D2-D1)/2, and inversely proportional to its thermal conductivity, kInsulant. Likewise,
the thermal resistance of the soil layer is directly proportional to its thickness, z, and
inversely proportional to its thermal conductivity, kSoil.
The figure shows the relevant dimensions of the pipeline segment. Variable names match
those specified in the model. The inner insulation diameter, D1, is also the hydraulic
diameter of the pipeline segment.
2-16
Heat Transfer in Insulated Oil Pipeline
Simscape Model
The Simscape model ssc_tl_oil_pipeline represents an insulated oil pipeline
segment buried underground. To open this model, at the MATLAB command prompt,
enter ssc_tl_oil_pipeline. The figure shows the model.
2-17
2
Thermal Liquid Models
The Pipe (TL) block represents the physical system in this example, i.e., the oil pipeline
segment. Port A represents its inlet and port B its outlet. Port W represents thermal
conduction through the pipe wall. The block accounts for viscous heating.
The Mass Flow Rate Source (TL) block provides the flow rate through the pipe. The From
upstream segment block acts as a temperature source for the pipe inlet, while the To
downstream segment block acts as a temperature sink at the pipe outlet.
The Conduction through insulant and Conduction through soil blocks represent thermal
conduction through insulant and soil layers, respectively. These blocks appear in the
Simscape Thermal library as Conductive Heat Transfer. The Soil subsystem block
provides the temperature boundary condition at the soil surface.
The Thermal Liquid Settings (TL) block provides the physical properties of the
oil, expressed as two-sided lookup tables containing the temperature and pressure
dependence of the properties. The table summarizes these blocks.
Block
Description
Pipe (TL)
Pipeline segment
Conduction through insulant
Insulant thermal conduction
Conduction through soil
Soil thermal conduction
Soil (Subsystem)
Soil temperature
From upstream segment
Pipe inlet temperature sink
To downstream segment
Pipe outlet temperature sink
Mass Flow Rate Source (TL)
Oil mass flow rate
Thermal Liquid Settings (TL)
Oil thermodynamic properties
Run Simulation
To analyze the performance of the oil pipeline segment, simulate the model. The
Comparison scope plots the upstream and downstream oil temperatures. Open this scope.
The insulation thickness is near its optimal value, resulting in only a small temperature
change over a 1000 meter length. At a rate of ~0.020 K/km, oil temperature changes
approximately 2 K over a 100 kilometer length.
2-18
Heat Transfer in Insulated Oil Pipeline
Plot Physical Properties Using Data Logging
By using Simscape data logging, you can plot the physical properties of the oil as a
function of simulation time. Such a plot clearly shows any variability in the value of a
physical property. One example is the kinematic viscosity of oil in the pipeline segment,
represented by the Pipe (TL) block.
1
At the MATLAB command line, enter simlog.Pipe_TL.print.
In the data tree, the kinematic viscosity nu appears under the node pipe_model,
which itself appears under the node simlog.Pipe_TL. The logging object for the
kinematic viscosity of oil in the pipe, then, is simlog.Pipe_TL.pipe_model.nu.
2-19
2
Thermal Liquid Models
2-20
Heat Transfer in Insulated Oil Pipeline
2
At the MATLAB command line, enter
simscape.logging.plot({simlog.Pipe_TL.pipe_model.nu}).
As expected, the kinematic viscosity remains approximately constant throughout the
simulation, reflecting the minimal temperature changes that occur in the oil.
Note: For more information about Simscape logging, see “About Simulation Data
Logging”.
Simulate Effects of Changing Insulation Diameter
Experiment with different values for the insulation inner diameter. By varying this
parameter, you offset the balance between viscous dissipation, which heats the oil, and
thermal conduction, which cools the oil.
1
Open Model Explorer.
2
In the Model Hierarchy pane, select Base Workspace.
3
In the Contents pane, click the value of parameter D1.
4
Enter 0.20.
2-21
2
Thermal Liquid Models
By reducing the inner diameter of the insulation layer to 0.20, you increase the
insulation thickness, slowing down heat loss through the pipe wall via thermal
conduction. Run the simulation. Then, open the Comparison scope and autoscale to view
full plot.
The new plot shows an oil temperature at the pipe outlet (top curve) that significantly
exceeds that at the pipe inlet (bottom line). Viscous dissipation now dominates the
thermal energy balance in the pipeline segment. The new insulation thickness poses a
design problem: in a long pipeline, a 1.1 K/km heating rate can raise the oil temperature
substantially at the receiving end of the pipeline.
Plotting the kinematic viscosity as a function of time shows that its variability is now
quite significant also. At the MATLAB command line, enter the logging command:
simscape.logging.plot({simlog.Pipe_TL.pipe_model.nu}).
2-22
Heat Transfer in Insulated Oil Pipeline
Try increasing the inner diameter of the insulation layer, D1, to 0.55. By increasing this
value, you decrease the insulation thickness, accelerating heat loss through the pipe
wall via thermal conduction. Then, run the simulation. Open the Comparison scope and
autoscale to view the full plot.
2-23
2
Thermal Liquid Models
The resulting plot shows that the oil temperature at the pipe outlet is now significantly
lower than that at the pipe inlet. Thermal conduction clearly dominates the thermal
energy balance in the pipeline segment. This insulation thickness also poses a
design issue: at a rate of 0.25K/km, oil flowing through a long pipeline will cool down
substantially.
Plot the kinematic viscosity as a function of time using Simscape logging. Because the
temperature change is now more modest, changes in viscosity are less significant.
2-24
Heat Transfer in Insulated Oil Pipeline
Run Optimization Script
The model provides an optimization script that you can run to determine the optimal
inner diameter of the pipe insulation, D1. The script iterates the model simulation
at different D1 values, plotting the rates of viscous warming and conductive cooling
against each other. The intersection point between the two curves identifies the optimal
insulation thickness for the model:
1
In the model window, double-click Run optimization script.
2-25
2
Thermal Liquid Models
2
In the plot that opens, visually determine the horizontal-axis value for the
intersection point between the two curves.
The optimal inner diameter of the insulation layer is 0.37 m. Update parameter D1 to
this value:
1
Open Model Explorer.
2
In the Model Hierarchy pane, click Base Workspace.
3
In the Contents pane, click the value of D1.
4
Enter 0.37.
Now, run the simulation. Open the Comparison scope and autoscale to view the full plot.
The temperature difference between the inlet and the outlet is negligible.
2-26
Heat Transfer in Insulated Oil Pipeline
More About
•
“Modeling Thermal Liquid Systems” on page 2-2
•
“Thermal Liquid Library” on page 2-6
•
“Thermal Liquid Modeling Framework” on page 2-10
2-27
3
Model Simulation
• “How Simscape Models Represent Physical Systems” on page 3-2
• “How Simscape Simulation Works” on page 3-5
• “Setting Up Solvers for Physical Models” on page 3-11
• “Customizing Solvers for Physical Models” on page 3-17
• “Troubleshooting Simulation Errors” on page 3-25
• “Code Generation” on page 3-31
• “Real-Time Simulation” on page 3-34
• “Finding an Operating Point” on page 3-43
• “Linearizing at an Operating Point” on page 3-48
• “Linearize an Electronic Circuit” on page 3-54
• “Linearize a Plant Model for Use in Feedback Control Design” on page 3-64
• “Limitations” on page 3-70
• “References” on page 3-75
3
Model Simulation
How Simscape Models Represent Physical Systems
In this section...
“Representations of Physical Systems” on page 3-2
“Differential, Differential-Algebraic, and Algebraic Systems” on page 3-2
“Stiffness” on page 3-3
“Events and Zero Crossings” on page 3-3
“Working with Simscape Representation” on page 3-3
Representations of Physical Systems
This section describes important characteristics of the mathematical representations
of physical systems, and how Simscape software implements such representations. You
might find this overview helpful if you:
• Require details of such representations to improve your model fidelity or simulation
performance.
• Are constructing your Simscape model or its components with the Simscape language.
• Need to troubleshoot Simscape modeling or simulation failures.
Mathematical representations are the foundation for physical simulation. For more
information about simulation, see “How Simscape Simulation Works” on page 3-5.
Differential, Differential-Algebraic, and Algebraic Systems
The mathematical representation of a physical system contains ordinary differential
equations (ODEs), algebraic equations, or both.
• ODEs govern the rates of change of system variables and contain some or all of the
time derivatives of the system variables.
• Algebraic equations specify functional constraints among system variables, but
contain no time derivatives of system variables.
• Without algebraic constraints, the system is differential (ODEs).
• Without ODEs, the system is algebraic.
• With ODEs and algebraic constraints, the system is mixed differential-algebraic
(DAEs).
3-2
How Simscape Models Represent Physical Systems
A system variable is differential or algebraic, depending on whether or not its time
derivative appears in the system equations.
Stiffness
A mathematical problem is stiff if the solution you are seeking varies slowly, but there
are other solutions within the error tolerances that vary rapidly. A stiff system has
several intrinsic time scales of very different magnitude [1].
A stiff physical system has one or more components that behave “stiffly” in the ordinary
sense, such as a spring with a large spring constant. Mathematical equivalents include
quasi-incompressible fluids and low electrical inductance. Such systems often exhibit
high frequency oscillations in some of their components or modes.
Events and Zero Crossings
Events are discontinuous changes in system state or dynamics as the system evolves in
time; for example, a valve opening, or a hard stop.
A zero crossing is a specific event type, represented by the value of a mathematical
function changing sign.
Working with Simscape Representation
A Simscape model is equivalent to a set of equations representing one or more physical
systems as physical networks.
• Start by assuming that your physical network is a DAE system: a mix of differential
and algebraic equations and variables.
Remember that some physical networks are represented by ODEs only.
• Physical networks may contain stiff differential equations.
• Identify discrete and continuous components that might change discontinuously
during a simulation.
Creating and Detecting Zero Crossings in Simscape Models
Simulink and Simscape software have specific methods for detecting and locating zerocrossing events. For general information, see “Zero-Crossing Detection” in the Simulink
documentation.
3-3
3
Model Simulation
Your model can contain zero-crossing conditions arising from several sources:
• Simscape and normal Simulink blocks copied from their respective block libraries
• Expressions programmed in the Simscape language
You can disable zero-crossing detection on individual blocks, or globally across the
entire model. Zero-crossing detection often improves simulation accuracy, but can slow
simulation speed.
Tip If the exact times of zero crossings are important in your model, then keep zerocrossing detection enabled. Disabling it can lead to major simulation inaccuracies.
Enabling and Disabling Zero-Crossing Conditions in Simscape Language
In the Simscape language, you can create or avoid Simulink zero-crossing conditions in
your model by switching between different implementations of discontinuous conditional
expressions. You can:
• Use relational operators, which create zero-crossing conditions. For example,
programming the operator relation: a < b creates a zero-crossing condition.
• Use relational functions, which do not create zero-crossing conditions. For example,
programming the functional relation: lt(a,b) does not create a zero-crossing
condition.
3-4
How Simscape Simulation Works
How Simscape Simulation Works
In this section...
“Simscape Simulation Phases” on page 3-5
“Model Validation” on page 3-7
“Network Construction” on page 3-7
“Equation Construction” on page 3-8
“Initial Conditions Computation” on page 3-8
“Transient Initialization” on page 3-9
“Transient Solve” on page 3-10
Simscape Simulation Phases
You might find this brief overview helpful for constructing models and understanding
errors. For more information, see “How Simscape Models Represent Physical Systems” on
page 3-2.
Simscape software gives you multiple ways to simulate and analyze physical systems
in the Simulink environment. Running a physical model simulation is similar to
simulating any Simulink model. It entails setting various simulation options, starting
the simulation, and viewing the simulation results. This topic describes various aspects
of simulation specific to Simscape models. For specifics of simulating and analyzing with
individual Simscape add-on products, refer to the documentation for those individual
add-on products.
This flow chart presents the Simscape simulation sequence.
3-5
3
Model Simulation
The flow chart consists of the following major phases:
3-6
1
“Model Validation” on page 3-7
2
“Network Construction” on page 3-7
3
“Equation Construction” on page 3-8
4
“Initial Conditions Computation” on page 3-8
5
“Transient Initialization” on page 3-9
How Simscape Simulation Works
6
“Transient Solve” on page 3-10
Model Validation
The Simscape solver first validates the model configuration and checks your data entries
from the block dialog boxes.
• All Simscape blocks in a diagram must be connected into one or more physical
networks. Unconnected Conserving ports are not allowed.
• Each topologically distinct physical network in a diagram requires exactly one Solver
Configuration block.
• If your model contains hydraulic elements, each topologically distinct hydraulic
circuit in a diagram must connect to a Custom Hydraulic Fluid block (or Hydraulic
Fluid block, available with SimHydraulics block libraries). These blocks define the
fluid properties that act as global parameters for all the blocks that connect to the
hydraulic circuit. If no hydraulic fluid block is attached to a loop, the hydraulic blocks
in this loop use the default fluid. However, more than one hydraulic fluid block in a
loop generates an error.
Similarly, if your model contains pneumatic elements, default gas properties for
a pneumatic network are for dry air and ambient conditions of 101325 Pa and 20
degrees Celsius. If you attach a Gas Properties block to a pneumatic circuit, you can
change gas properties and ambient conditions for all the blocks connected to the
circuit. However, more than one Gas Properties block in a pneumatic circuit generates
an error.
• Signal units specified in a Simulink-PS Converter block must match the input type
expected by the Simscape block connected to it. For example, when you provide the
input signal for an Ideal Angular Velocity Source block, specify angular velocity
units, such as rad/s or rpm, in the Simulink-PS Converter block, or leave it unitless.
Similarly, units specified in a PS-Simulink Converter block must match the type of
physical signal provided by the Simscape block outport.
Network Construction
After validating the model, the Simscape solver constructs the physical network based on
the following principles:
• Two directly connected Conserving ports have the same values for all their Across
variables (such as voltage or angular velocity).
3-7
3
Model Simulation
• Any Through variable (such as current or torque) transferred along the Physical
connection line is divided among the multiple components connected by the branches.
For each Through variable, the sum of all its values flowing into a branch point equals
the sum of all its values flowing out.
Equation Construction
Based on the network configuration, the parameter values in the block dialog boxes, and
the global parameters defined by the fluid properties, if applicable, the Simscape solver
constructs the system of equations for the model.
These equations contain system variables of the following types:
• Dynamic — Time derivatives of these variables appear in equations. Dynamic, or
differential, variables add dynamics to the system and require the solver to use
numerical integration to compute their values. Dynamic variables can produce either
independent or dependent states for simulation.
• Algebraic — Time derivatives of these variables do not appear in equations. These
variables appear in algebraic equations but add no dynamics, and this typically
occurs in physical systems due to conservation laws, such as conservation of mass and
energy. The states of algebraic variables are always dependent on dynamic variables,
other algebraic variables, or inputs.
The solver then performs the analysis and eliminates variables that are not needed
to solve the system of equations. After variable elimination, the remaining variables
(algebraic, dynamic dependent, and dynamic independent) get mapped to Simulink state
vector of the model.
For information on how to view and analyze model variables, see “Model Statistics”.
Initial Conditions Computation
The Simscape solver computes the initial conditions only once, at the beginning of
simulation (t = 0). In the Solver Configuration block dialog box, the default is that the
Start simulation from steady state check box is not selected. If it is selected in your
model, see “Finding an Initial Steady State” on page 3-9.
The solver computes the initial conditions by finding initial values for all the system
variables that exactly satisfy all the model equations. You can affect the initial conditions
3-8
How Simscape Simulation Works
computation by block-level variable initialization, that is, by specifying the priority and
target initial values on the Variables tab of the block dialog boxes.
The values you specify during block-level variable initialization are not the actual values
of the respective variables, but rather their target values at the beginning of simulation
(t = 0). Depending on the results of the solve, some of these targets may or may not be
satisfied. The solver tries to satisfy the high-priority targets first, then the low-priority
ones:
• At first, the solver tries to find a solution where all the high-priority variable
targets are met exactly, and the low-priority targets are approximated as closely as
possible. If the solution is found during this stage, it satisfies all the high-priority
targets. Some of the low-priority targets might also be met exactly, the others are
approximated.
• If the solver cannot find a solution that exactly satisfies all the high-priority targets,
it issues a warning and enters the second stage, where High priority is relaxed
to Low. That is, the solver tries to find a solution by approximating both the highpriority and the low-priority targets as closely as possible.
After you initialize the block variables and prior to simulating the model, you can open
the Variable Viewer to see which of the variable targets have been satisfied. For more
information on block-level variable initialization, see “Variable Initialization”.
Finding an Initial Steady State
When you select the Start simulation from steady state check box, the solver
attempts to find the steady state that would result if the inputs to the system were held
constant for a long enough time, starting from the initial state obtained from the initial
conditions computation just described. If the steady-state solve succeeds, the state found
is some steady state (within tolerance), but not necessarily the state expected from the
given initial conditions. Steady state means that the system variables are no longer
changing with time. Simulation then starts from this steady state.
A model can have more than one steady state. In this case, the solver selects the steadystate solution that is consistent with the variable targets specified during block-level
variable initialization. For more information, see “Variable Initialization”.
Transient Initialization
After computing the initial conditions, or after a subsequent event (such as a
discontinuity resulting, for example, from a valve opening, or from a hard stop), the
3-9
3
Model Simulation
Simscape solver performs transient initialization. Transient initialization fixes all
dynamic variables and solves for algebraic variables and derivatives of dynamic
variables. The goal of transient initialization is to provide a consistent set of initial
conditions for the next phase, transient solve.
Transient Solve
Finally, the Simscape solver performs transient solve of the system of equations. In
transient solve, continuous differential equations are integrated in time to compute all
the variables as a function of time.
The solver continues to perform the simulation according to the results of the transient
solve until the solver encounters an event, such as a zero crossing or discontinuity. The
event may be within the physical network or elsewhere in the Simulink model. If the
solver encounters an event, the solver returns to the phase of transient initialization, and
then back to transient solve. This cycle continues until the end of simulation.
3-10
Setting Up Solvers for Physical Models
Setting Up Solvers for Physical Models
In this section...
“About Simulink and Simscape Solvers” on page 3-11
“Choosing Simulink and Simscape Solvers” on page 3-11
“Harmonizing Simulink and Simscape Solvers” on page 3-13
About Simulink and Simscape Solvers
This section explains how to select solvers for physical simulation. Proper simulation
of Simscape models requires certain changes to Simulink defaults and consideration of
physical simulation trade-offs. For recommended choices, see “Customizing Solvers for
Physical Models” on page 3-17.
Choosing Simulink and Simscape Solvers
Simulink and Simscape solver technologies provide a range of tools to simulate physical
systems, including the powerful Simscape technique of local solvers. You choose global,
or model-wide, solvers through Simulink. After making these choices, check that they are
consistent; see “Harmonizing Simulink and Simscape Solvers” on page 3-13.
• “Working with Global Simulink Solvers” on page 3-11
• “Working with Local Simscape Solvers” on page 3-12
Working with Global Simulink Solvers
In the Configuration Parameters dialog box of your model, on the Solver pane, the solver
and related settings that you select are global choices. For more information, see “Choose
a Solver” in the Simulink documentation.
When you first create a model, the default Simulink solver is ode45. To select a different
solver, follow a procedure similar to the procedure in “Modifying Initial Settings”.
• You can choose one from a suite of both variable-step and fixed-step solvers. A
variable-step solver is the default.
• You can also select from among explicit and implicit solvers. An explicit solver is the
default. But for physical models, MathWorks recommends implicit solvers, such as
3-11
3
Model Simulation
ode14x, ode23t, and ode15s. Implicit solvers require fewer time steps than explicit
solvers, such as ode45, ode113, and ode1.
See “Switching from the Default Explicit Solver to Other Simulink Solvers” on page
3-14.
• If all the Simulink and Simscape states in your model are discrete, Simulink
automatically switches to a discrete solver and issues a warning. Otherwise, a
continuous solver is the default.
• By default, Simulink variable-step solvers attempt to locate events in time by zerocrossing detection. See “Enabling or Disabling Simulink Zero-Crossing Detection” on
page 3-16.
Working with Local Simscape Solvers
You can switch one or more physical networks to a local implicit, fixed-step Simscape
solver by selecting Use local solver in the network Solver Configuration block. The
solver and related settings you make in each Solver Configuration block are specific to
the connected physical network and can differ from network to network.
A physical network using a local solver appears to the global Simulink solver as if it has
discrete states. You can still use any continuous global solver.
Choosing Local Solvers and Sample Times
To use a local solver, choose a solver type (Backward Euler or Trapezoidal Rule) and a
sample time. Backward Euler is the default.
Choosing Fixed-Cost Simulation
You can select a fixed-cost simulation for one or more physical networks by selecting Use
fixed-cost runtime consistency iterations, as well as Use local solver, and fixing
the number of nonlinear and mode iterations. Fixed-cost simulation requires a global
fixed-step solver.
Choosing Multirate Simulation
With the local solver option, you can perform multirate simulations, with:
• Different sample times in different physical networks, through their respective Solver
Configuration blocks
• A sample-based Simulink block in the model with a sample time different from the
Solver Configuration block or blocks
3-12
Setting Up Solvers for Physical Models
Harmonizing Simulink and Simscape Solvers
Your Simulink and Simscape solver choices must work together consistently. To ensure
consistency of your Simulink and Simscape solver choices for a particular model, open
the model Configuration Parameters dialog box. From the top menu bar in the model
window, select Simulation > Model Configuration Parameters. Review and adjust
the following settings.
• “Switching from the Default Explicit Solver to Other Simulink Solvers” on page
3-14
• “Filtering Input Signals and Providing Time Derivatives” on page 3-14
• “Enabling or Disabling Simulink Zero-Crossing Detection” on page 3-16
• “Making Multirate Simulation Consistent” on page 3-16
Simscape Pane of the Configuration Parameters Dialog Box
3-13
3
Model Simulation
Switching from the Default Explicit Solver to Other Simulink Solvers
If you do not modify the default (explicit) solver, your performance may not be optimal.
Implicit solvers are better for most physical simulations. For more information about
implicit solvers and physical systems, see “Customizing Solvers for Physical Models” on
page 3-17.
Diagnostic Messages About Explicit Solvers
When you use an explicit solver in a model containing Simscape blocks, the system issues
a warning to alert you to a potential problem.
To turn off this default warning or to change it to an error message, go to the Simscape
pane of the Configuration Parameters dialog box:
1
From the Explicit solver used in model containing Physical Networks blocks
drop-down list, select the option that you want:
• warning — If the model uses an explicit solver, the system issues a warning
upon simulation. This is the default option that alerts you to a potential problem
if you use the default solver.
• error — If the model uses an explicit solver, the system issues an error message
upon simulation. If your model is stiff, and you do not want to use explicit solvers,
select this option to avoid future errors.
• none — If the model uses an explicit solver, the system issues no warning or
error message upon simulation. If you want to work with explicit solvers, in
particular for models that are not stiff, select this option.
2
Click OK.
Filtering Input Signals and Providing Time Derivatives
You may need to provide time derivatives of some of the input signals, especially if you
use an explicit solver. One way of providing the necessary input derivatives is by filtering
the input through a low-pass filter. Input filtering makes the input signal smoother
and generally improves model performance. The additional benefit is that the Simscape
engine computes the time derivatives of the filtered input. The first-order filter provides
one derivative, while the second-order filter provides the first and second derivatives. If
you use input filtering, it is very important to select the appropriate value for the filter
time constant.
The filter time constant controls the filtering of the input signal. The filtered input
follows the true input but is smoothed, with a lag on the order of the time constant that
3-14
Setting Up Solvers for Physical Models
you choose. Set the time constant to a value no larger than the smallest time interval in
the system that interests you. If you choose a very small time constant, the filtered input
signal is closer to the true input signal. However, this filtered input signal increases the
stiffness of the system and slows the simulation.
Instead of using input filtering, you can provide time derivatives for the input signal
directly, as additional physical signals.
You can control the way you provide time derivatives for each input signal by configuring
the Simulink-PS Converter block connected to that input signal:
1
Open the Simulink-PS Converter block dialog box.
2
Click the Input handling tab.
3
To turn on input filtering, set the Filtering and derivatives parameter to
Filter input. Select the first-order or second-order filter, by using the Input
filtering order parameter, and set the appropriate Input filtering time constant
parameter value for your model.
4
To avoid filtering the input signal, set the Filtering and derivatives parameter
to Provide input derivative(s). Then set the Input derivatives parameter
value:
3-15
3
Model Simulation
• Provide first derivative — If you select this option, an additional
Simulink input port appears on the Simulink-PS Converter block, to let you
connect the signal providing input derivatives.
• Provide first and second derivatives — If you select this option, two
additional Simulink input ports appear on the Simulink-PS Converter block, to
let you connect the signals providing input derivatives.
Enabling or Disabling Simulink Zero-Crossing Detection
By default, Simulink tracks an important class of simulation events by detecting zero
crossings. With a global variable-step solver and without a local solver, Simulink
attempts to locate the simulated times of zero crossings, if present. See “Working with
Simscape Representation” on page 3-3.
Diagnostic Messages About Globally Disabling Zero-Crossing Detection
You can globally disable zero-crossing detection in the Solver pane of the Configuration
Parameters dialog box, under Zero-crossing options. If you do, and if you are using a
global variable-step solver without a local solver, the system issues a warning or error
when you simulate with Simscape blocks.
You can choose between warning and error messages in the Simscape pane of the
Configuration Parameters dialog box.
1
From the Zero-crossing control is globally disabled in Simulink drop-down
list, select the option that you want, if you globally disable zero-crossing detection:
• warning — The system issues a warning message upon simulation. This option
is the default.
• error — The system issues an error message upon simulation, which stops.
2
Click OK.
Making Multirate Simulation Consistent
The sample time or step size of the global Simulink solver must be the smallest time step
of all the solvers in a multirate Simscape simulation.
To avoid simulation errors in sample time propagation, go to the Solver pane in the
Configuration Parameters dialog box and select the Automatically handle rate
transition for data transfer check box.
3-16
Customizing Solvers for Physical Models
Customizing Solvers for Physical Models
In this section...
“Important Concepts and Choices in Physical Simulation” on page 3-17
“Making Optimal Solver Choices for Physical Simulation” on page 3-20
Important Concepts and Choices in Physical Simulation
This section describes advanced concepts and trade-offs you might want to consider
as you configure and test solvers and other simulation settings for your Simscape
model. For a summary of recommended settings, see “Making Optimal Solver Choices
for Physical Simulation” on page 3-20. For background information, consult “How
Simscape Models Represent Physical Systems” on page 3-2 and “How Simscape
Simulation Works” on page 3-5.
• “Variable-Step and Fixed-Step Solvers” on page 3-17
• “Explicit and Implicit Solvers” on page 3-18
• “Full and Sparse Linear Algebra” on page 3-18
• “Event Detection and Location” on page 3-18
• “Unbounded, Bounded, and Fixed-Cost Simulation” on page 3-19
• “Global and Local Solvers” on page 3-19
Variable-Step and Fixed-Step Solvers
Variable-step solvers are the usual choice for design, prototyping, and exploratory
simulation, and to precisely locate events during simulation. They are not useful for realtime simulation and can be costly if there are many events.
A variable-step solver automatically adjusts its step size as it moves forward in time to
adapt to how well it controls solution error. You control the accuracy and speed of the
variable-step solution by adjusting the solver tolerance. With many variable-step solvers,
you can also limit the minimum and maximum time step size.
Fixed-step solvers are recommended or required if you want to make performance
comparisons across platforms and operating systems, to generate a code version of
your model, and to bound or fix simulation cost. A typical application is real-time
simulation. For more information, see “Code Generation” on page 3-31 and “RealTime Simulation” on page 3-34.
3-17
3
Model Simulation
With a fixed-step solver, you specify the time step size to control the accuracy and speed
of your simulation. Fixed-step solvers do not adapt to improve accuracy or to locate
events. These limitations can lead to significant simulation inaccuracies.
Explicit and Implicit Solvers
The degree of stiffness and the presence of algebraic constraints in your model influence
the choice between an explicit or implicit solver. Explicit and implicit solvers use
different numerical methods to simulate a system.
• If the system is a nonstiff ODE system, choose an explicit solver. Explicit solvers
require less computational effort than implicit solvers, if other simulation
characteristics are fixed.
To find a solution for each time step, an explicit solver uses a formula based on the
local gradient of the ODE system.
• If the system is stiff, use an implicit solver. Though an explicit solver may require less
computational effort, for stiff problems an implicit solver is more accurate and often
essential to obtain a solution. Implicit solvers require per-step iterations within the
simulated time steps. With some implicit solvers, you can limit or fix these iterations.
An implicit solver starts with the solution at the current step and iteratively solves for
the solution at the next time step with an algebraic solver. An implicit algorithm does
more work per simulation step, but can take fewer, larger steps.
• If the system contains DAEs, even if it is not stiff, use an implicit solver. Such solvers
are designed to simultaneously solve algebraic constraints and integrate differential
equations.
Full and Sparse Linear Algebra
When you simulate a system with more than one state, the solver manipulates the
mathematical system with matrices. For a large number of states, sparse linear algebra
methods applied to large matrices can make the simulation more efficient.
Event Detection and Location
Events, in most cases, occur between simulated time steps.
• Fixed-step solvers detect events after “stepping over” them, but cannot adaptively
locate events in time. This can lead to large inaccuracies or failure to converge on a
solution.
3-18
Customizing Solvers for Physical Models
• Variable-step solvers can both detect events and estimate the instants when they
occur by adapting the timing and length of the time steps.
Tip To estimate the timing of events or rapid changes in your simulation, use a variablestep solver.
If your simulation has to frequently adapt to events or rapid changes by changing its step
size, much or all of the advantage of implicit solvers over explicit solvers is lost.
Unbounded, Bounded, and Fixed-Cost Simulation
In certain cases, such as real-time simulation, you need to simulate with an execution
time that is not only bounded, but practically fixed to a predictable value. Fixing
execution time can also improve performance when simulating frequent events.
The real-time cost of a variable-step simulation is potentially unlimited. The solver
can take an indefinite amount of real time to solve a system over a finite simulated
time, because the number and size of the time steps are adapted to the system. You
can configure a fixed-step solver to take a bounded amount of real time to complete a
simulation, although the exact amount of real time might still be difficult to predict
before simulation. Even a fixed-step solver can take multiple iterations to find a solution
at each time step. Such iterations are variable and not generally limited in number; the
solver iterates as much as it needs to.
Fixing execution time implies fixed-cost simulation, which both fixes the time step
and limits the number of per-step iterations. Fixed-cost simulation prevents execution
overruns, when the execution time is longer than the simulation sample time. A bounded
execution time without a known fixed cost might still cause some steps to overrun the
sample time.
The actual amount of computational effort required by a solver is based on a number
of other factors as well, including model complexity and computer processor. For more
information, see “Real-Time Simulation” on page 3-34.
Global and Local Solvers
You can use different solvers on different parts of the system. For example, you might
want to use implicit solvers on stiff parts of a system and explicit solvers everywhere
else. Such local solvers make the simulation more efficient and reduce computational
cost.
3-19
3
Model Simulation
Such multisolver simulations must coordinate the separate sequences of time steps of
each solver and each subsystem so that the various solvers can pass simulation updates
to one another on some or all of the shared time steps.
Making Optimal Solver Choices for Physical Simulation
For the key simulation concepts to consider before making these choices, see “Important
Concepts and Choices in Physical Simulation” on page 3-17.
• “Simulating with Variable Time Step” on page 3-20
• “Simulating with Fixed Time Step — Local and Global Fixed-Step Solvers” on page
3-20
• “Simulating with Fixed Cost” on page 3-21
• “Troubleshooting and Improving Solver Performance” on page 3-22
• “Multiple Local Solvers Example with a Mixed Stiff-Nonstiff System” on page 3-23
Simulating with Variable Time Step
For a typical Simscape model, MathWorks recommends the Simulink variable-step
solvers ode15s and ode23t. Of these two global solvers:
• The ode15s solver is more stable, but tends to damp out oscillations.
• The ode23t solver captures oscillations better but is less stable.
With Simscape models, these solvers solve the differential and algebraic parts of the
physical model simultaneously, making the simulation more accurate and efficient.
Simulating with Fixed Time Step — Local and Global Fixed-Step Solvers
In a Simscape model, MathWorks recommends that you implement fixed-step solvers
by continuing to use a global variable-step solver and switching the physical networks
within your model to local fixed-step solvers through each network Solver Configuration
block. The local solver choices are Backward Euler and Trapezoidal Rule. Of these two
local solvers:
• The Backward Euler tends to damp out oscillations, but is more stable, especially if
you increase the time step.
• The Trapezoidal Rule solver captures oscillations better but is less stable.
3-20
Customizing Solvers for Physical Models
Regardless of which local solver you choose, the Backward Euler method is always
applied:
• Right at the start of simulation.
• Right after an instantaneous change, when the corresponding block undergoes an
internal discrete change. Such changes include clutches locking and unlocking, valve
actuators opening and closing, and the switching of the Asynchronous Sample & Hold
block.
Switching to Discrete States and Solvers
• If you switch a physical network to a local solver, the global solver treats that network
as having discrete states.
• If other physical networks in your model are not using local solvers, or if the nonSimscape parts of your model have continuous states, then you must use a continuous
global solver.
• If all physical networks in your model use local solvers, and any non-Simscape parts
of your model have only discrete states, then the global solver effectively sees only
discrete states. In that case, MathWorks recommends a discrete, fixed-step global
solver. If you are attempting a fixed-cost simulation with discrete states, you must use
a discrete, fixed-step global solver.
For Maximum Accuracy with Fixed-Step Simulation
If solution accuracy is your single overriding requirement, use the global Simulink fixedstep solver ode14x, without local solvers. This implicit solver is the best global fixed-step
choice for physical systems. While it is more accurate than the Simscape local solvers for
most models, ode14x can be computationally more intensive and slower when you use it
by itself than it is when you use it in combination with local solvers.
In this solver, you must limit the number of global implicit iterations per time step.
Control these iterations with the Number Newton’s iterations parameter in the
Solver pane of the Configuration Parameters dialog box.
Simulating with Fixed Cost
Many Simscape models need to iterate multiple times within one time step to find
a solution. If you want to fix the cost of simulation per time step, you must limit the
number of these iterations, regardless of whether you are using a local solver, or a global
solver like ode14x. For more information, see “Unbounded, Bounded, and Fixed-Cost
Simulation” on page 3-19 and “Real-Time Simulation” on page 3-34.
3-21
3
Model Simulation
To limit the iterations, open the Solver Configuration block of each physical network.
Select Use fixed-cost runtime consistency iterations and set limits for the number
of nonlinear and mode iterations per time step.
Tip Fixed-cost simulation with variable-step solvers is not possible in most simulations.
Attempt fixed-cost simulation with a fixed-step solver only and avoid using fixed-cost
iterations with variable-step solvers.
Troubleshooting and Improving Solver Performance
Consider the basic trade-off of speed versus accuracy and stability. A larger time step or
tolerance results in faster simulation, but also less accurate and less stable simulation.
If a system undergoes sudden or rapid changes, larger tolerance or step size can cause
major errors. Consider tightening the tolerance or step size if your simulation:
• Is not accurate enough or looks unphysical.
• Exhibits discontinuities in state values.
• Reaches the minimum step size allowed without converging, usually a sign that one or
more events or rapid changes occur within a time step.
Any one or all of these steps increase accuracy, but make the simulation run more slowly.
For Local Solvers
Models with friction or hard stops are particularly difficult for local solvers, and may not
work or may require a very small time step.
With the Trapezoidal Rule solver, oscillatory “ringing” can become more of a problem as
the time step is increased. For a larger time step in a local solver, consider switching to
Backward Euler.
For ODE Systems
In certain cases, your model reduces to an ODE system, with no dependent algebraic
variables. (See “How Simscape Models Represent Physical Systems” on page 3-2.) If so,
you can use any global Simulink solver, with no special physical modeling considerations.
An explicit solver is often the best choice in such situations.
• Through careful analysis, you can sometimes determine if your model is represented
by an ODE system.
3-22
Customizing Solvers for Physical Models
• If you create a Simscape model from a mathematical representation using the
Simscape language, you can determine directly if the resulting system is ODE.
For Large Systems
Depending on the number of system states, you can simulate more efficiently if you
switch the value of the Linear Algebra setting in the Solver Configuration block.
For smaller systems, Full provides faster results. For larger systems, Sparse is
typically faster.
Multiple Local Solvers Example with a Mixed Stiff-Nonstiff System
In this example, a Simscape model contains three physical networks.
• Two networks (numbers 1 and 3) use local solvers, making these two networks appear
to the global solver as if they had discrete states. Internally, these networks still have
continuous states. These networks are moderately and highly stiff, respectively.
One of these networks (number 1) uses the Backward Euler (BE) local solver. The
other (number 3) uses the Trapezoidal Rule (TR) local solver.
• The remaining network (number 2) uses the global Simulink solver. Its states appear
to the model as continuous. This network is not stiff and is pure ODE. Use an explicit
global solver.
• Because at least one network appears to the model as continuous, you must use a
continuous solver. However, if you remove network 2, and if the model contains no
continuous Simulink states, Simulink automatically switches to a discrete global
solver.
3-23
3
Model Simulation
3-24
Troubleshooting Simulation Errors
Troubleshooting Simulation Errors
In this section...
“Troubleshooting Tips and Techniques” on page 3-25
“System Configuration Errors” on page 3-26
“Numerical Simulation Issues” on page 3-28
“Initial Conditions Solve Failure” on page 3-29
“Transient Simulation Issues” on page 3-29
Troubleshooting Tips and Techniques
Simscape simulations can stop before completion with one or more error messages. This
section discusses generic error types and error-fixing strategies. You might find the
previous section, “How Simscape Simulation Works” on page 3-5, useful for identifying
and tracing errors.
If a simulation failed:
• Review the model configuration. If your error message contains a list of blocks, look at
these blocks first. Also look for:
• Wrong connections — Verify that the model makes sense as a physical system. For
example, look for actuators connected against each other, so that they try to move
in opposite directions, or incorrect connections to reference nodes that prevent
movement. In electrical circuits, verify polarity and connections to ground.
• Wrong units — Simscape unit manager offers great flexibility in using physical
units. However, you must exercise care in specifying the correct units, especially in
the Simulink-PS Converter and PS-Simulink Converter blocks. Start analyzing the
circuit by opening all the converter blocks and checking the correctness of specified
units.
• Try to simplify the circuit. Unnecessary circuit complexity is the most common cause
of simulation errors.
• Break the system into subsystems and test every unit until you are positive that the
unit behaves as expected.
• Build the system by gradually increasing its complexity.
MathWorks recommends that you build, simulate, and test your model incrementally.
Start with an idealized, simplified model of your system, simulate it, verify that it works
3-25
3
Model Simulation
the way you expected. Then incrementally make your model more realistic, factoring in
effects such as friction loss, motor shaft compliance, hard stops, and the other things that
describe real-world phenomena. Simulate and test your model at every incremental step.
Use subsystems to capture the model hierarchy, and simulate and test your subsystems
separately before testing the whole model configuration. This approach helps you keep
your models well organized and makes it easier to troubleshoot them.
System Configuration Errors
• “Missing Solver Configuration Block” on page 3-26
• “Extra Fluid Block or Gas Properties Block” on page 3-26
• “Missing Reference Block” on page 3-27
• “Basic Errors in Physical System Representation” on page 3-27
Missing Solver Configuration Block
Each topologically distinct Simscape block diagram requires exactly one Solver
Configuration block to be connected to it. The Solver Configuration block specifies the
global environment information and provides parameters for the solver that your model
needs before you can begin simulation.
If you get an error message about a missing Solver Configuration block, open the
Simscape Utilities library and add the Solver Configuration block anywhere on the
circuit.
Extra Fluid Block or Gas Properties Block
If your model contains hydraulic elements, each topologically distinct hydraulic circuit in
a diagram requires a Custom Hydraulic Fluid block (or Hydraulic Fluid block, available
with SimHydraulics block libraries) to be connected to it. These blocks define the fluid
properties that act as global parameters for all the blocks connected to the hydraulic
circuit. If no hydraulic fluid block is attached to a loop, the hydraulic blocks in this loop
use the default fluid. However, more than one hydraulic fluid block in a loop generates an
error.
Similarly, more than one Gas Properties block in a pneumatic circuit generates an error.
If you get an error message about too many domain-specific global parameter blocks
attached to the network, look for an extra Hydraulic Fluid block, Custom Hydraulic Fluid
block, or Gas Properties block and remove it.
3-26
Troubleshooting Simulation Errors
Missing Reference Block
Simscape libraries contain domain-specific reference blocks, which represent reference
points for the conserving ports of the appropriate type. For example, each topologically
distinct electrical circuit must contain at least one Electrical Reference block, which
represents connection to ground. Similarly, hydraulic conserving ports of all the blocks
that are referenced to atmosphere (for example, suction ports of hydraulic pumps, or
return ports of valves, cylinders, pipelines, if they are considered directly connected
to atmosphere) must be connected to a Hydraulic Reference block, which represents
connection to atmospheric pressure. Mechanical translational ports that are rigidly
clamped to the frame (ground) must be connected to a Mechanical Translational
Reference block, and so on.
If you get an error message about a missing reference block, or node, check your system
configuration and add the appropriate reference block based on the rules described
above. The missing reference node diagnostic messages include information about the
particular block and variable that needs a reference node. This is especially helpful when
multiple domains are involved in the model. For more information and examples of best
modeling practices, see “Grounding Rules”.
Basic Errors in Physical System Representation
Physical systems are represented in the Simscape modeling environment as Physical
Networks according to the Kirchhoff's generalized circuit laws. Certain model
configurations violate these laws and are therefore illegal. There are two broad
violations:
• Sources of domain-specific Across variable connected in parallel (for example, voltage
sources, hydraulic pressure sources, or velocity sources)
• Sources of domain-specific Through variable connected in series (for example, electric
current sources, hydraulic flow rate sources, force or torque sources)
These configurations are impossible in the real world and illegal theoretically. If your
model contains such a configuration, upon simulation the solver issues an error followed
by a list of blocks, as shown in the following example.
Example
The model shown in the following illustration contains two Ideal Translational Velocity
Sources connected in parallel. This produces a loop of independent velocity sources, and
the solver cannot construct a consistent system of equations for the circuit.
3-27
3
Model Simulation
When you try to simulate the model, the solver issues an error message with links
to the Ideal Translational Velocity Source and Ideal Translational Velocity Source1
blocks. To fix the circuit, you can either replace the two velocity sources by a single Ideal
Translational Velocity Source block, or add a Translational Damper block between them.
Numerical Simulation Issues
• “Dependent Dynamic States” on page 3-28
• “Parameter Discontinuities” on page 3-29
Numerical simulation issues can be either a result of certain circuit configurations or of
parameter discontinuities.
Dependent Dynamic States
Certain circuit configurations can result in dependent dynamic states, or the so-called
higher-index differential algebraic equations (DAEs). Simscape solver can handle
dependencies among dynamic states that are linear in the states and independent of
time and inputs to the system. For example, capacitors connected in parallel or inductors
connected in series will not cause any problems. Other circuit configurations with
dependent dynamic states, in certain cases, may slow down the simulation or lead to an
error when the solver fails to initialize.
Problems may occur when dynamic states have a nonlinear algebraic relationship. An
example is two inertias connected by a nonlinear gear constraint, such as an elliptical
gear. In case of simulation failure, the Simscape solver may be able to identify the
3-28
Troubleshooting Simulation Errors
components involved, and provide an error message with links to the blocks and to the
equations within each block.
Parameter Discontinuities
Nonlinear parameters, dependent on time or other variables, may also lead to numerical
simulation issues as a result of parameter discontinuity. These issues usually manifest
themselves at the transient initialization stage (see “Transient Simulation Issues” on
page 3-29).
Initial Conditions Solve Failure
The initial conditions solve, which solves for all system variables (with initial conditions
specified on some system variables), may fail. This has several possible causes:
• System configuration error. In this case, the Simulation Diagnostics window usually
contains additional, more specific, error messages, such as a missing reference
node, or a warning about the component equations, followed by a list of components
involved. See “System Configuration Errors” on page 3-26 for more information.
• Dependent dynamic state. In this case, the Simulation Diagnostics window also
may contain additional, more specific, error messages, such as a warning about the
component equations, followed by a list of components involved. See “Dependent
Dynamic States” on page 3-28 for more information.
• The constraint residual tolerance may be too tight to produce a consistent solution to
the algebraic constraints at the beginning of simulation. You can try to increase the
Constraint Residual Tolerance parameter value (that is, relax the tolerance) in
the Solver Configuration block.
If the Simulation Diagnostics window has other, more specific, error messages, address
them first and try rerunning the simulation. See also “Troubleshooting Tips and
Techniques” on page 3-25.
Transient Simulation Issues
• “Transient Initialization Not Converging” on page 3-30
• “Step-Size-Related Errors — Dependent States — High Stiffness” on page 3-30
Transient initialization happens at the beginning of simulation (after computing the
initial conditions) or after a subsequent event, such as a discontinuity (for example,
3-29
3
Model Simulation
when a hard stop hits the stop). It is performed by fixing all dynamic variables and
solving for algebraic variables and derivatives of dynamic variables. The goal of transient
initialization is to provide a consistent set of initial conditions for the next transient solve
step.
Transient Initialization Not Converging
Error messages stating that transient initialization failed to converge, or that a set of
consistent initial conditions could not be generated, indicate transient initialization
issues. They can be a result of parameter discontinuity. Review your model to find the
possible sources of discontinuity. See also “Troubleshooting Tips and Techniques” on page
3-25.
You can also try to decrease the Constraint Residual Tolerance parameter value (that
is, tighten the tolerance) in the Solver Configuration block.
Step-Size-Related Errors — Dependent States — High Stiffness
A typical step-size-related error message may state that the system is unable to reduce
the step size without violating the minimum step size for a certain number of consecutive
times. This error message indicates numerical difficulties in solving the Differential
Algebraic Equations (DAEs) for the model. This might be caused by dependent dynamic
states (higher-index DAEs) or by the high stiffness of the system. You can try the
following:
• Tighten the solver tolerance (decrease the Relative Tolerance parameter value in
the Configuration Parameters dialog box)
• Specify a value, other than auto, for the Absolute Tolerance parameter in the
Configuration Parameters dialog box. Experiment with this parameter value.
• Tighten the residual tolerance (decrease the Constraint Residual Tolerance
parameter value in the Solver Configuration block)
• Increase the value of the Number of consecutive min step size violations
allowed parameter in the Configuration Parameters dialog box (set it to a value
greater than the number of consecutive step size violations given in the error
message)
• Review the model configuration and try to simplify the circuit, or add small parasitic
terms to your circuit to avoid dependent dynamic states. For more information, see
“Numerical Simulation Issues” on page 3-28.
3-30
Code Generation
Code Generation
In this section...
“About Code Generation from Simscape Models” on page 3-31
“Reasons for Generating Code” on page 3-31
“Using Code-Related Products and Features” on page 3-32
“How Simscape Code Generation Differs from Simulink” on page 3-32
About Code Generation from Simscape Models
You can use Simulink Coder™ software to generate stand-alone C or C++ code from
your Physical Networks models and enhance simulation speed and portability. Certain
features of Simulink software also make use of generated or external code. This section
explains code-related tasks you can perform with your Simscape models.
Code versions of Simscape models typically require fixed-step Simulink solvers, which
are discussed in the Simulink documentation. Some features of Simscape software are
restricted when you translate a model into code. See “How Simscape Code Generation
Differs from Simulink” on page 3-32, as well as “Limitations” on page 3-70.
Note: Code generated from Simscape models is intended for rapid prototyping and
hardware-in-the-loop applications. It is not intended for use as production code in
embedded controller applications.
Add-on products based on the Simscape platform also support code generation, with some
variations and exceptions described in their respective documentation.
Reasons for Generating Code
Code generation has many purposes and methods. There are two essential rationales:
• Compiled code versions of Simulink and Simscape models run faster than the original
block diagram models. The time savings can be dramatic.
• An equally important consideration for Simscape models is the stand-alone
implementation of generated and compiled code. Once you convert part or all of your
model to code, you can deploy the stand-alone executable program on virtually any
platform, independently of MATLAB.
3-31
3
Model Simulation
Converting a model or subsystem to code also hides the original model or subsystem.
Using Code-Related Products and Features
With Simulink, Simulink Coder, and Simulink Real-Time™ software, using several
code-related technologies, you can link existing code to your models and generate code
versions of your models.
Code-Related Task
Component or Feature
Link existing code written in C or
other supported languages to Simulink
models
Simulink S-functions to generate customized
blocks
Speed up Simulink simulations
Accelerator mode
Rapid Accelerator mode
Generate stand-alone fixed-step code
from Simulink models
Simulink Coder software
Generate stand-alone variable-step code Simulink Coder Rapid Simulation Target
from Simulink models
(RSim)
Convert Simulink model to code and
compile and run it on a target PC
Simulink Coder and Simulink Real-Time
software
How Simscape Code Generation Differs from Simulink
In general, using the code generated from Simscape models is similar to using code
generated from regular Simulink models. However, there are certain differences.
Simscape and Simulink Code Generated Separately
Simulink Coder software generates code from the Simscape blocks separately from the
Simulink blocks in your model. The generated Simscape code does not pass through
model.rtw or the Target Language Compiler. All the code generated from a single model
resides in the same directory, however.
Compiler and Processor Architecture Requirements
To generate and execute Simscape code, you must have a compiler and a processor that
support:
3-32
Code Generation
• 64-bit precision floating-point arithmetic
• 32-bit integer size
For details on supported compiler versions, see
http://www.mathworks.com/support/compilers/current_release
Precompiled Libraries Provided for Selected Compilers
Simscape software and its add-on products provide static runtime libraries precompiled
for compilers supported by Simulink Coder software. These are the standard UNIX
compilers for UNIX operating systems, lcc and Microsoft® Visual Studio® for 32-bit
Windows®, and Microsoft Visual Studio for 64-bit Windows.
For all other compilers, the static runtime libraries needed by code generated from
Simscape models are compiled once per model during the code generation build process.
Simscape Code Reuse Not Supported
Reusable subsystems in Simulink reuse code that is generated once from the subsystem.
You cannot generate reusable code from subsystems containing Simscape blocks.
Tunable Parameters Not Supported
A tunable parameter is a Simulink run-time parameter that you can change while the
simulation is running. Simscape blocks do not support tunable parameters in either
simulations or generated code.
Simscape Run-Time Parameter Inlining Override of Global Exceptions
If you choose to enable parameter inlining for code generated from a Simscape model,
the software inlines all its run-time parameters. If you choose to make some of the global
Simscape block parameters exceptions to inlining, the exceptions are ignored. You can
change global tunable parameters only by regenerating code from the model.
3-33
3
Model Simulation
Real-Time Simulation
In this section...
“What Is Real-Time Simulation?” on page 3-34
“Requirements for Real-Time Simulation” on page 3-35
“Simulating Physical Models in Real Time” on page 3-36
“Preparing a Model for Real-Time Simulation” on page 3-37
“Troubleshooting Real-Time Simulation Problems” on page 3-40
What Is Real-Time Simulation?
Real-time simulation of an engineering system becomes possible when you replace
physical devices with virtual devices. This replacement reduces costs and improves
the quality of physical and control systems, including their software, by enabling
more complete testing of the entire system. It also enables continuous testing, without
interruption and under possibly dangerous conditions. Real-time simulation allows you to
test even when you have no prototypes.
Real-time simulation becomes a necessity if you want to simulate a system realistically
responding to its environment. Such realistic simulation means that the inputs and
outputs in the virtual world of simulation must be read or updated synchronously with
the real world. When the simulation clock reaches a certain time in real-time simulation,
the same amount of time must have passed in the real world.
Using Real-Time Simulation to Test Virtual Controllers and Systems
In desktop simulation, you use models to develop and test control and signal processing
algorithms. Once the designs are complete and you have converted these algorithms to
embedded code, you must test that code as well as the actual controller. If the model is
capable of running in real time, you can use the model created in the design phase to
test the embedded code and processor, instead of connecting it directly to a hardware
prototype. Such real-to-virtual substitution, simulating in real time, is referred to as
hardware-in-the-loop (HIL) testing.
Example
Systems with a human in the simulation loop require real-time simulation. For example,
flight simulators that train pilots require real-time simulation of the plane, its control
system, the weather, and other environmental conditions.
3-34
Real-Time Simulation
Requirements for Real-Time Simulation
Configuring a model and a numerical integrator to simulate in real time is often more
challenging than ordinary simulation. You simulate with a more restrictive version of the
universal computational tradeoff of accuracy versus speed.
The simulation execution time per time step must be consistently short enough to permit
any other tasks that the simulation environment must perform, such as reading sensor
input or generating output actuator signals. This requirement must be satisfied even
if the simulation changes its qualitative character: the system stiffness might change,
and discrete components can switch states. Such changes occasionally require more
computations to achieve an accurate result.
Bounding and Stabilizing Execution Time with Fixed-Step Solvers and Fixed-Cost Simulation
When real-time simulation is the goal, the execution time per simulation time step must
be bounded. Variable-step solvers, which are often used in desktop simulation, take
smaller steps to accurately capture events that occur during the simulation. But you
cannot vary the step size in a real-time simulation. Instead, you must
• Choose a fixed-step solver that can capture the system dynamics accurately and
minimize the amount of computation required per time step, without changing the
step size. If the system states are all discrete, the fixed-step solver can be discrete as
well.
If you choose a small enough step size, most fixed-step solvers produce the same
simulation results as a variable-step solver. However, different fixed-step solvers
(implicit/explicit, lower/higher order, and so on) require different step sizes to produce
accurate results. They also require different amounts of computation per time step.
• Choose a fixed step size large enough to permit stable real-time simulation. The step
size must not be so large that the simulation results are inaccurate, but not so small
that real-time simulation is impossible.
You often need trial and error to find the right combination of settings that satisfy
both criteria.
Real-time simulation requires not only bounding the execution time, but fixing it to a
stable value. This requires a fixed-cost simulation method. For more information, see
“Customizing Solvers for Physical Models” on page 3-17.
3-35
3
Model Simulation
Simulating Physical Models in Real Time
Achieving real-time simulation with any Simscape model includes:
• Enabling simulation with fixed-step, fixed-cost solvers
• Converting the model with Simulink Coder to code for a particular computer
hardware target
• Testing real-time simulation on PC-compatible hardware with Simulink Real-Time, if
desired
For more information, see “Code Generation” on page 3-31.
Preparation for real-time simulation requires particular choices and adjustment of
Simulink variable-step solvers. Actual real-time simulation requires Simulink fixed-step
solvers. Certain Simscape features enable and enhance real-time simulation of physical
systems with Simulink fixed-step solvers, both explicit and implicit. These features
include fixed-cost algorithms and local solvers, with the trapezoidal rule or backward
Euler method. See “Customizing Solvers for Physical Models” on page 3-17.
This figure plots the normalized computational cost of all fixed-step solvers available for
Simscape models, obtained for a nonlinear model example with one physical network. For
comparison, the step size was kept the same, with similar settings for the total number of
solver iterations.
3-36
Real-Time Simulation
Preparing a Model for Real-Time Simulation
To move from desktop to real-time simulation on your real-time hardware target, adjust
the following simulation properties until the simulation can execute in real time and
deliver results close to the results from desktop simulation:
• Solver choice
• Number of solver iterations
• Simulation time step size
• Model size and fidelity
Follow these high-level tasks to prepare a model for real-time simulation. Each task is
also a link to specific instructions for that part of the procedure.
1
“Simulate and Converge with Variable-Step Solver” on page 3-38
2
“Check Variable Time Steps for Optimal Step Size” on page 3-38
3
“Simulate with Fixed-Cost Solver and Compare to Variable-Step Simulation” on page
3-38
4
“Adjust Step Size and Iterations to Approximate Variable-Step Simulation Results”
on page 3-39
3-37
3
Model Simulation
5
“Attempt to Simulate in Real Time” on page 3-40
6
“Respond to Real-Time Simulation Failures” on page 3-40
Simulate and Converge with Variable-Step Solver
The first task is to obtain a converged set of results with a variable-step solver.
To ensure that the results obtained with the fixed-step solver are accurate, you need a
set of reference results. You can obtain these by simulating the system with a variablestep solver. Ensure that the results converge by tightening the error tolerances until the
simulation results do not change significantly.
Check Variable Time Steps for Optimal Step Size
The second task is to examine the time step sizes during the desktop simulation and
determine if the model is likely to run with a large enough step size to permit real-time
simulation.
A variable-step solver varies the step size to keep the solution within error tolerances
and to react to zero crossing events. If the solver abruptly reduces the step size to a small
value (for example, 1e-15 s), the solver is trying to accurately identify a zero crossing
event. A fixed-step solver might have trouble capturing these events at a step size large
enough to permit real-time simulation.
Analysis of these particular variable time steps provides an estimate of a step size that
can be used to run the simulation. Modifying or eliminating the effects are causing these
events makes it easier to simulate the system with a fixed-step solver at a reasonably
large step size and produce results comparable to the variable-step simulation. See
“Troubleshooting Real-Time Simulation Problems” on page 3-40.
Simulate with Fixed-Cost Solver and Compare to Variable-Step Simulation
The third task is to simulate the system with a fixed-step, fixed-cost solver and compare
these results to the reference results from the variable-step simulation.
Limiting Per-Step Solver Iterations
Simulating physical systems often requires multiple iterations per time step to converge
on a solution. To perform a fixed-cost simulation, you must limit these iterations. In
each physical network Solver Configuration block, select the Use fixed-cost runtime
consistency iterations check box and enter the number of allowed iterations.
3-38
Real-Time Simulation
Switching to Local Solvers
You can further minimize the computations done per time step by choosing a local solver
on each physical network in the model. To switch to a local solver in a physical network,
open the Solver Configuration block of that network and select Use local solver. By
using this option, you can use an implicit fixed-step solver only on the stiff portions of the
model and an explicit fixed-step solver on the remainder of the model. This minimizes the
computations done per time step, making it more likely that the model can run in real
time.
Adjust Step Size and Iterations to Approximate Variable-Step Simulation Results
The fourth task is to reduce the step size and adjust the number of nonlinear iterations,
in order to produce results that are sufficiently close to the reference results from
variable-step simulation. The step size must still be large enough for a safety margin to
prevent an execution overrun.
During each time step, the real-time simulation must calculate the result for the next
time step (simulation execution), and read inputs and write outputs (I/O processing and
other tasks). If these actions take less time than the specified time step, the processor
remains idle during the remainder of the step. Choosing a computationally more
intensive solver, increasing the number of nonlinear iterations, or reducing the step size
both increases the simulation accuracy and reduces the amount of idle time, raising the
risk that the simulation cannot run in real time. Adjusting these settings in the opposite
way increases the amount of idle time but reduce accuracy.
Estimating the budget for the execution time helps ensure that you choose a feasible
combination of settings. If you know the amount of time spent processing inputs and
outputs and performing other actions, as well as the percentage of idle time that you
want, the amount of time available for simulation execution can be calculated as follows:
Simulation Execution Time Budget =
Step Size – [I/O Processing Time + (Desired Percentage of Idle Time)·(Step Size)]
Estimating Real-Time Execution Time
You can use the desktop simulation speed to estimate the execution time on a realtime hardware target. Many factors affect the real-time target execution time, so that
comparing processor speeds might not be sufficient.
A better method is to measure the execution time of desktop simulation and then
to determine the average execution time per time step on the real-time target for a
3-39
3
Model Simulation
particular model. Knowing how these execution times compare for one model means that
you can estimate execution time on the real-time target from the desktop simulation
execution time when you test other models.
Attempt to Simulate in Real Time
The fifth task is to use the selected solver, the number of nonlinear iterations, and the
step size to simulate on the real-time target and to verify if the simulation can run in real
time.
If the simulation does not run in real time on the target hardware, the model might not
be real-time capable.
Respond to Real-Time Simulation Failures
If the simulation does not run in real time on the selected real-time target, perform a
sixth, contingent task, described in “Troubleshooting Real-Time Simulation Problems” on
page 3-40.
Troubleshooting Real-Time Simulation Problems
If the simulation does not run in real time on the real-time platform, or if the simulation
performance is unacceptable, you should determine the causes and find an appropriate
solution. The combination of effects captured in the model and the speed of the real-time
platform might make it impossible to find solver settings that permit it to run in real
time. Consider the following options to make it real-time capable.
Once you modify your model, return to the third, fourth, and fifth tasks of “Preparing
a Model for Real-Time Simulation” on page 3-37 to identify and implement the
appropriate settings to enable real-time simulation.
Speeding Up Real-Time Execution
You can speed up the real-time simulation by using a faster real-time target computer.
Alternatively, you can achieve the same goal by determining new model settings that
permit a larger step size or reduce the execution time (for example, by reducing the
number of nonlinear iterations).
Simulating Parts of the System in Parallel
If possible, configure the model to evaluate multiple physical networks in parallel. You
can do this if the networks are not dependent upon one another. You need experience and
3-40
Real-Time Simulation
experimentation with your model, the generated code, and the real-time target to make
effective use of this option.
Eliminating Effects That Require Intensive Computation
Certain effects in your model can prevent real-time simulation. Such effects include
instantaneous events and rapid changes in parts of the system with very small time
constants. Identify and modify or remove these elements before searching again for a
combination of solver settings and step size that permits real-time simulation.
Identifying Elements Causing Rapid or Instantaneous Changes
Watch for certain system elements becoming excited to high frequencies. Examine
the system eigenmodes to isolate which system states have the highest frequency.
Mapping those states to individual components often points to the source of the problem.
Because you can only do this at a particular operating point, choose an operating point
corresponding to simulation times in the variable-step simulation that had small step
sizes. At such simulation times, the variable-step solver is struggling to simulate a rapid
change.
With scripts written in MATLAB, you can interrogate the model, identify these
components quickly, and narrow the search for the effects that you need to modify. You
can automate and extend these searches to other models with tools like the Simulink
Model Advisor. The troublesome components that you need to locate include:
• Elements that create events and change the solution nearly instantaneously. A fixedstep solver might not be able to step over such rapid changes and find the right
solution on the other side of the event. If it fails to find the solution, the solver may
become unstable. Examples of elements that create these kinds of events include:
• Hard stops or backlash
• Stick-slip friction
• Switches or clutches
• Elements with very small time constants. The dynamics of these elements require
a small step size so that a fixed-step solver can accurately simulate them, perhaps
too small for real-time simulation. Examples of systems with a small time constant
include:
• Small masses attached to stiff springs with minimal damping
• Electrical circuits with small capacitance and inductance and low resistance
• Hydraulic circuits with small compressible volumes
3-41
3
Model Simulation
Modifying or Removing Elements Causing Rapid or Instantaneous Changes
Once you have identified these elements, change or eliminate them by:
• Replacing nonlinear components with linearized versions
• Replacing complex equations with lookup tables for their solution
• Replacing complicated components with simplified models by using system
identification theory on their input and output data
• Smoothing discontinuous functions (step changes) by using filters, delays, and other
techniques.
3-42
Finding an Operating Point
Finding an Operating Point
In this section...
“What Is an Operating Point?” on page 3-43
“Finding Operating Points in Physical Models” on page 3-44
What Is an Operating Point?
An operating point of a system is a dynamic configuration that satisfies design and
use requirements called operating specifications. You can express such operating
specifications as requirements on the system state x and inputs u. It is not always
possible to find a dynamic state that satisfies all operating conditions. Also, a system
might have multiple operating points satisfying the same requirements.
Operating points are essential for designing and implementing system controllers.
You can optimize a system at an operating point for performance, stability, safety, and
reliability.
The most important and common type of operating point is a steady state, where some or
all of the system dynamic variables are constant.
Using Operating Points for Linearization
An important motive for finding operating points is linearization, which determines
the system response to small disturbances at an operating point. Linearization results
influence the design of feedback controllers to govern dynamic behavior near the
operating point. A full linearization analysis requires one or more system outputs, y, in
addition to inputs.
See “Linearizing at an Operating Point” on page 3-48.
Example
A pilot flying an aircraft wants to find, for a given environment, a state of the aircraft
engine and control surfaces that produces level, constant-velocity, and constant-altitude
flight relative to the ground. The requirements of "level," "constant velocity," "constant
altitude," and "relative to the ground" constitute operating specifications. This operating
point is a steady state of the aircraft velocity, altitude, and orientation in space.
3-43
3
Model Simulation
Finding Operating Points in Physical Models
You have a number of ways to find an operating point in a Simscape model. You can
impose operating specifications and isolate operating points using Simscape and
Simulink features.
Tip To find a steady state, the Simscape steady-state solver is the most direct method.
For a comprehensive suite of operating point and linearization tools, MathWorks
recommends Simulink Control Design™ software.
To analyze operating points, you work with the full state vector of your model, which
contains:
• Simulink components, which can be continuous or discrete.
• Simscape components, which are continuous.
Whichever method that you choose to find an operating point, if you want to use it for
linearization, you must save the operating point information in the form of an operating
point object, a simulation time t0, or a state vector x0 and input vector u0.
• “Simulating in Time to Search for an Operating Point” on page 3-44
• “Using the Simscape Initial Condition Solver” on page 3-45
• “Using Simulink Control Design Techniques to Find Operating Points” on page
3-45
• “Using Sources to Find Operating Points Not Recommended” on page 3-47
• “Simulink trim Function Not Supported with Simscape Models” on page 3-47
Simulating in Time to Search for an Operating Point
One way to identify operating points is to simulate your model and inspect its state x and
output y as a time series.
3-44
1
In your Simscape model, set up sensor outputs for whatever block outputs you want
to observe.
2
Connect Scope blocks, To Workspace blocks, or both, to your Simscape block outputs
to observe and record simulation behavior.
Finding an Operating Point
3
In the Data Import/Export pane of your model Configuration Parameters
settings, select the Time, States, and Output check boxes to record this simulation
information in your workspace.
Using the Simscape Initial Condition Solver
Simscape software provides two workflows to initialize a physical model. The first
solves for steady state, where all differential variables have zero derivative. Using
this approach you can search for multiple steady states with the steady-state solver by
varying the model inputs, parameters, and initial conditions. The second approach is to
directly specify initial conditions by specifying initialization priority and targets for block
variables. For more information on this approach, see “Variable Initialization”.
To use the first approach, enable the steady-state solver:
1
In each, some, or all of the physical networks in your Simscape model, open the
Solver Configuration block.
2
In each block dialog box, select the Start simulation from steady state check box.
3
In the model Configuration Parameters settings, on the Data Import/Export pane,
select the States check box to record the time series of x values in your workspace.
If you also have input signals u in the model, you can capture those inputs by
connecting To Workspace blocks to the input Simulink signal lines.
4
Close these dialog boxes and start simulation.
The first vector of values x(t=0) that you capture during simulation reflects the steady
state x0 that the Simscape solver identified.
Tip Finding an initial steady state is part of the nondefault Simscape simulation
sequence. See “Initial Conditions Computation” on page 3-8.
You can simplify the initial steady-state computation by setting the simulation time to 0.
The simulation then solves for one time step only (time zero) and returns a single state
vector x(t=0).
Using Simulink Control Design Techniques to Find Operating Points
Note: The techniques described in this section require the Simulink Control Design
product.
3-45
3
Model Simulation
You must use the features of this product on the Simulink lines in your model, not
directly on Simscape physical network lines or blocks. Simulink Control Design offers
both command line and graphical interfaces for finding and analyzing operating points.
Simulink Control Design methods are state-based, giving you full access to state names
and values, and allow you to impose operating specifications or use simulation snapshots.
MathWorks® does not recommend imposing operating specifications state-by-state using
the Simulink Control Design dialogs (or findop function), but simulation snapshots
work well.
To find operating points, it is simplest to use the operspec and findop functions,
customizing where necessary. Create an operating specification object with operspec,
then compute an operating point object with findop. The findop function attempts
to find an operating point that satisfies the operating specifications and reports on its
success or failure. If the search is successful, find_op returns state values satisfying the
operating specifications.
You have several choices for operating specifications for the components of the state
vector.
Assumed Operating
Condition
Operating Specification
Default
Request that all state component derivatives be zero.
This is a steady-state for the whole model, not just a Simscape
network within the model.
Nondefault
Request any value you want independently for each state
component.
Nondefault
Request that a particular state component derivative be zero.
This is a steady-state condition for that state component.
Additional Simulink Control Design Methods
You can also use the graphical user interface, through the model menu bar: Analysis >
Control Design > Linear Analysis. This interface gives you access to state, input, and
output names, structure, and initial values.
For more details on the use of operating point specification objects, related functions, and
the graphical interface, see the Simulink Control Design documentation.
3-46
Finding an Operating Point
Using Sources to Find Operating Points Not Recommended
You can impose an operating specification on part of a Simscape model by inserting
source blocks from the Simscape Foundation Library. These impose specified values of
system variables in parts of the model. You can simulate and save the state vector.
However, you cannot obtain an operating point for the original system (without the
source blocks) by saving the state values from the model and then removing the source
blocks. In general, the number, order, and identity of state components change after
adding and removing Simscape blocks in a model.
Simulink trim Function Not Supported with Simscape Models
The Simulink trim function is not supported for models containing Simscape
components.
3-47
3
Model Simulation
Linearizing at an Operating Point
In this section...
“What Is Linearization?” on page 3-48
“Linearizing a Physical Model” on page 3-50
What Is Linearization?
Determining the response of a system to small perturbations at an operating point is a
critical step in system and controller design. Once you find an operating point, you can
linearize the model about that operating point to explore the response and stability of
the system. To find an operating point in a Simscape model, see “Finding an Operating
Point” on page 3-43.
• “What Is a Linearized Model?” on page 3-48
• “Example” on page 3-49
• “Choosing a Good Operating Point for Linearization” on page 3-49
What Is a Linearized Model?
Near an operating point, you can express the system state x, inputs u, and outputs y
relative to that operating point in terms of x – x0, u – u0, and y – y0. For convenience,
shift the vectors by subtracting the operating point: x – x0 → x, and so on.
If the system dynamics do not explicitly depend on time and the operating point is a
steady state, the system response to state and input perturbations near the steady state
is approximately governed by a linear time-invariant (LTI) state space model:
dx/dt = A·x + B·u
y = C·x + D·u.
The matrices A, B, C, D have components and structures that are independent of the
simulation time. A system is stable to changes in state at an operating point if the
eigenvalues of A are negative.
If the operating point is not a steady state or the system dynamics depend explicitly
on time, the linearized dynamics near the operating point are more complicated. The
matrices A, B, C, D are not constant and depend on the simulation time t0 , as well as the
operating point x0 and u0 [3].
3-48
Linearizing at an Operating Point
Tip While you can linearize a closed system with no inputs or outputs and obtain a
nonzero A matrix, obtaining a nontrivial linearized input-output model requires at least
one input component in u and one output component in y.
Example
A pilot is flying, or simulating, an aircraft in level, constant-velocity, and constantaltitude flight relative to the ground. A crucial question for the aircraft pilot and
designers is: will the aircraft return to the steady state if perturbed from it by a
disturbance, such as a wind gust — in other words, is this steady state stable? If the
operating point is unstable, the aircraft trajectory can diverge from the steady state,
requiring human or automatic intervention to maintain steady flight.
Choosing a Good Operating Point for Linearization
Although steady-state and other operating points (state x0 and inputs u0) might exist for
your model, that is no guarantee that such operating points are suitable for linearization.
The critical question is: how good is the linearized approximation compared to the exact
system dynamics?
• When perturbed slightly, a problematic operating point might exhibit strong
asymmetries, with strongly nonlinear behavior when perturbed in one direction and
smoother behavior in another.
• Small perturbations might result in a discontinuous change in a state value, making
the current state unsuitable for linear approximation.
Operating points with a strongly nonlinear or discontinuous character are not suitable
for linearization. You should analyze such models in full simulation, away from any
discontinuities, and perturb the system by varying its inputs, parameters, and initial
conditions. A common example is actuation systems, which should be linearized away
from any hard constraints or end stops.
Tip Check for such an unsuitable operating point by linearizing at several nearby
operating points. If the results differ greatly, the operating point is strongly nonlinear or
discontinuous.
3-49
3
Model Simulation
Linearizing a Physical Model
Use the following methods to create numerical linearized state-space models from a
model containing Simscape components.
Tip MathWorks recommends the Simulink Control Design product for linearization
analysis.
• “Independent Versus Dependent States” on page 3-50
• “Linearizing with Simulink Control Design Software” on page 3-51
• “Linearizing with the Simulink linmod and dlinmod Functions” on page 3-51
• “Linearizing with Simulink Linearization Blocks” on page 3-53
Independent Versus Dependent States
An important difference from basic Simulink models is that the states in a physical
network are not independent in general, because some states have dependencies on other
states through constraints.
• The independent states are a subset of system variables and consist of independent
(unconstrained) Simscape dynamic variables and other Simulink states.
• The dependent states consist of Simscape algebraic variables and dependent
(constrained) Simscape dynamic variables.
For more information on Simscape dynamic and algebraic variables, see “How Simscape
Simulation Works” on page 3-5.
The complete, unreduced LTI A, B, C, D matrices have the following structure.
• The A matrix, of size n_states by n_states, is all zeros except for a submatrix of
size n_ind by n_ind, where n_ind is the number of independent states.
• The B matrix, of size n_states by n_inputs, is all zeros except for a submatrix of
size n_ind by n_inputs.
• The C matrix, of size n_outputs by n_states, is all zeros except for a submatrix of
size n_outputs by n_ind.
• The D matrix, of size n_outputs by n_inputs, can be nonzeros everywhere.
3-50
Linearizing at an Operating Point
Obtaining the Independent Subset of States
A minimal linearized solution uses only an independent subset of system states. From
the matrices A, B, C, D, you can obtain a minimal input-output linearized model with:
• The minreal and sminreal functions from Control System Toolbox™ software
• Automatically with the Simulink Control Design approach
Linearizing with Simulink Control Design Software
Note: The techniques described in this section require the Simulink Control Design
product.
You must use the features of this product on the Simulink lines in your model, not
directly on Simscape physical network lines or blocks.
This approach requires that you start with an operating point object saved from
trimming the model to an operating specification, as explained in “Using Simulink
Control Design Techniques to Find Operating Points” on page 3-45.
To linearize a model with an operating point object, use the linearize function,
customizing where necessary. The resulting state-space object contains the matrices A, B,
C, D.
Additional Simulink Control Design Methods
You can also use the graphical user interface, through the model menu bar: Analysis >
Control Design > Linear Analysis. For more details on linearization, operating points
and state-space objects, related functions, and the graphical interface, see the Simulink
Control Design documentation.
Linearizing with the Simulink linmod and dlinmod Functions
You have several ways that you can use the Simulink functions linmod and dlinmod,
and the linearization results can differ depending on the method chosen. To use these
functions, you do not have to open the model, just have the model file on your MATLAB
path.
For more information about Simulink linearization, see “Linearizing Models” in the
Simulink documentation.
3-51
3
Model Simulation
Tip If your model has continuous states, use linmod. (Continuous states are the
Simscape default.) If your model has mixed continuous and discrete states, or purely
discrete states, use dlinmod.
Linearizing a model with the local solver enabled (in the Solver Configuration block) is
not supported.
Linearizing with Default State and Input
You can call linmod without specifying state or input. Enter linmod('modelname') at
the command line.
With this form of linmod, Simulink linearization solves for consistent initial conditions
in the same way it does on the first step of any simulation. Any initial conditions, such as
initial offset from equilibrium for a spring, are set as if the simulation were starting from
the initial time.
linmod allows you to change the time of externally specified signals (but not the internal
system dynamics) from the default. For this and more details, see the linmod function
reference page.
Linearizing with the Steady-State Solver at an Initial Steady State
You can linearize at an operating point found by the Simscape steady-state solver:
1
Open one or more Solver Configuration blocks in your model.
2
Select the Start simulation from steady state check box for the physical networks
that you want to linearize.
3
Close the Solver Configuration dialog boxes and save the modified model.
4
Enter linmod('modelname') at the command line.
linmod linearizes at the first step of simulation. In this case, the initial state is also an
operating point, a steady state.
For more about setting up the steady-state solver, see the Solver Configuration block
reference page. For more details on its use, see “Using the Simscape Initial Condition
Solver” on page 3-45.
Linearizing with Specified State and Input — Ensuring Consistency of States
You can call linmod and specify state and input. Enter linmod('modelname',x0,u0)
at the command line. The extra arguments specify, respectively, the steady state x0 and
3-52
Linearizing at an Operating Point
inputs u0 for linearizing the simulation. When you specify a state to linmod, ensure that
it is self-consistent, within solver tolerance.
With this form of linmod, Simulink linearization does not solve for initial conditions.
Because not all states in the model have to be independent, it is possible, though
erroneous, to provide linmod with an inconsistent state to linearize about.
If you specify a state that is not self-consistent (within solver tolerance), the Simscape
solver issues a warning at the command line when you attempt linearization. The
Simscape solver then attempts to make the specified x0 consistent by changing some of
its components, possibly by large amounts.
Tip You most easily ensure a self-consistent state by taking the state from some
simulated time. For example, by selecting the States check box on the Data Import/
Export pane of the model Configuration Parameters dialog box, you can capture a time
series of state values in a simulation run.
Linearizing with Simulink Linearization Blocks
You can generate linearized state-space models from your Simscape model by adding
a Timed-Based Linearization or Trigger-Based Linearization block to the model and
simulating. These blocks combine time-based simulation, up to specified times or internal
trigger points, with state-based linearization at those times or trigger points.
For complete details about these blocks, see their respective block reference pages.
Note If your model contains PS Constant Delay or PS Variable Delay blocks, or custom
blocks utilizing the delay operator in the Simscape language, MathWorks recommends
that you linearize the model by using the Timed-Based Linearization or Trigger-Based
Linearization block and simulating the model for a time period longer than the specified
delay time.
3-53
3
Model Simulation
Linearize an Electronic Circuit
This example shows how to linearize a model of a nonlinear bipolar transistor circuit and
create a Bode plot for small-signal frequency-domain analysis.
Depending on the software you have available, use the appropriate sections of this
example to explore various linearization and analysis techniques.
In this section...
“Explore the Model” on page 3-54
“Linearize with Steady-State Solver and linmod Function” on page 3-58
“Linearize with Simulink Control Design Software” on page 3-60
“Use Control System Toolbox Software for Bode Analysis” on page 3-61
Explore the Model
To open the Nonlinear Bipolar Transistor example model, type
ssc_bipolar_nonlinear in the MATLAB Command Window.
3-54
Linearize an Electronic Circuit
The model represents a single-transistor audio amplifier. The transistor is an NPN
bipolar device, and as such has a nonlinear set of current-voltage characteristics.
Therefore the overall behavior of the amplifier is dependent on the operating point of
the transistor. The transistor itself is represented by and Ebers-Moll equivalent circuit
implemented using a masked subsystem. The circuit has a sinusoidal input test signal
with amplitude 10 mV and frequency 1 kHz. The Scope block displays the resulting
collector output voltage after the DC is filtered out by the output decoupling capacitor.
R1 and R2 set the nominal operating point, and the small signal gain is approximately
set by the ratio R3/R4. The 1uF decoupling capacitors have been chosen to present
negligible impedance at 1 kHz.
The model is configured for linearization. You can quickly generate and view the smallsignal frequency response by double-clicking the Linearize block. To view the MATLAB
script that generates the frequency response, double-click the Open script block. This
documentation provides background information and alternative ways of linearization
based on the software you have.
In general, to obtain a nontrivial linearized input-output model and generate a frequency
response, you must specify model-level inputs and outputs. The Nonlinear Bipolar
Transistor model meets this requirement in two ways, depending on how you linearize:
• Simulink requires top- or model-level input and output ports for linearization with
linmod. The Nonlinear Bipolar Transistor model has such ports, marked u and y.
• Simulink Control Design software requires that you specify input and output signal
lines with linearization points. The specified lines must be Simulink signal lines, not
Simscape physical connection lines. The Nonlinear Bipolar Transistor model has such
linearization points specified. For more information on using Simulink Control Design
software for trimming and linearization, see documentation for that product.
Open the Solver Configuration block and see that the Start simulation from steady
state check box is selected. Then open the Scope and run the simulation to see the
basic circuit behavior. The transistor junction capacitance initial voltages are set to
be consistent with the bias conditions defined by the resistors. The output is a steady
sinusoid with zero average, its amplitude amplified by the transistor and bias circuit.
3-55
3
Model Simulation
To see the circuit relax from a nonsteady initial state, in the Solver Configuration block,
clear the Start simulation from steady state check box and click OK. With the
Scope open, simulate again. In this case, the output voltage starts at zero because the
transistor junction capacitances start with zero charge.
3-56
Linearize an Electronic Circuit
You can get a more comprehensive understanding of the circuit behavior and how it
approaches the steady state by long-time transient simulation. Increase the simulation
time to 1 s and rerun the simulation. The circuit starts from its initial nonsteady state,
and the transistor collector voltage approaches and eventually settles into steady
sinusoidal oscillation.
3-57
3
Model Simulation
Open the Solver Configuration block, select the Start simulation from steady state
check box (as it was when you first opened the model), and click OK. Change the
simulation time back to .01 s and rerun the simulation.
Linearize with Steady-State Solver and linmod Function
In this example, you:
1
Use the Simscape steady-state solver to find an operating point
2
Linearize the model using the Simulink linmod function
3
Generate the Bode plot using a series of MATLAB commands
Open the Solver Configuration block and make sure the Start simulation from steady
state check box is selected. When you simulate the model with the Simscape steadystate solver enabled, the circuit is initialized at the state defined by the transistor bias
resistors. This steady-state solution is an operating point suitable for linearization.
Note: Also make sure that the Use local solver check box is cleared. Linearizing a
model with the local solver enabled is not supported.
3-58
Linearize an Electronic Circuit
To linearize the model, type the following in the MATLAB Command Window:
[a,b,c,d]=linmod('ssc_bipolar_nonlinear');
You can alternatively call the linmod function with a single output argument, in which
case it generates a structure with states, inputs, and outputs, as well as the linear timeinvariant (LTI) model.
The state vector of the Nonlinear Bipolar Transistor model contains 17 components. The
full model has one input and one output. Thus, the LTI state-space model derived from
linearization has the following matrix sizes:
• a is 17-by-17
• b is 17-by-1
• c is 1-by-17
• d is 1-by-1
To generate a Bode plot with negative feedback convention, type the following in the
MATLAB Command Window:
c = -c; d = -d;
npts = 100; f = logspace(-2,10,npts); G = zeros(1,npts);
for i=1:npts
G(i) = c*(2*pi*1i*f(i)*eye(size(a))-a)^-1*b +d;
end
subplot(211), semilogx(f,20*log10(abs(G)))
grid
ylabel('Magnitude (dB)')
subplot(212), semilogx(f,180/pi*unwrap(angle(G)))
ylabel('Phase (degrees)')
xlabel('Frequency (Hz)')
grid
3-59
3
Model Simulation
Linearize with Simulink Control Design Software
Note: To work through this section, you must have a Simulink Control Design license.
Simulink Control Design software has tools that help you find operating points and
returns a state-space model object that defines state names. This is the recommended
way to linearize Simscape models.
3-60
1
In the top menu bar of the Nonlinear Bipolar Transistor model, select Analysis >
Control Design > Linear Analysis .
2
In the Linear Analysis Tool, from the Plot Result list, select New Bode.
3
Click the Linearize button.
Linearize an Electronic Circuit
For more information on using Simulink Control Design software for trimming and
linearization, see the Simulink Control Design documentation.
Use Control System Toolbox Software for Bode Analysis
Note: To work through this section, you must have a Control System Toolbox license.
You can use the built-in analysis and plotting capabilities of Control System Toolbox
software to analyze and compare Bode plots of different steady states.
First, use the Simulink linmod function to obtain the linear time-invariant (LTI) model.
[a,b,c,d]=linmod('ssc_bipolar_nonlinear');
Not all the states of the LTI model derived in this example are independent. Confirm
this by calculating the determinant of the a matrix, det(a). The determinant vanishes,
3-61
3
Model Simulation
which implies one or more zero eigenvalues. To analyze the LTI model, reduce the LTI
matrices to a minimal realization. Obtain a minimal realization using the minreal
function.
[a0,b0,c0,d0] = minreal(a,b,c,d);
13 states removed.
Extracting the minimal realization eliminates 13 dependent states from the LTI model,
leaving four independent states. Analyze the control characteristics of the reduced a0,
b0, c0, d0 LTI model using a Bode plot.
bode(a0,b0,c0,d0) % Creates first Bode plot
The circuit with R1 changed from 47 to 15 kOhm has a different steady state and
response. Double-click the R1 block, change the Resistance value to 15 kOhm, and
click OK. Open the Scope and simulate the model. The collector voltage is now no longer
amplified relative to the 10 mV AC source but attenuated.
Produce the LTI model at the second steady state, reduce it to a minimal realization, and
superpose the second Bode plot on the first one.
3-62
Linearize an Electronic Circuit
[a_R1,b_R1,c_R1,d_R1]=linmod('ssc_bipolar_nonlinear');
[a0_R1,b0_R1,c0_R1,d0_R1] = minreal(a_R1,b_R1,c_R1,d_R1); % 13 states removed.
hold on % Keeps first Bode plot open
bode(a0_R1,b0_R1,c0_R1,d0_R1) % Superposes second Bode plot on first
For more information on using Control System Toolbox software for Bode analysis, see
the Control System Toolbox documentation.
Related Examples
•
“Linearize a Plant Model for Use in Feedback Control Design”
More About
•
“Finding Operating Points in Physical Models”
•
“Linearizing a Physical Model”
3-63
3
Model Simulation
Linearize a Plant Model for Use in Feedback Control Design
This example shows how you can linearize a hydraulic plant model to support control
system stability analysis and design.
Depending on the software you have available, use the appropriate sections of this
example to explore various linearization and analysis techniques.
In this section...
“Explore the Model” on page 3-64
“Trim Using the Controller and Linearize with Simulink linmod Function” on page
3-66
“Linearize with Simulink Control Design Software” on page 3-68
Explore the Model
To open the Hydraulic Actuator with Digital Position Controller example model, type
ssc_hydraulic_actuator_digital_control in the MATLAB Command Window.
The model represents a two-way valve acting in a closed-loop circuit together with a
double-acting cylinder. Double-click the Hydraulic Plant subsystem to see the model
configuration.
3-64
Linearize a Plant Model for Use in Feedback Control Design
The controller is represented as a continuous-time transfer function plus a transport
delay that allows for computational time and a zero-order hold when implemented in
discrete time. The Linearization I/O points subsystem lets you easily break and restore
the feedback control loop by setting the base workspace variable ClosedLoop to 0 or 1,
respectively.
The model is configured for linearization. You can quickly generate and view the smallsignal frequency response by double-clicking the Linearize block. To view the MATLAB
script that generates the frequency response, double-click the Open script block. This
documentation provides background information and alternative ways of linearization
based on the software you have.
In general, to obtain a nontrivial linearized input-output model and generate a frequency
response, you must specify model-level inputs and outputs. The Hydraulic Actuator with
Digital Position Controller model meets this requirement in two ways, depending on how
you linearize:
• Simulink requires top- or model-level input and output ports for linearization with
linmod. The model has such ports, marked In1 and Out1.
3-65
3
Model Simulation
• Simulink Control Design software requires that you specify input and output signal
lines with linearization points. The specified lines must be Simulink signal lines, not
Simscape physical connection lines. The model has such linearization points specified.
For more information on using Simulink Control Design software for trimming and
linearization, see documentation for that product.
Open the Position scope and simulate the model in a normal closed-loop controller
configuration.
You can see that the model has a quasi-linear steady-state response between 2 and
3 seconds, when the two-way valve is open. Therefore, the state at 2.5 seconds is an
operating point suitable for linearization.
Trim Using the Controller and Linearize with Simulink linmod Function
1
Set the controller parameters.
To specify sample time for controller discrete-time implementation, type the
following in the MATLAB Command Window:
3-66
Linearize a Plant Model for Use in Feedback Control Design
ts = 0.001;
To specify continuous-time controller numerator and denominator, type:
num = -0.5;
den = [1e-3 1];
2
Find an operating point by running closed-loop and selecting the state at 2.5 seconds
when the custom two-way valve is open.
To close the feedback loop, type:
assignin('base','ClosedLoop',1);
To simulate the model and save the operating point information in the form of a
state vector X and input vector U, type:
[t,x,y] = sim('ssc_hydraulic_actuator_digital_control');
idx = find(t>2.5,1);
X = x(idx,:); U = y(idx);
3
Linearize the model using the Simulink linmod function.
To break the feedback loop, type:
assignin('base','ClosedLoop',0);
To linearize the model, type:
[a,b,c,d] = linmod('ssc_hydraulic_actuator_digital_control',X,U);
Close the feedback loop by typing:
assignin('base','ClosedLoop',1);
4
To generate a Bode plot with negative feedback convention, type the following in the
MATLAB Command Window:
c = -c; d = -d;
npts = 100; w = logspace(-3,5,npts); G = zeros(1,npts);
for i = 1:npts
G(i) = c*(1i*w(i)*eye(size(a))-a)^-1*b +d;
end
subplot(211), semilogx(w,20*log10(abs(G)))
grid
ylabel('Magnitude (dB)')
3-67
3
Model Simulation
subplot(212), semilogx(w,180/pi*unwrap(angle(G)))
ylabel('Phase (degrees)')
xlabel('Frequency (rad/s)')
grid
Linearize with Simulink Control Design Software
Note: To work through this section, you must have a Simulink Control Design license.
Simulink Control Design software has tools that help you find operating points and
returns a state-space model object that defines state names. This is the recommended
way to linearize Simscape models.
3-68
1
In the top menu bar of the Hydraulic Actuator with Digital Position Controller
model, select Analysis > Control Design > Linear Analysis .
2
In the Linear Analysis Tool, from the Operating Point list, select Linearize At.
Enter simulation snapshot time of 2.5 seconds and click OK.
Linearize a Plant Model for Use in Feedback Control Design
3
From the Plot Result list, select New Bode.
4
Click the Linearize button.
For more information on using Simulink Control Design software for trimming and
linearization, see the Simulink Control Design documentation.
Related Examples
•
“Linearize an Electronic Circuit”
More About
•
“Finding Operating Points in Physical Models”
•
“Linearizing a Physical Model”
3-69
3
Model Simulation
Limitations
In this section...
“Sample Time and Solver Restrictions” on page 3-70
“Algebraic Loops” on page 3-70
“Restricted Simulink Tools” on page 3-71
“Unsupported Simulink Tools” on page 3-73
“Simulink Tools Not Compatible with Simscape Blocks” on page 3-73
“Code Generation” on page 3-73
Sample Time and Solver Restrictions
The default sample times of Simscape blocks are continuous. You cannot simulate
Simscape blocks with discrete solvers using the default sample times.
If you switch to a local solver in the Solver Configuration block, the states of the
associated physical network become discrete. If there are no continuous Simulink or
Simscape states anywhere in a model, you are free to use a discrete solver to simulate the
model.
You cannot override the sample time of a nonvirtual subsystem containing Simscape
blocks.
Algebraic Loops
A Simscape physical network should not exist within a Simulink algebraic loop. This
means that you should not directly connect an output of a PS-Simulink Converter block
to an input of a Simulink-PS Converter block of the same physical network.
For example, the following model contains a direct feedthrough between the PS-Simulink
Converter block and the Simulink-PS Converter block (highlighted in magenta). To
avoid the algebraic loop, you can insert a Transfer Function block anywhere along the
highlighted loop.
3-70
Limitations
A better way to avoid an algebraic loop without introducing additional dynamics is shown
in the modified model below.
Restricted Simulink Tools
Certain Simulink tools are restricted for use with Simscape software:
• You can use the Simulink set_param and get_param commands to set or get
Simscape block parameters, if the parameters correspond to fields in the block dialog
box. MathWorks does not recommend that you use these commands to find or change
any other block parameters.
3-71
3
Model Simulation
If you make changes to block parameters at the command line, run your model first
before saving it. Otherwise, you might save invalid block parameters. Any block
parameter changes that you make with set_param are not validated unless you run
the model.
• Simscape blocks accept Simulink.Parameter objects as parameter values in
get_param and set_param, within the restrictions specified here.
• Enabled subsystems can contain Simscape blocks. Always set the States when
enabling parameter in the Enable dialog to held for the subsystem's Enable port.
Setting States when enabling to reset is not supported and can lead to fatal
simulation errors.
• You can place Simscape blocks within nonvirtual subsystems that support continuous
states. Nonvirtual subsystems that support continuous states include Enabled
subsystems and Atomic subsystems. However, physical connections and physical
signals must not cross nonvirtual boundaries. When placing Simscape blocks in a
nonvirtual subsystem, make sure to place all blocks belonging to a given Physical
Network in the same nonvirtual subsystem.
• Nonvirtual subsystems that do not support continuous sample time blocks (such as
If Action, For Iterator, Function-Call, Triggered, While Iterator, and so on) cannot
contain Simscape blocks.
• An atomic subsystem with a user-specified (noninherited) sample time cannot contain
Simscape blocks.
• Simulink configurable subsystems work with Simscape blocks only if all of the block
choices have consistent port signatures.
• When using SimState to save and restore simulations of models, you cannot make any
changes to the Simscape blocks in the model between the time at which you save the
SimState and the time at which you restore the simulation using the SimState.
This is an extension of the Simulink limitation prohibiting structural changes to the
model between these two points in time (see “Limitations of SimState”). Changes to
Simscape block parameters can cause equation changes and result in changes to the
state representation. Therefore, modifying parameters of Simscape blocks between
saving and restoring the SimState is not allowed.
• Linearization with the Simulink linmod function or with equivalent Simulink
Control Design functions and graphical interfaces is not supported with Simscape
models if you use local solvers.
• Model referencing is supported, with some restrictions:
3-72
Limitations
• All Physical connection lines must be contained within the referenced model.
Such lines cannot cross the boundary of the referenced model subsystem in the
referencing model.
• The referencing model and the referenced model must use the same solver.
• You cannot create Simulink signal objects directly on the PS-Simulink Converter
block outputs. Insert a Signal Conversion block after the output port of a PS-Simulink
Converter block and specify the signal object on the output of the Signal Conversion
block instead.
Unsupported Simulink Tools
Certain Simulink tools and features do not work with Simscape software:
• The Simulink Profiler tool does not work with Simscape models.
• Exporting a model to a format used by an earlier version (File > Export Model to >
Previous Version) is not supported for models containing Simscape blocks.
• Physical signals and physical connection lines between conserving ports are different
from Simulink signals. Therefore, the Signal and Scope Manager tool and the signal
label functionality are not supported.
Simulink Tools Not Compatible with Simscape Blocks
Some Simulink tools and features do not work with Simscape blocks:
• Execution order tags do not appear on Simscape blocks.
• Simscape blocks do not invoke user-defined callbacks.
• You cannot set breakpoints on Simscape blocks.
• Reusable subsystems cannot contain Simscape blocks.
• You cannot use the Simulink Fixed-Point Tool with Simscape blocks.
• The Report Generator reports Simscape block properties incompletely.
Code Generation
Code generation is supported for Simscape physical modeling software and its family
of add-on products. However, there are restrictions on code generated from Simscape
models.
3-73
3
Model Simulation
• Code reuse is not supported.
• Encapsulated C++ code generation is not supported.
• Tunable parameters are not supported.
• Run-time parameter inlining ignores global exceptions.
• Simulation of Simscape models on fixed-point processors is not supported.
• Block diagnostics in error messages are not supported. This means that if you get
an error message from simulating generated code, it does not contain a list of blocks
involved.
• Conversion of models or subsystems containing Simscape blocks to S-functions is not
supported.
“Code Generation” on page 3-31 describes Simscape code generation features. “Restricted
Simulink Tools” on page 3-71 describes limitations on model referencing.
There are variations and exceptions as well in the code generation features of the add-on
products based on Simscape platform. For details, see documentation for individual addon products.
Code Generation and Fixed-Step Solvers
Most code generation options for Simscape models require the use of fixed-step Simulink
solvers. This table summarizes the available solver choices, depending on how you
generate code.
Code Generation Option
Solver Choices
Accelerator mode
Rapid Accelerator mode
Variable-step or fixed-step
Simulink Coder software: RSim Target*
Variable-step or fixed-step
Simulink Coder software: Targets other than
RSim
Fixed-step only
* For the RSim Target, Simscape software supports only the Simulink solver module.
In the model Configuration Parameters dialog box, see the Code Generation: RSim
Target: Solver selection menu. The default is automatic selection, which might fail to
choose the Simulink solver module.
3-74
References
References
[1] Moler, C. B., Numerical Computing with MATLAB, Philadelphia, Society for
Industrial and Applied Mathematics, 2004, chapter 7
[2] Horowitz, P., and Hill, W., The Art of Electronics, 2nd Ed., Cambridge, Cambridge
University Press, 1989, chapter 2
[3] Brogan, W. L., Modern Control Theory, 2nd Ed., Englewood Cliffs, New Jersey,
Prentice-Hall, 1985
3-75
4
Variable Initialization and State
Viewer
• “About Variable Initialization” on page 4-2
• “Set Priority and Initial Target for Block Variables” on page 4-5
• “Initialize Variables for a Mass-Spring-Damper System” on page 4-8
• “Variable Viewer” on page 4-22
4
Variable Initialization and State Viewer
About Variable Initialization
In this section...
“Initializing Block Variables for Model Simulation” on page 4-2
“Variable Initialization Priority” on page 4-3
“Suggested Workflow” on page 4-4
Initializing Block Variables for Model Simulation
At the beginning of simulation (t = 0), the solver computes the initial conditions
to determine the simulation starting point, as described in “Initial Conditions
Computation”. Finding a solution means finding initial values for all system variables.
You can affect the initial conditions computation by block-level variable initialization,
that is, by specifying the priority and target initial values for certain variables on the
Variables tab of the respective block dialog boxes.
The values you specify during block-level variable initialization are not the actual values
of the respective variables, but rather their target values at the beginning of simulation
(t = 0). Depending on the results of the solve, some of these targets may or may not be
satisfied.
The solver tries to find a solution that:
• Exactly satisfies all the model equations
• Exactly satisfies all the high-priority targets
• Approximates the low-priority targets as closely as possible (as a result, some of the
low-priority targets might be satisfied exactly, the others are approximated)
If the solver cannot find a solution that exactly satisfies all the high-priority targets, it
issues a warning and enters the second stage of the solve process, where it tries to find a
solution by approximating both the high-priority and the low-priority targets as closely
as possible.
If you have selected the Start simulation from steady state check box in the Solver
block dialog box, the solver attempts to find the steady state (when the system variables
are no longer changing with time). If the steady-state solve succeeds, the state found
is some steady state (within tolerance), but not necessarily the state expected from the
4-2
About Variable Initialization
given initial conditions. In other words, if simulation starts from steady state, even the
high-priority variable targets might no longer be satisfied at the start of simulation.
However, if the model has more than one steady state, the variable targets you specify
can affect which steady-state solution is selected by the solver.
After you initialize the block variables and prior to simulating the model, you can open
the Variable Viewer to see which of the variable targets have been satisfied. The Variable
Viewer displays the actual initial values of the variables obtained as a result of the solve,
along with the variable target values, priority, and other information about the variable.
For details, see “Variable Viewer” on page 4-22.
Variable Initialization Priority
During block-level variable initialization, you specify the variable initial target (value
and unit) and the initialization priority. The priority can be one of the following:
• High — If a variable has high priority, the solver tries to find a solution where the
actual initial value of this variable exactly satisfies its target value.
• Low — If a variable has low priority, the solver tries to approximate the target value
of this variable as closely as possible when finding a solution. Depending on the
results of the solve for high-priority variables, some of the low-priority targets might
be met exactly, the others are approximated.
• None — A variable has no initialization priority when its Specify check box is
cleared, and the Priority, Value, and Unit fields display Unused. This does not
mean that the variable itself is not used in the initialization process, only that its
target is not used. The solver finds initial values for all system variables, but if a
variable has priority of none, (i.e. Unused), the solver does not try to satisfy any
specific initial value for this variable when solving the system.
When you specify too many high-priority targets for system variables, it is possible to
over-specify your model. In this case, the solver might not be able to find a solution that
exactly satisfies all the high-priority targets, or even fail to find a solution altogether. For
an example of how you can deal with over-specification by using the Variable Viewer and
changing the variable priority and targets, see “Initialize Variables for a Mass-SpringDamper System” on page 4-8.
For detailed information on how to specify variable priority and targets in block dialog
boxes, see “Set Priority and Initial Target for Block Variables” on page 4-5.
4-3
4
Variable Initialization and State Viewer
Suggested Workflow
1
Using the Variables tab of the respective block dialog boxes, specify which variable
targets should be used for initialization and set their priority, target values, and
units.
2
Open the Variable Viewer to see which of the initial targets have been satisfied.
Although the viewer does not simulate the model, it runs the simulation for 0
seconds to initialize it, and therefore the model must be in an executable state.
3
If initialization fails, or you are not satisfied with the results, iterate by changing the
block variable target values and priority, then refreshing the viewer.
4
When satisfied with initialization, run the simulation to see the results.
Related Examples
•
“Set Priority and Initial Target for Block Variables” on page 4-5
•
“Initialize Variables for a Mass-Spring-Damper System” on page 4-8
More About
•
4-4
“Variable Viewer” on page 4-22
Set Priority and Initial Target for Block Variables
Set Priority and Initial Target for Block Variables
When you open the Variables tab of a block dialog box, it lists all the public variables
specified in the underlying component file, along with priority, target value, and unit.
In most cases, the default value for each of these is Unused. For example, if you add a
Translational Spring block to your model, double-click it to open its dialog box, and then
click the Variables tab, it looks like this:
For details on these variables and their usage in the block equations, click the Source
code link in the block dialog box to view the underlying Simscape source file. The
Source code link is available for all the Foundation library blocks that have a
Variables tab.
To specify the initial deformation of the spring, select the check box next to the
Deformation variable. Once you select the check box next to a variable, its Priority
changes to High, while Value and Unit assume the values specified in the variable
declaration in the underlying component file.
4-5
4
Variable Initialization and State Viewer
Type a new number into the Value field and change the unit, if desired. The Unit dropdown lists contains all the units defined in the unit registry that are commensurate with
the one specified in the variable declaration. You can also change the priority from High
to Low. In the following dialog box, Deformation is specified as a high-priority variable
with the initial target of 20 mm.
4-6
Set Priority and Initial Target for Block Variables
If you clear the check box next to a variable name, its Priority, Value, and Unit fields
switch to Unused. However, if you select it again, these fields will retain their last
specified value for when they were in use.
Related Examples
•
“Initialize Variables for a Mass-Spring-Damper System” on page 4-8
More About
•
“About Variable Initialization” on page 4-2
4-7
4
Variable Initialization and State Viewer
Initialize Variables for a Mass-Spring-Damper System
This example shows how to use block variable initialization, and how it affects the
simulation results of a simple mechanical system.
The model is a classical unforced mass-spring-damper system, with the oscillations of the
mass caused by the initial deformation of the spring.
Create and Set Up the Model
4-8
1
Create a simple mass-spring-damper system. Use the Mass, Translational Spring,
Translational Damper, Mechanical Translational Reference, Ideal Translational
Motion Sensor, PS-Simulink Converter, Solver Configuration, and Scope blocks, and
connect them as shown in the following illustration.
2
Prepare the model for simulation. On the top menu bar of the model window, select
Simulation > Model Configuration Parameters. Under Solver options, set
Solver to ode23t (mod.stiff/Trapezoidal) and Max step size to 0.2. Also
adjust the Simulation time to be between 0 and 2 seconds, by setting Stop time to
2.0.
3
Specify the initial deformation of the spring. Double-click the Translational Spring
block. In the block dialog box, click the Variables tab, and then select the check box
next to the Deformation variable. Once you select the check box next to a variable,
its Priority changes to High, while Value and Unit assume the values specified in
the variable declaration in the underlying component file. Change the Value to 0.1.
Leave the Unit unchanged as m.
Initialize Variables for a Mass-Spring-Damper System
4
Adjust the initial position of the sensor, to compensate for the spring deformation.
Double-click the Ideal Translational Motion Sensor block and set its Initial
position parameter value to 0.1 m as well. This way, when you simulate the model,
mass oscillations center around 0.
5
Simulate the model.
4-9
4
Variable Initialization and State Viewer
6
Open the Variable Viewer. In the top menu bar of the model window, select
Analysis > Simscape > Variable Viewer.
The Translational Spring variable x, in the bottom row, has high priority and the
target value of 0.1 m. This is the Deformation variable that you have just set up in
4-10
Initialize Variables for a Mass-Spring-Damper System
the block dialog box. Its actual start value matches its target value, and therefore its
Status column displays a green circle.
The other high-priority variable in this model is the position, x, of the Ideal
Translational Motion Sensor block, which is set inside the component file because
it is necessary for the correct operation of the sensor. Its actual start value also
matches its target value, and its Status column also displays a green circle.
The rest of the variables in the model do not have initialization priority specified,
therefore their Status column also displays green circles. The overall status at the
bottom of the Variable Viewer window displays a green circle as well, and says that
all the variable targets are satisfied.
Change Initialization Targets
You can now see how specifying different variable targets affects system initialization
and simulation results.
1
Specify the initial velocity of the mass. Double-click the Mass block, go to the
Variables tab, select the check box next to the Velocity variable, and enter a value
of 10. Keep the priority High and the unit m/s.
2
Refresh the Variable Viewer by clicking
.
4-11
4
Variable Initialization and State Viewer
You can see that the solver has found a different initial solution, which satisfies
your variable targets for spring deformation and mass velocity. The Status column
displays green circles, and the overall status at the bottom of the Variable Viewer
window also displays a green circle and says that all the variable targets are
satisfied.
3
Notice that when you refreshed the Variable Viewer, the scopes turned blank. This
happens because solver runs the simulation for 0 seconds to find the initial solution
and display it in the Variable Viewer.
Rerun the simulation and examine the Velocity and Position scope windows, to see
the effect of the new initial value for mass velocity on the simulation results.
4-12
Initialize Variables for a Mass-Spring-Damper System
Deal with Over-Specification
As you specify additional variable targets, sometimes it is possible to over-specify the
constraints.
4-13
4
Variable Initialization and State Viewer
1
Double-click the Translational Damper block, go to the Variables tab, select the
check box next to the Force variable, and enter a value of 200. Keep the priority
High and the unit N.
2
Refresh the Variable Viewer.
The overall status at the bottom of the Variable Viewer window now displays a red
square and says that the solver is unable to satisfy all the high-priority variable
4-14
Initialize Variables for a Mass-Spring-Damper System
targets. There are red squares in the Status column for the two high-priority
variables with targets not satisfied, as well as for their parent blocks.
Notice that the solver has been able to find a solution for model initialization. If you
rerun the simulation, it runs without errors and you can see the new simulation
results.
4-15
4
Variable Initialization and State Viewer
However, the Variable Viewer shows that the model initialization solution does not
satisfy your target values for block variables. This happens because placing highpriority constraints on all three elements of the mass-spring-damper system results
in a conflict. You can resolve the over-specification issue by relaxing the priority of
some of the conflicting variable targets.
4-16
3
Double-click the Translational Damper block again, go to the Variables tab, and
change the priority of the Force variable to Low.
4
Refresh the Variable Viewer.
Initialize Variables for a Mass-Spring-Damper System
The overall status at the bottom of the Variable Viewer window now displays a
yellow triangle and says that all the high-priority targets are satisfied, but some of
the low-priority targets are not satisfied. There are now two yellow triangles in the
status column: one for the low-priority force variable f and one for its parent block,
Translational Damper.
Essentially, the solution found in this case is the same as when you previously
specified high-priority target for the mass velocity, and the simulation results are the
same.
4-17
4
Variable Initialization and State Viewer
5
4-18
Another way to deal with over-specification is to keep the high priority on the
damper force and relax the priority on mass initial velocity. Double-click the
Translational Damper block again, go to the Variables tab, and change the priority
of the Force variable back to High. Then double-click the Mass block, go to the
Variables tab, and change the priority of the Velocity variable to Low.
Initialize Variables for a Mass-Spring-Damper System
6
Refresh the Variable Viewer.
Again, the Variable Viewer status says that all the high-priority targets have
been satisfied and that some of the low-priority targets are not satisfied. However,
because you changed the variable priorities, the solver now tried to satisfy the initial
force on the damper rather than the mass velocity, and the solution is different in
this case, as are the simulation results.
4-19
4
Variable Initialization and State Viewer
Related Examples
•
“Set Priority and Initial Target for Block Variables” on page 4-5
More About
•
4-20
“About Variable Initialization” on page 4-2
Initialize Variables for a Mass-Spring-Damper System
•
“Variable Viewer” on page 4-22
4-21
4
Variable Initialization and State Viewer
Variable Viewer
In this section...
“About Variable Viewer” on page 4-22
“Advanced Configuration” on page 4-24
“Switching Between Tree View and Flat View” on page 4-26
“Useful Filtering Techniques” on page 4-28
“Link to Block Diagram” on page 4-28
“Interaction with Model Updates and Simulation” on page 4-30
About Variable Viewer
Prior to simulating the model, you can use the Variable Viewer to check the results of the
initial conditions computation for the model and to see which of the block-level variable
initialization targets have been satisfied. The Variable Viewer displays the variable
priority and target values, where specified, along with the actual initial values for all the
variables obtained as a result of the solve.
To open the Variable Viewer, in the top menu bar of the model window, select Analysis >
Simscape > Variable Viewer.
The Variable Viewer is a table, its rows listing all the blocks in the model and all the
public variables under each block, and the columns providing the initialization status,
priority, target and actual start values, and other information for each variable.
4-22
Variable Viewer
By default, the Variable Viewer opens in basic configuration, which has the following
columns:
Name
Description
Status
Initialization status of each variable, can be one of:
• Green circle — Displayed for variables with initialization targets
satisfied, and also for all variables with no initialization priority.
• Yellow triangle — Displayed for low-priority variables if the target
is not satisfied.
• Red square — Displayed for high-priority variables if the target is
not satisfied.
• Red cross — If initial condition solve fails, displayed for variables
that could not be initialized.
• Gray rectangle — Displayed when status is not available. This can
happen, for example, if model initialization failed, or if the viewer
was left open during diagram update. For more information, see
“Interaction with Model Updates and Simulation” on page 4-30.
Priority
Variable initialization priority, as specified in the block dialog box
or in the underlying component file. For more information, see “Set
Priority and Initial Target for Block Variables” on page 4-5 and
“Variable Priority for Model Initialization”. If the variable has no
initialization priority (priority.none or Unused), then this field is
empty.
Target
Initial target value for a high-priority or low-priority variable. If the
variable has no initialization priority, then this field is empty.
Start
The actual initial value of the variable computed by the solver.
Unit
The variable base unit, common for all the values (Target, Prestart,
and Start). Simscape unit manager automatically converts all the
values as needed. For example, if you specified the target Value in
the block dialog box as 20 and the Unit as mm, the Variable Viewer
displays the Target as 0.2 and Unit as m.
A downward-pointing arrow next to a column name indicates that you can filter the table
rows based on their value in this column. For more information on the filtering options,
see “Useful Filtering Techniques” on page 4-28.
The Variable Viewer toolbar buttons perform the following actions:
4-23
4
Variable Initialization and State Viewer
Displays the data in the Variable Viewer in tree view, with variable nodes grouped
under the parent port, block, and subsystem nodes. This is the default view.
Displays the data in the Variable Viewer in flat view, to minimize the number of
rows in the table. In flat view, the rows for parent nodes are not shown, and the
table contains just one row per variable, with the Name column including the
complete path to the variable from the model root. If the Variable Viewer is in flat
view, the buttons that expand and collapse nodes are disabled.
Expands all nodes, showing all variables under each block name. This button is
available only if the Variable Viewer is in tree view.
Collapses all variables under each block name. You can then expand the block
nodes individually to see the variables under this block. This button is available
only if the Variable Viewer is in tree view.
Recomputes the initial conditions for the model and refreshes the values displayed
in the viewer. Use this button after adjusting the block parameter values,
changing variable priorities and targets, or updating the block diagram. For more
information, see “Interaction with Model Updates and Simulation” on page 4-30.
Clears all the column filtering options and displays all the rows in the table. For
more information, see “Useful Filtering Techniques” on page 4-28.
Shows the Variable Viewer in its default, basic, configuration, with only the
following columns displayed: Status, Priority, Target, Start, and Unit.
Shows the Variable Viewer in advanced configuration, with all the columns
displayed. Use this view for troubleshooting your model, for example, if the model
initialization failed.
Advanced Configuration
In most cases, the default Variable Viewer configuration contains sufficient data for
viewing the variable targets and verifying the model initialization results. However,
if the solver is unable to satisfy all the high-priority variable targets, or if the model
initialization fails, the advanced Variable Viewer configuration might provide additional
data that can help you troubleshoot your model.
To switch to the advanced configuration, click
4-24
in the Variable Viewer toolbar.
Variable Viewer
In advanced configuration, the Variable Viewer displays the following additional
columns:
Name
Description
Prestart
The value of the variable that the solver uses at the beginning of the
initial conditions solve process. For variables with no initialization
priority, the prestart values come from the variable declaration in
the underlying component file. If the initialization process fails, these
values can help you determine the reason (for example, a prestart
value of 0 for a variable used as a denominator in a model equation). If
a variable has an undesirable prestart value, specify a better value as
a low-priority initialization target, to make the solver start iterations
from a different point.
Eliminated
These variables are eliminated by the software prior to numerical
integration and are not used in solving the system. Prestart values for
these variables have no effect on the system solution. However, you
can set the initialization priority and targets on these variables, in
which case their targets will be represented in terms of the variables
that are retained by the solver.
Determined
The values of these variables depend on the system inputs, or
their values are predetermined based on the analysis of equations.
Therefore, specifying initialization priority and targets for these
variables has little or no impact on system solution. Also, if you
specify a high-priority target for a predetermined variable, the solver
4-25
4
Variable Initialization and State Viewer
Name
Description
most likely will not be able to satisfy this target but will spend extra
time trying to find a second-stage solution.
Differential
Time derivatives of these variables appear in equations. These
variables add dynamics to the system and can produce independent
states. Therefore, these variables are more likely to require high
initialization priority.
You can change the default order of columns by clicking a column heading and dragging
it, while holding down the mouse button, to the desired location. You can also hide
columns by right-clicking their headers and selecting Hide This Column from the
context menu, or clearing the check mark next to a column name. Clicking
or
in
the Variable Viewer toolbar restores the default basic or advanced layout, respectively.
Switching Between Tree View and Flat View
You can control the number of rows in the Variable Viewer by switching between the
tree view (the default) and the flat view. By default, the Variable Viewer opens in
tree view, with variable nodes grouped under the parent port, block, and subsystem
nodes. Therefore, the Variable Viewer table contains the rows for the parent nodes
(ports, blocks, and subsystems) in addition to the rows that correspond to all the public
variables. Only the rows that represent variables contain data such as targets and actual
values. All rows display a status, with the status of a parent node being determined by
the status of its children variables: if all the children are green, then the row for the
parent node also displays a green circle in its Status column.
For example, in the Variable Viewer table below, the first row represents the Ideal
Translational Motion Sensor block, the second row — port C of this block, and only the
third row contains the data for the actual variable v (velocity at port C).
4-26
Variable Viewer
To switch to the flat view, click
in the Variable Viewer toolbar.
In flat view, the rows for parent nodes are not shown, and the table contains just one
row per variable, with the Name column including the complete path to the variable
from the top-level model. For example, the first row of the Variable Viewer table in flat
view represents the same variable v (velocity at port C of the Ideal Translational Motion
Sensor block), and the Name column includes the names of its parents and shows the
path to the variable. Flat view makes the Variable Viewer table more compact.
4-27
4
Variable Initialization and State Viewer
If the Variable Viewer is in flat view, the buttons that expand and collapse nodes are
disabled.
To switch back to the tree view, click
in the Variable Viewer toolbar.
Useful Filtering Techniques
A downward-pointing arrow next to a column name indicates that you can filter the table
rows based on their value in this column.
To filter the rows, click the arrow, and then select or clear the check boxes in the dropdown list to indicate which rows you want to be displayed, based on their value. Selecting
All clears all the filters for that column. To clear all filters for all columns, click
the Variable Viewer toolbar.
in
For example, filtering on the Priority column values (selecting only the check boxes for
HIGH and LOW) lets you view all the targets and actual values in a compact format, which
can be helpful for a large model.
You might also find the following filtering techniques useful in troubleshooting your
models:
• Filter the Differential column on TRUE, to display only the rows for differential
variables. Time derivatives of these variables appear in equations. These variables
add dynamics to the system and can produce independent states, therefore these
variables are more likely to require high initialization priority.
• Filter the Determined column on TRUE, to verify that these variables have no
initialization priority. The values of these variables are either predetermined by
the equation analysis or depend on the system inputs, and therefore specifying
initialization priority and targets for these variables has little or no effect on model
initialization.
Link to Block Diagram
The Variable Viewer tool provides direct linking to the block diagram. This link lets
you highlight the appropriate block, or easily go from a variable listed in the Variable
Viewer to the Variables tab in the corresponding block dialog box, to modify the variable
priorities and targets.
4-28
Variable Viewer
When you right-click in the Name column of any row in the Variable Viewer table, a
context menu opens with the following options:
• Highlight block — Highlights the corresponding block in the block diagram, opening
the appropriate subsystem if needed. If the row represents a variable, highlights the
parent block for this variable.
• Open block dialog — Opens the corresponding block dialog box (for a variable,
opens the parent block dialog box). In the block dialog box, click the Variables tab
to view or modify the variable priorities and targets. If the selected row represents a
subsystem, this option is not available.
4-29
4
Variable Initialization and State Viewer
Interaction with Model Updates and Simulation
The Variable Viewer computes the actual initial values of the variables by running the
simulation for 0 seconds. Therefore:
• The model must be in an executable state when you open or refresh the viewer,
otherwise you get an error message.
• If the scopes are open, they turn blank every time you open or refresh the viewer.
Rerun the simulation to see the new results.
• If you rerun the simulation while the Variable Viewer is open, the results in the
viewer are automatically refreshed when the simulation starts running.
• If you change variable priorities and targets or adjust the block parameters while
the Variable Viewer is open, the results in the viewer are not updated automatically.
Refresh the viewer (by clicking
in the Variable Viewer toolbar) to compute the
new actual values of the variables and update the status.
4-30
Variable Viewer
• If you update block diagram (by selecting Simulation > Update Diagram in the
top menu bar of the model window) while the Variable Viewer is open, the previously
computed actual values become unavailable and the Status column displays gray
rectangles. The overall status at the bottom of the Variable Viewer window is also not
available. Refresh the viewer to compute the new actual values of the variables and
update the status.
Related Examples
•
“Initialize Variables for a Mass-Spring-Damper System” on page 4-8
More About
•
“About Variable Initialization” on page 4-2
4-31
5
Data Logging
• “About Simulation Data Logging” on page 5-2
• “Enable Data Logging for the Whole Model” on page 5-4
• “Log Data for Selected Blocks Only” on page 5-5
• “Data Logging Options” on page 5-6
• “Log and Plot Simulation Data” on page 5-8
• “Log Simulation Statistics” on page 5-13
• “Log and View Simulation Data for Selected Blocks” on page 5-17
• “Log, Navigate, and Plot Simulation Data” on page 5-22
• “About the Simscape Results Explorer” on page 5-27
• “View Sparkline Plots of Simulation Data” on page 5-28
5
Data Logging
About Simulation Data Logging
In this section...
“Suggested Workflows” on page 5-2
“Limitations” on page 5-3
Suggested Workflows
You can log simulation data to the workspace for debugging and verification. Data
logging lets you analyze how internal block variables change with time during
simulation. For example, you might want to see that the pressure in a hydraulic cylinder
is above some minimum value or compare it against the pump pressure. If you log
simulation data to the workspace, you can later query, plot, and analyze it without
rerunning the simulation.
Simulation data logging can also replace connecting sensors and scopes to track
simulation data. These blocks increase model complexity and slow down simulation. “Log
and Plot Simulation Data” on page 5-8 shows how you can log and plot simulation
data instead of adding sensors to your model. It also shows how you can print the
complete logging tree for a model and plot simulation results for a selected variable.
You can log data either for the whole model, or on a block-by-block basis. In the second
case, the workspace variable will contain simulation data for selected blocks only. To log
data for selected blocks only, you have to:
• Set the logging configuration parameter
• Select the blocks in your model
You can perform these two steps in any order. For more information, see “Log Data for
Selected Blocks Only” on page 5-5.
After running the simulation, you can use the Simscape Results Explorer tool to navigate
and plot the data logging results.
For additional information on how you can query, plot, and analyze data
stored in the simulation log variable, see the reference pages for the classes
simscape.logging.Node, simscape.logging.Series, and their associated methods.
You can also configure your model to automatically record Simscape logging data, along
with the rest of the simulation data obtained from a model run, using the Simulation
5-2
About Simulation Data Logging
Data Inspector. Set up your model to log simulation data, either for the whole model or
on a block-by-block basis, and enable data recording. Simulate the model, and then open
the Simulation Data Inspector and view the results. For detailed information on how to
enable data recording and how to configure and use the Simulation Data Inspector, see
“Inspect Signal Data with Simulation Data Inspector”.
To make your model simulation and data logging compatible with the parfor command,
select the Save simulation output as single object check box on the Data Import/
Export pane of the Configuration Parameters dialog box. In this case, Simscape log data
will be part of the single output object instead of being stored as a separate workspace
variable. For more information, see “Save simulation output as single object”.
Limitations
Simulation data logging is not supported for:
• Model reference
• Generated code
• Accelerator mode
• Rapid Accelerator mode
Related Examples
•
“Log, Navigate, and Plot Simulation Data” on page 5-22
•
“Log and View Simulation Data for Selected Blocks” on page 5-17
•
“Log and Plot Simulation Data” on page 5-8
•
“Log Simulation Statistics” on page 5-13
More About
•
“Data Logging Options” on page 5-6
5-3
5
Data Logging
Enable Data Logging for the Whole Model
By default, simulation data is not logged. To turn on the data logging for a model, use the
Log simulation data configuration parameter.
1
In the model window, from the top menu bar, select Simulation > Model
Configuration Parameters. The Configuration Parameters dialog box opens.
2
In the Configuration Parameters dialog box, in the left pane, select Simscape.
The right pane displays the Log simulation data option, which is set to None, by
default.
3
From the drop-down list, select All, then click OK.
4
Simulate the model. This creates a workspace variable named simlog (as specified
by the Workspace variable name parameter), which contains the simulation data.
For information on how to access and use the data stored in this variable, see
the related examples listed below. For information on additional data logging
configuration options, see “Data Logging Options” on page 5-6.
Related Examples
•
“Log, Navigate, and Plot Simulation Data” on page 5-22
•
“Log and Plot Simulation Data” on page 5-8
•
“Log Simulation Statistics” on page 5-13
More About
•
5-4
“Data Logging Options” on page 5-6
Log Data for Selected Blocks Only
Log Data for Selected Blocks Only
Instead of logging the simulation data for the whole model, you can log data just for the
selected blocks.
1
Set the logging configuration parameter to enable simulation data logging on a
block-by-block basis.
In the model window, from the top menu bar, select Simulation > Model
Configuration Parameters. In the Configuration Parameters dialog box, in the
left pane, select Simscape, then set the Log simulation data parameter to Use
local settings. Click OK.
2
Select the blocks in your model. You can do this before or after setting the logging
configuration parameter.
For each block that you want to select for data logging, right-click on the block. From
the context menu, select Simscape > Log simulation data. A check mark appears
in front of the Log simulation data option.
3
Simulate the model. When the simulation is done, the simulation data log contains
only the data from the selected blocks.
To stop logging data for a previously selected block, right-click on it and select Simscape
> Log simulation data again to remove the check mark.
If you set the Log simulation data parameter to All, the simulation log will
contain data from the whole model, regardless of the block selections. Setting the Log
simulation data parameter to None disables data logging for the whole model.
Related Examples
•
“Log and View Simulation Data for Selected Blocks” on page 5-17
More About
•
“Data Logging Options” on page 5-6
5-5
5
Data Logging
Data Logging Options
When you set the Log simulation data configuration parameter to All or Use local
settings, other options in the Data Logging group box become available.
• Log simulation statistics — Select this check box if you want to access and analyze
information on zero crossings during simulation. By default, this check box is not
selected and the zero-crossing data is not logged. For more information on using this
check box, see “Log Simulation Statistics” on page 5-13.
• Open viewer after simulation — Select this check box if you want to open
Simscape Results Explorer, which is an interactive tool that lets you navigate and
plot the simulation data logging results. By default, this check box is not selected. For
more information, see “About the Simscape Results Explorer” on page 5-27.
• Workspace variable name — Specifies the name of the workspace variable
that stores the simulation data. Subsequent simulations overwrite the data in
the simulation log variable. If you want to compare data from two models or two
simulation runs, use different names for the respective log variables. The default
variable name is simlog.
• Decimation — Use this parameter to limit the number of data points saved, by
outputting data points for every nth time step, where n is the decimation factor.
The default is 1, which means that all points are logged. Specifying a different value
results in the first step, and every nth step thereafter, being logged. For example,
specifying 2 logs data points for every other time step, while specifying 10 logs data
points for just one in ten steps.
• Limit data points — Use this check box in conjunction with the Data history
(last N steps) parameter to limit the number of data points saved. The check box is
selected by default. If you clear it, the simulation log variable contains the data points
for the whole simulation, at the price of slower simulation speed and heavier memory
consumption.
• Data history (last N steps) — Specify the number of simulation steps to limit
the number of data points output to the workspace. The simulation log variable
contains the data points corresponding to the last N steps of the simulation, where
N is the value that you specify for the Data history (last N steps) parameter. You
have to select the Limit data points check box to make this parameter available.
The default value logs simulation data for the last 5000 steps. You can specify
any other positive integer number. If the simulation contains fewer steps than the
number specified, the simulation log variable contains the data points for the whole
simulation.
5-6
Data Logging Options
Saving data to the workspace can slow down the simulation and consume memory. To
avoid this, you can use either the Decimation parameter, or Limit data points in
conjunction with Data history (last N steps), or both methods, to limit the number
of data points saved. The two methods work independently from each other and can be
used separately or together. For example, if you specify a decimation factor of 2 and
keep the default value of 5000 for the Data history (last N steps) parameter, your
workspace variable will contain downsampled data from the last 10,000 time steps in the
simulation.
Note The Output options parameter, on the Data Import/Export pane of the
Configuration Parameters dialog box, also affects which data points are logged. For more
information, see “Data Import/Export Pane” in the Simulink documentation.
After changing your data logging preferences, rerun the simulation to generate a new
data log.
Related Examples
•
“Enable Data Logging for the Whole Model” on page 5-4
•
“Log Data for Selected Blocks Only” on page 5-5
More About
•
“About Simulation Data Logging” on page 5-2
5-7
5
Data Logging
Log and Plot Simulation Data
This example shows how you can log and plot simulation data instead of adding sensors
to your model.
The model shown represents a permanent magnet DC motor.
This model is very similar to the Permanent Magnet DC Motor example, but, unlike the
example model, it does not include the Ideal Rotational Motion Sensor and the Current
Sensor blocks, along with the respective PS-Simulink Converter blocks and scopes. For
a detailed description of the Permanent Magnet DC Motor example, see “Evaluating
Performance of a DC Motor”.
5-8
1
Build the model, as shown in the preceding illustration.
2
To enable data logging, open the Configuration Parameters dialog box, in the left
pane, select Simscape, then set the Log simulation data parameter to All and
click OK.
Log and Plot Simulation Data
3
Simulate the model. This creates a workspace variable named simlog (as specified
by the Workspace variable name parameter), which contains the simulation data.
4
The simlog variable has the same hierarchy as the model. To see the whole variable
structure, at the command prompt, type:
simlog.print
This command prints the whole data tree.
mlog_ex_dcmotor1
+-Electrical_Reference2
| +-V
| | +-v
| +-i
+-Friction_Mr
5-9
5
Data Logging
| +-C
| | +-w
| +-R
| | +-w
| +-t
| +-w
+-L
| +-i
| +-i_L
| +-n
| | +-v
| +-p
| | +-v
| +-v
+-Load_Torque
| +-C
| | +-w
| +-R
| | +-w
| +-S
| +-t
| +-w
+-Mechanical_Rotational_Reference
| +-W
| | +-w
| +-t
+-Mechanical_Rotational_Reference1
| +-W
| | +-w
| +-t
+-Motor_Inertia_J
| +-I
| | +-w
| +-t
+-Rotational_Electromechanical_Converter
| +-C
| | +-w
| +-R
| | +-w
| +-i
| +-n
| | +-v
| +-p
| | +-v
| +-t
| +-v
| +-w
+-Rotor_Resistance_R
| +-i
| +-n
| | +-v
| +-p
| | +-v
| +-v
+-Simulink_PS_Converter
5-10
Log and Plot Simulation Data
+-x1_5V
+-i
+-n
| +-v
+-p
| +-v
+-v
5
Every node that represents an Across, Through, or internal block variable contains
series data. To get to the series, you have to specify the complete path to it through
the tree, starting with the top-level variable name. For example, to get a handle on
the series representing the angular velocity of the motor, type:
s1 = simlog.Rotational_Electromechanical_Converter.R.w.series;
From here, you can access the values and time vectors for the series and analyze
them.
6
You do not have to isolate series data to plot its values against time, or against
another series. For example, to see how the motor speed (in revolutions per minute)
changes with time, type:
plot(simlog.Rotational_Electromechanical_Converter.R.w,'units','rpm')
5-11
5
Data Logging
7
Compare this figure to the RPM scope display in the Permanent Magnet DC Motor
example. The results are exactly the same.
8
To plot the motor torque against its angular velocity, in rpm, and add descriptive
axis names, type:
plotxy(simlog.Rotational_Electromechanical_Converter.R.w,simlog.Motor_Inertia_J.t,...
'xunit','rpm','xname','Angular velocity','yname','Torque')
For more information on plotting logged simulation data, see the
simscape.logging.plot and simscape.logging.plotxy reference pages.
5-12
Log Simulation Statistics
Log Simulation Statistics
This example shows how you can access and analyze information on zero crossings
during simulation. By default, the zero-crossing data is not logged. If you select the Log
simulation statistics check box, the simulation log variable contains an additional
SimulationStatistics node for each block that can produce zero crossings, at the
price of slower simulation speed and heavier memory consumption.
The model shown represents a permanent magnet DC motor.
This model is the same as the one used in the “Log and Plot Simulation Data” on page
5-8 example.
1
Build the model, as shown in the preceding illustration.
2
To enable data logging, open the Configuration Parameters dialog box, in the left
pane, select Simscape, then set the Log simulation data parameter to All, select
the Log simulation statistics check box, and click OK.
5-13
5
Data Logging
3
Simulate the model. This creates a workspace variable named simlog (as specified
by the Workspace variable name parameter), which contains the simulation
data. Because you selected the Log simulation statistics checkbox, the workspace
variable contains additional nodes that represent zero-crossing data.
4
The simlog variable has the same hierarchy as the model. To see the whole variable
structure, at the command prompt, type:
simlog.print
This command prints the whole data tree.
mlog_ex_dcmotor1
+-Electrical_Reference2
| +-V
5-14
Log Simulation Statistics
| | +-v
| +-i
+-Friction_Mr
| +-C
| | +-w
| +-R
| | +-w
| +-SimulationStatistics
| | +-zc_0
| | | +-crossings
| | | +-values
| | +-zc_1
| | | +-crossings
| | | +-values
| | +-zc_2
| |
+-crossings
| |
+-values
| +-t
| +-w
+-L
| +-i
| +-i_L
| +-n
| | +-v
| +-p
| | +-v
| +-v
+-Load_Torque
| +-C
| | +-w
| +-R
| | +-w
| +-S
| +-t
| +-w
+-Mechanical_Rotational_Reference
| +-W
| | +-w
| +-t
+-Mechanical_Rotational_Reference1
| +-W
| | +-w
| +-t
+-Motor_Inertia_J
| +-I
| | +-w
| +-t
+-Rotational_Electromechanical_Converter
| +-C
| | +-w
| +-R
| | +-w
| +-i
| +-n
| | +-v
5-15
5
Data Logging
| +-p
| | +-v
| +-t
| +-v
| +-w
+-Rotor_ResistanceR
| +-i
| +-n
| | +-v
| +-p
| | +-v
| +-v
+-x1_5V
+-i
+-n
| +-v
+-p
| +-v
+-v
5-16
5
If you compare this tree to the one used in the “Log and Plot Simulation Data” on
page 5-8 example, you can see that under the Friction_Mr node there is now an
additional node called SimulationStatistics. The rest of the tree is unchanged.
This means that Friction Mr is the only block in the model that can generate zerocrossings during simulation.
6
You can access and analyze this data similar to other data that is logged to
workspace during simulation. For more information, see simscape.logging.Node
class and simscape.logging.Series class reference pages.
Log and View Simulation Data for Selected Blocks
Log and View Simulation Data for Selected Blocks
This example shows how you can set your model to log simulation data for selected blocks
only and how to view simulation data using Simscape Results Explorer.
The model shown represents a permanent magnet DC motor.
This model is the same as the one used in the “Log and Plot Simulation Data” on page
5-8 example.
1
Build the model, as shown in the preceding illustration.
2
To enable data logging on a block-by-block basis, open the Configuration Parameters
dialog box. In the left pane, select Simscape, then set the Log simulation data
parameter to Use local settings and click OK.
5-17
5
Data Logging
3
5-18
Select the blocks for data logging. Right-click the Rotational Electromechanical
Converter block. From the context menu, select Simscape > Log simulation data .
Log and View Simulation Data for Selected Blocks
After you select a block for data logging, a check mark appears in front of the Log
simulation data option in the context menu for that block.
4
Right-click the Motor Inertia block and select it for data logging, as described in the
previous step.
5
Simulate the model. This creates a workspace variable named simlog (as specified
by the Workspace variable name parameter), which contains the simulation data
for selected blocks only.
6
To open the Simscape Results Explorer, right-click one of the blocks previously
selected for data logging, for example, the Rotational Electromechanical Converter
block. From the context menu, select Simscape > View simulation data > simlog.
5-19
5
Data Logging
Note: If you right-click a block that has not been selected for simulation data
logging, for example, the Load Torque block, the View simulation data option is
not available.
If you change the name of the log variable between simulation runs, the context
menu lists the names of all the log variables associated with the block. For
example, to compare data from two simulation runs, you can use different
variable names (such as simlog1 and simlog2). Open a Simscape Results
Explorer window with simlog1 results, then unlink it from the session and
open another window with simlog2 results. For more information, see “About
the Simscape Results Explorer” on page 5-27.
The Simscape Results Explorer window opens, with the
Rotational_Electromechanical_Converter node already selected in the left
pane, and all the node plots for this block displayed in the right pane. You can
see that it contains simulation data only for the two selected blocks, Rotational
Electromechanical Converter and Motor Inertia.
5-20
Log and View Simulation Data for Selected Blocks
Related Examples
•
“Log, Navigate, and Plot Simulation Data” on page 5-22
More About
•
“About Simulation Data Logging” on page 5-2
•
“About the Simscape Results Explorer” on page 5-27
5-21
5
Data Logging
Log, Navigate, and Plot Simulation Data
This example shows the basic workflow for logging simulation data for the whole model
and then navigating and plotting the logged data using Simscape Results Explorer.
5-22
1
Open the Permanent Magnet DC Motor example model by typing ssc_dcmotor in
the MATLAB Command Window.
2
To enable data logging, open the Configuration Parameters dialog box, in the left
pane, select Simscape, then set the Log simulation data parameter to All. Select
the Open viewer after simulation check box and click OK.
Log, Navigate, and Plot Simulation Data
3
Simulate the model. When the simulation is done, the Simscape Results Explorer
window opens. In the left pane, it contains the simulation log tree hierarchy, which
corresponds to the model hierarchy.
5-23
5
Data Logging
4
5-24
When you click on a node in the left pane, the corresponding plots
appear in the right pane. Expand the DC_Motor node, and then click the
Rotational_Electromechanical_Converter node to see all the node plots for
this block.
Log, Navigate, and Plot Simulation Data
5
To isolate the plot of the rotor angular velocity series against time, keep expanding
the nodes in the left pane until you get to the series data.
5-25
5
Data Logging
Related Examples
•
“Log and View Simulation Data for Selected Blocks” on page 5-17
More About
5-26
•
“About Simulation Data Logging” on page 5-2
•
“About the Simscape Results Explorer” on page 5-27
About the Simscape Results Explorer
About the Simscape Results Explorer
Simscape Results Explorer is an interactive tool that lets you navigate and plot the
simulation data logging results.
When you configure the model to log simulation data (for the whole model or just
the selected blocks), you can make the Simscape Results Explorer window open
automatically upon completing a simulation run by selecting the Open viewer after
simulation check box in the Configuration Parameters dialog box. For more information
on this workflow, see “Log, Navigate, and Plot Simulation Data” on page 5-22.
Another way to open the Simscape Results Explorer window is to right-click on a block
and, from the context menu, select Simscape > View simulation data. For more
information, see “Log and View Simulation Data for Selected Blocks” on page 5-17.
You can control whether the Simscape Results Explorer window is reused when you
rerun the simulation, or a new window is opened after the next simulation run, by
linking and unlinking the window.
When you first open the Simscape Results Explorer window, it is linked to the current
MATLAB session. This means that when you run a new simulation, the results in the
window will be overwritten. To retain the current results and open a new window after
the next simulation, click the
button located in the toolbar above the left pane. The
button appearance changes to
and, when the new window opens after simulation,
that window will be linked to the session. Only one window can be linked to the session,
so if you have multiple windows open, linking one of them (by clicking on its
unlinks the previous one.
button)
Related Examples
•
“Log, Navigate, and Plot Simulation Data” on page 5-22
•
“Log and View Simulation Data for Selected Blocks” on page 5-17
5-27
5
Data Logging
View Sparkline Plots of Simulation Data
This example shows the basic workflow for viewing sparkline plots of logged simulation
data for selected blocks and variables directly on the model canvas. Before viewing
sparkline plots, you must enable data logging for the whole model, or at least for those
blocks where you want to display the data, and run the simulation.
5-28
1
Open the Permanent Magnet DC Motor example model by typing ssc_dcmotor in
the MATLAB Command Window.
2
To enable data logging, open the Configuration Parameters dialog box, in the left
pane, select Simscape, then set the Log simulation data parameter to All.
3
Simulate the model.
4
To enable display of the sparkline plots on the model canvas, in the model window,
from the top menu bar, select Display > Simscape > Toggle Sparklines When
Clicked. This action adds the check mark next to the Toggle Sparklines When
View Sparkline Plots of Simulation Data
Clicked menu option, and you can start selecting blocks to display sparkline plots of
logged data for their variables. Repeatedly selecting a block toggles the display of its
sparkline plots on and off.
5
Select the Ideal Rotational Motion Sensor block. Sparkline plots of the first three
variables available for this block are displayed on the canvas, and the field below the
plots shows that 4 more variables are available.
6
To customize which plots are shown on the canvas, click the little wrench symbol in
the field below the plots.
5-29
5
Data Logging
This action displays a list of all the block variables available, with check marks next
to the one currently plotted.
5-30
View Sparkline Plots of Simulation Data
7
Clear all the check marks and select the last variable w instead. Then click anywhere
on the model canvas to close the variable selection box.
As you hover over the field with the variable name on the canvas, it expands into a
sparkline plot of logged simulation data for that variable.
5-31
5
Data Logging
The plot display includes the minimum and maximum values, as well as time and
value for the current cursor position.
8
5-32
As you move your cursor past the right edge of the plot, the current value is replaced
with the last value of the variable. Clicking or hovering over the arrow to the right
of the sparkline plot opens an additional field underneath, which contains a link
to the Simscape Results Explorer. When you click the icon, the Simscape Results
Explorer window opens, displaying the corresponding plot in the right pane, with the
appropriate node selected in the left pane.
View Sparkline Plots of Simulation Data
Tips
5-33
5
Data Logging
• If you select a block for which simulation data is not being logged, it displays No
variables instead of the sparkline plots. Right-click the block, select Simscape >
Log simulation data, and rerun the simulation.
• To clear all plots and start again with a clean canvas, select Display > Simscape >
Remove All Sparklines. Then you can select more blocks and variables to display
their sparkline plots.
• Repeatedly selecting the Toggle Sparklines When Clicked menu option toggles the
ability to view the sparkline plots for the model on or off, as indicated by the check
mark. When the check mark is on, repeatedly selecting a block toggles the display of
its sparkline plots on and off.
Related Examples
•
“Log, Navigate, and Plot Simulation Data” on page 5-22
•
“Log and View Simulation Data for Selected Blocks” on page 5-17
More About
5-34
•
“About Simulation Data Logging” on page 5-2
•
“About the Simscape Results Explorer” on page 5-27
6
Model Statistics
• “Simscape Model Statistics” on page 6-2
• “1-D Physical System Statistics” on page 6-4
• “3-D Multibody System Statistics” on page 6-7
• “1-D/3-D Interface Statistics” on page 6-10
• “View Model Statistics” on page 6-11
• “Access Block Variables Using Statistics Viewer” on page 6-16
6
Model Statistics
Simscape Model Statistics
Viewing Simscape model statistics is a good way to evaluate the model prior to
simulation. Model statistics provide feedback on the model complexity, so that you can
make informed choices about whether you want to simulate the model in its current
configuration or make changes to it. This approach helps you achieve the desired
simulation performance and goals.
Unlike other derived data (such as data logging or simulation statistics), which is
generated during simulation, model statistics is compile-time data that is generated
before the model is simulated. When you generate model statistics, the model must
be in a compilable state, that is, it must satisfy the requirements described in “Model
Validation”.
Use model statistics as part of the iterative model building process. For example, after
you make a change to the model, you can view model statistics to answer the following
questions:
• Did the change increase the number of variables?
• Does the model have redundant constraints or have I resolved them?
• How many potential zero-crossing signals does the model have?
• Is the circuit high-index, and therefore hard to solve? Did my change have any effect
on the index?
The Statistics Viewer analysis tool is available for models containing Simscape blocks
and blocks from add-on products. Depending on the types of blocks in the model, the
analysis can produce any or all of the following statistics categories:
• 1-D Physical System — This node represents aggregate statistics generated from
all physical networks that are associated with blocks from Simscape, SimDriveline™,
SimHydraulics, SimElectronics®, and SimPowerSystems™ Simscape Components
libraries.
• 3-D Multibody System — This node represents aggregate statistics generated from
all physical networks that are associated with blocks from SimMechanics™ Second
Generation library.
• 1-D/3-D Interface — This node lists the connections between the two types of
physical networks. It appears only for models that connect blocks from SimMechanics
Second Generation library to Simscape blocks, or blocks from other add-on products.
6-2
Simscape Model Statistics
Each statistic is generated separately from each topologically distinct physical network of
these blocks and then aggregated to appear as a single statistic in the Statistics Viewer.
The Sources section of the Statistics Viewer window lists variable sources for the
selected statistic:
• If you select a connection under the 1-D/3-D Interface statistic category, the
Sources section lists the source and destination for this connection, with links to
relevant blocks.
• If you select a statistic with a nonzero value under the 1-D Physical System
category, the Sources section lists all the variables that fall under this statistic.
For each variable, the Source column contains the full path to the variable, starting
from the top-level model, with a link to the relevant block. If you click the link in the
Source column, the corresponding block is highlighted in the block diagram. The
Value column contains the name of the variable, as it would appear in the Variables
tab of the block dialog box.
Related Examples
•
“View Model Statistics” on page 6-11
•
“Access Block Variables Using Statistics Viewer” on page 6-16
More About
•
“1-D Physical System Statistics” on page 6-4
•
“3-D Multibody System Statistics” on page 6-7
•
“1-D/3-D Interface Statistics” on page 6-10
6-3
6
Model Statistics
1-D Physical System Statistics
This node represents aggregate statistics generated from all physical networks that are
associated with blocks from Simscape, SimDriveline, SimHydraulics, SimElectronics, and
SimPowerSystems Simscape Components libraries.
Each statistic is generated separately from each topologically distinct physical network of
these blocks and then aggregated to appear as a single statistic.
The individual statistics are:
• Number of variables — This statistic represents the number of variables associated
with all 1-D physical systems in the model. Variables are categorized further as
continuous, eliminated, and discrete variables.
• Number of continuous variables (retained) — This statistic represents the
number of continuous variables associated with all 1-D physical systems in the model.
Continuous variables are those variables whose values vary continuously with time,
although some continuous variables can change values discontinuously after events.
Continuous variables are categorized further as algebraic and differential variables.
This statistic represents the number of continuous variables in the system after
variable elimination. If a system is truly input-output with no dynamics, it is possible
to completely eliminate all variables and, in that case, the number of variables is zero.
• Number of differential variables — This statistic represents the number
of differential variables associated with all 1-D physical systems in the model.
Differential variables are continuous variables whose time derivative appears in
one or more system equations. These variables add dynamics to the system and
require the solver to use numerical integration to compute their values.
This statistic represents the number of differential variables in the model after
variable elimination.
• Number of algebraic variables — This statistic represents the number
of algebraic variables associated with all 1-D physical systems in the model.
Algebraic variables are continuous system variables whose time derivative
does not appear in any system equations. These variables appear in algebraic
equations but add no dynamics, and this typically occurs in physical systems due
to conservation laws, such as conservation of mass and energy.
This statistic represents the number of algebraic variables in the model after
variable elimination.
6-4
1-D Physical System Statistics
• Number of continuous variables (eliminated) — This statistic represents the
number of eliminated variables associated with all 1-D physical systems in the model.
Eliminated variables are continuous variables that are eliminated by the software
and are not used in solving the system. Eliminated variables are categorized further
as algebraic and differential variables.
• Number of differential variables — This statistic represents the number of
eliminated differential variables associated with all 1-D physical systems in the
model. Differential variables are continuous variables whose time derivative
appears in one or more system equations. These variables add dynamics to the
system and require the solver to use numerical integration to compute their
values.
This statistic represents the number of differential variables in the model that
have been eliminated.
• Number of algebraic variables — This statistic represents the number of
eliminated algebraic variables associated with all 1-D physical systems in the
model. Algebraic variables are continuous system variables whose time derivative
does not appear in any system equations. These variables appear in algebraic
equations but add no dynamics, and this typically occurs in physical systems due
to conservation laws, such as conservation of mass and energy.
This statistic represents the number of algebraic variables in the model that have
been eliminated.
• Number of discrete variables — This statistic represents the number of discrete,
or event, variables associated with all 1-D physical systems in the model. Discrete
variables are those variables whose values can change only at specific events. Discrete
variables are categorized further as integer-valued and real-valued discrete variables.
• Number of integer-valued variables — This statistic represents the number of
integer-valued discrete variables associated with all 1-D physical systems in the
model. Integer-valued discrete variables are system variables that take on integer
values only and can change their values only at specific events, such as sample
time hits. These variables are typically generated from blocks that are sampled
and run at specified sample times.
• Number of real-valued variables — This statistic represents the number of
real-valued discrete variables associated with all 1-D physical systems in the
model. Real-valued discrete variables are system variables that take on real values
and can change their values only at specific events.
6-5
6
Model Statistics
If you select a local solver in the Solver Configuration block, then all continuous
variables associated with that system are discretized and represented as realvalued discrete variables.
• Number of zero-crossing signals — This statistic represents the number of scalar
signals that are monitored by the Simulink zero-crossing detection algorithm. Zerocrossing signals are scalar functions of states, inputs, and time whose crossing zero
indicates discontinuity in the system. These signals are typically generated from
operators and functions that contain discontinuities, such as comparison operators,
abs, sqrt functions, and so on. Times when these signals cross zero are reported
as zero-crossing events. During simulation it is possible for none of these signals to
produce a zero-crossing event or for one or more of these signals to have multiple zerocrossing events.
• Number of dynamic variable constraints — This statistic represents the number
of constraints involving only dynamic variables and inputs. Such constraints result in
high-index differential algebraic equations (DAEs) and therefore can cause numerical
difficulties or slow down your simulation.
If you select a statistic with a nonzero value, the Sources section lists all the variables
that fall under this statistic. For each variable:
• The Source column contains the full path to the variable, starting from the top-level
model, with a link to the relevant block. If you click the link in the Source column,
the corresponding block is highlighted in the block diagram.
• The Value column contains the name of the variable, as it would appear in the
Variables tab of the block dialog box.
Related Examples
6-6
•
“View Model Statistics” on page 6-11
•
“Access Block Variables Using Statistics Viewer” on page 6-16
3-D Multibody System Statistics
3-D Multibody System Statistics
This node represents aggregate statistics generated from all physical networks that are
associated with blocks from SimMechanics Second Generation library.
Each statistic is generated separately from each topologically distinct physical network of
these blocks and then aggregated to appear as a single statistic.
The individual statistics are:
• Number of rigidly connected components (excluding ground) — This statistic
provides the number of rigid components present in a mechanical system. Rigid
components are subsets of rigidly connected blocks that represent rigid bodies or rigid
frame networks in a model. These subsets generally include blocks from the Body
Elements library as well as Rigid Transform blocks.
Rigid connections within a rigid component can include Rigid Transform blocks but
not Weld Joint blocks. Rigid Transform blocks provide rigid connections between
blocks in the same rigid component. Weld Joint blocks, like all joint blocks, provide
connections between blocks in different rigid components.
This statistic excludes from the count any rigid component that rigidly connects to the
World Frame block.
• Number of joints (total) — This statistic provides the total number of joints
present in a mechanical system. This number equals the sum of three types of joints:
explicit tree, cut, and implicit 6-DOF joints. For more information, see the statistic
descriptions for these joints.
The kinematic graph provides a practical means to understand the topology of
a model. This graph is a connected, undirected diagram in which each vertex
corresponds to a rigid component and each edge corresponds to a joint. The total
number of joints equals the total number of edges present in this graph.
The kinematic tree is a spanning tree of the kinematic graph in which each closed
loop is opened by cutting one of its edges. If the kinematic graph contains no closed
loops, it is identical to the kinematic tree.
• Number of explicit tree joints — This statistic provides the number of joints in the
kinematic tree of a mechanical system that correspond to explicit joint blocks. Each
tree joint corresponds to an edge in the kinematic tree. The number of explicit tree
joints excludes joints cut from the kinematic graph to generate the kinematic tree.
6-7
6
Model Statistics
For more information about kinematic graphs and trees, see the statistic description
for Number of joints (total).
• Number of implicit 6-DOF tree joints — This statistic provides the number of 6DOF joints in the kinematic tree of a mechanical system that do not correspond to
explicit joint blocks. SimMechanics adds implicit 6-DOF joints when the kinematic
graph of a model is not fully connected. These implicit joints connect previously
disconnected portions of the graph to the ground body, adding the edges required to
fully connect the graph. Implicit joints are always tree joints and do not create loops.
For more information about kinematic graphs and trees, see the statistic description
for Number of joints (total).
• Number of cut joints — This statistic provides the number of joints that are
cut from the kinematic graph of a mechanical system to generate the associated
kinematic tree. The number of cut joints equals the number of closed loops present in
the kinematic graph.
For more information about kinematic graphs and trees, see the statistic description
for Number of joints (total).
• Number of constraints — This statistic provides the total number of constraint
blocks in a mechanical system.
• Number of tree degrees of freedom — This statistic provides the total number of
degrees of freedom in the kinematic tree of a mechanical system. This number equals
the sum of all degrees of freedom that the tree joints provide. It excludes degrees of
freedom associated with cut joints.
For more information about kinematic graphs and trees, see the statistic description
for Number of joints (total).
• Number of position constraint equations (total) — This statistic provides the
number of scalar equations that impose position constraints on a mechanical system.
Constraint equations arise from two types of blocks: Constraints and Joints. Joint
blocks contribute constraint equations only if the joints are cut in the kinematic tree.
The number of position constraint equations that a cut joint contributes equals six
minus the number of degrees of freedom that joint provides.
For more information about kinematic graphs and trees, see the statistic description
for Number of joints (total).
• Number of position constraint equations (non-redundant) — This statistic
provides the number of unique position constraint equations associated with a model.
6-8
3-D Multibody System Statistics
This number is smaller than or equal to the total number of position constraint
equations. The difference between the two is the number of redundant position
constraint equations, which are satisfied whenever the unique position constraint
equations are satisfied. SimMechanics attempts to remove redundant equations to
improve simulation performance.
• Number of mechanism degrees of freedom (minimum) — This statistic provides
a lower bound on the number of degrees of freedom in a mechanical system. It equals
the difference between the number of tree degrees of freedom and the number of nonredundant position constraint equations. The actual number of degrees of freedom can
exceed this lower bound if SimMechanics fails to detect a position constraint equation.
Some position constraint equations become redundant only in certain configurations.
If an equation becomes redundant during simulation, the actual number of degrees of
freedom in a model can change. However, that number must still equal or exceed the
lower bound that this statistic provides.
• State vector size — This statistic provides the number of scalar values in the state
vector of a mechanical system.
• Average kinematic loop length — This statistic provides the average number
of edges—or, equivalently, vertices—in the closed loops of a kinematic graph. The
average number is taken over all loops in the graph. If the graph has no kinematic
loops, this number equals zero.
For more information about kinematic graphs and trees, see the statistic description
for Number of joints (total).
6-9
6
Model Statistics
1-D/3-D Interface Statistics
This node lists statistics related to the interface between all 1-D physical and 3-D
multibody systems present in the model. It appears only for models that connect blocks
from SimMechanics Second Generation library to blocks from Simscape, SimDriveline,
SimHydraulics, SimElectronics, and SimPowerSystems Simscape Components libraries.
All connections are listed individually as Connection 1, Connection 2, and so on. If
you select an individual connection, the Sources section lists the source and destination
ports for this connection:
• The Source column contains the full path to the interface port, starting from the
top-level model, with a link to the relevant block. If you click the link in the Source
column, the corresponding block is highlighted in the block diagram.
• The Value column specifies whether the port is the source or destination.
If you expand a connection node, the Statistics Viewer provides the filtering information:
whether a filter is used, and, if yes, the filter order and time constant.
6-10
View Model Statistics
View Model Statistics
This example shows how you can use model statistics to determine the effect of a change
on model complexity.
1
Open the Simple Mechanical System example model.
2
To view model statistics, in the top menu bar of the model window, select Analysis >
Simscape > Statistics Viewer.
The Simscape Statistics window opens, displaying the name of the model and an
overview of the models statistics in a collapsed state.
3
Click
to expand all nodes.
6-11
6
Model Statistics
You can see that, after variable elimination, the model contains seven continuous
differential variables, no algebraic variables, no discrete variables, and no zerocrossing signals.
4
6-12
Replace the Translational Damper block D in the model diagram with a
Translational Friction block, as shown in the following figure.
View Model Statistics
5
Select Analysis > Simscape > Statistics Viewer to refresh the model statistics.
6-13
6
Model Statistics
The revised model contains six algebraic variables, seven differential variables,
and three zero-crossing signals. This happened because you replaced a linear block
(Translational Damper) with a nonlinear one (Translational Friction). Therefore
the linear optimization that the solver initially performed on the model no longer
applies.
6-14
View Model Statistics
Related Examples
•
“Access Block Variables Using Statistics Viewer” on page 6-16
More About
•
“1-D Physical System Statistics” on page 6-4
6-15
6
Model Statistics
Access Block Variables Using Statistics Viewer
This example shows how you can use the Sources section of the Statistics Viewer to
access a block variable of interest, to verify (or change) its initialization priority and
target value.
1
Open the Permanent Magnet DC Motor example model.
2
To view model statistics, in the top menu bar of the model window, select Analysis >
Simscape > Statistics Viewer.
The Simscape Statistics window opens, displaying the name of the model and an
overview of the models statistics in a collapsed state.
3
6-16
Expand the Number of variables node, then Number of continuous variables
(retained), and then click Number of differential variables.
Access Block Variables Using Statistics Viewer
You can see that, after variable elimination, the model contains three continuous
differential variables, and the Sources section of the Statistics Viewer lists these
three variables. For each variable:
• The Source column contains the full path to the variable, starting from the toplevel model, with a link to the relevant block.
• The Value column contains the name of the variable, as it would appear in the
Variables tab of the block dialog box.
4
Click the first link in the Source column. The full path indicates that the source
variable i_L belongs to block L (Inductor) in the DC Motor subsystem of the toplevel example model, therefore the DC Motor subsystem opens and the corresponding
block is highlighted in the block diagram, as shown in the following figure.
6-17
6
Model Statistics
6-18
5
Double-click the highlighted block.
6
In the block dialog box, click the Variables tab.
Access Block Variables Using Statistics Viewer
According to the Value column in the Statistics Viewer, the name of the variable in
the block dialog box is Inductor current. The dialog box shows that this variable
has high initialization priority and a target value of 0 A. You can modify the
priority and value, if needed, and then open the Variable Viewer to see the model
initialization results.
Related Examples
•
“Set Priority and Initial Target for Block Variables”
More About
•
“1-D Physical System Statistics” on page 6-4
•
“About Variable Initialization”
•
“Variable Viewer”
6-19
7
Physical Units
• “How to Work with Physical Units” on page 7-2
• “Unit Definitions” on page 7-4
• “How to Specify Units in Block Dialogs” on page 7-9
• “Thermal Unit Conversions” on page 7-11
• “Angular Units” on page 7-15
• “Units for Angular Velocity and Frequency” on page 7-16
7
Physical Units
How to Work with Physical Units
Unlike Simulink signals, which are essentially unitless, physical signals can have units
associated with them. You specify the units along with the parameter values in the block
dialogs, and Simscape unit manager performs the necessary unit conversion operations
when solving a physical network. Simscape blocks support standard measurement
systems. The default block units are meter-kilogram-second or MKS (SI).
Simscape software comes with a library of standard units, and you can define additional
units as needed (see “Unit Definitions” on page 7-4). You can use these units in your
block diagrams:
• To specify the units of an input physical signal, type a unit name, or a mathematical
expression with unit names, in the Input signal unit field of the Simulink-PS
Converter block dialog. You can also select a unit from a drop-down list, which is
prepopulated with some common input units. Signal units that you specify in a
Simulink-PS Converter block must match the input type expected by the Simscape
block connected to it. For example, when you provide the input signal for an Ideal
Angular Velocity Source block, specify angular velocity units, such as rad/s or
rpm, in the Simulink-PS Converter block, or leave it unitless. If you leave the block
unitless, with the Input signal unit parameter set to 1, then the physical signal
units are inferred from the destination block.
• Simscape block dialogs have drop-down combo boxes of units next to a parameter
value, letting you either select a unit from the drop-down list, or type a unit name
(or a mathematical expression with unit names) directly into the box. These dropdown lists are automatically populated by those units that are commensurate with
the unit of the parameter, based on the current list of unit definitions. For example,
if a parameter is specified, by default, with the units of meters per second, m/s, the
drop-down list of units contains commensurate units, such as mm/s, in/s, fps (feet
per second), fpm (feet per minute), and so on, including any other linear velocity units
currently defined in your unit registry.
• To specify the units of an output physical signal, type a unit name, or a mathematical
expression with unit names, in the Output signal unit field of the PS-Simulink
Converter block dialog. You can also select a unit from a drop-down list, which is
prepopulated with some common output units. The system compares the units you
specified with the actual units of the input physical signal coming into the converter
block and applies a gain equal to the conversion factor before outputting the Simulink
signal. The default value is 1, which means that the unit is not specified. If you do not
specify a unit, or if the unit matches the actual units of the input physical signal, no
gain is applied.
7-2
How to Work with Physical Units
For more information, see “How to Specify Units in Block Dialogs” on page 7-9.
Note Currently, the blocks in the Physical Signals library (such as PS Add, PS Gain, and
so on) ignore the physical unit of the input signal and just perform calculations on the
value. The output signals of the Physical Signals library blocks are unitless.
7-3
7
Physical Units
Unit Definitions
Simscape unit names are defined in the pm_units.m file, which is shipped with the
product. You can open this file to see how the physical units are defined in the product,
and also as an example when adding your own units. This file is located in the directory
matlabroot\toolbox\physmod\common\units\mli\m.
Default registered units and their abbreviations are listed in the following table. Use the
pm_getunits command to get an up-to-date list of units currently defined in your unit
registry. Use the pm_adddimension and pm_addunit commands to define additional
units.
Physical Unit Abbreviations Defined by Default in the Simscape Unit Registry
7-4
Quantity
Abbreviation
Unit
Acceleration
gee
Earth gravitational
acceleration (9.80665 m/s^2)
Amount of substance
mol
Mole
Angle
rad
Radian
deg
Degree
rev
Revolution
Angular velocity
rpm
Revolutions/minute
Capacitance
F
Farad
pF
Picofarad
nF
Nanofarad
uF
Microfarad
Charge
c
Coulomb
Conductance
S
Siemens
nS
Nanosiemens
uS
Microsiemens
mS
Millisiemens
Unit Definitions
Quantity
Abbreviation
Unit
Current
A
Ampere
pA
Picoampere
nA
Nanoampere
uA
Microampere
mA
Milliampere
kA
Kiloampere
J
Joule
Btu
British thermal unit
eV
Electronvolt
lpm
Liter/minute
gpm
Gallon/minute
N
Newton
dyn
Dyne
lbf
Pound-force
mN
Millinewton
Hz
Hertz
kHz
Kilohertz
MHz
Megahertz
GHz
Gigahertz
H
Henry
uH
Microhenry
mH
Millihenry
Energy
Flow rate
Force
Frequency
Inductance
7-5
7
Physical Units
Quantity
Abbreviation
Unit
Length
m
Meter
cm
Centimeter
mm
Millimeter
km
Kilometer
um
Micrometer
in
Inch
ft
Foot
mi
Mile
yd
Yard
Magnetic flux
Wb
Weber
Magnetic flux density
T
Tesla
G
Gauss
kg
Kilogram
g
Gram
mg
Milligram
lbm
Pound mass
oz
Ounce
slug
Slug
Pa
Pascal
kPa
Kilopascal
MPa
Megapascal
GPa
Gigapascal
Mass
Pressure
7-6
Unit Definitions
Quantity
Power
Resistance
Temperature
Time
Abbreviation
bar
Unit
Bar
kbar
Kilobar
atm
Atmosphere
psi
Pound/inch^2
W
Watt
uW
Microwatt
mW
Milliwatt
kW
Kilowatt
MW
Megawatt
HP
Horsepower
Ohm
Ohm
kOhm
Kiloohm
MOhm
Megaohm
GOhm
Gigaohm
K
Kelvin
C
Celsius
Fh
Fahrenheit
R
Rankine
s
Second
min
Minute
hr
Hour
ms
Millisecond
7-7
7
Physical Units
Quantity
Velocity
Viscosity absolute
Viscosity kinematic
Volume
Voltage
Abbreviation
us
Unit
Microsecond
ns
Nanosecond
mph
Miles/hour
fpm
Feet/minute
fps
Feet/second
Poise
Poise
cP
Centipoise
reyn
Reyn
St
Stokes
cSt
Centistokes
Newt
Newt
l
Liter
gal
US liquid gallon
igal
Imperial (UK) gallon
V
Volt
mV
Millivolt
kV
Kilovolt
Note This table lists the unit abbreviations defined in the product. For information
on how to use the abbreviations above, or mathematical expressions with these
abbreviations, to specify units for the parameter values in the block dialogs, see “How to
Specify Units in Block Dialogs” on page 7-9.
7-8
How to Specify Units in Block Dialogs
How to Specify Units in Block Dialogs
Simscape block dialogs have drop-down combo boxes for units next to a parameter value.
For example, in the Constant Volume Chamber block dialog box, the drop-down list for
the Chamber volume parameter contains l, gal, in^3, ft^3, mm^3, cm^3, m^3, and
km^3, and the drop-down list for the Initial pressure parameter contains Pa, bar, psi,
and atm.
You can either select a unit from the drop-down list, or type a commensurate unit name
(or a mathematical expression with unit names) directly into the unit combo box of the
block dialog. You can use the abbreviations for the units defined in your registry, or
any valid mathematical expressions with these abbreviations. For example, you can
specify torque in newton-meters (N*m) or pound-feet (lbf*ft). To specify velocity, you
can use one of the defined unit abbreviations (mph, fpm, fps), or an expression based on
any combination of the defined units of length and time, such as meters/second (m/s),
millimeters/second (mm/s), inches/minute (in/min), and so on.
Note Affine units (such as Celsius or Fahrenheit) are not allowed in unit expressions. For
more information, see “About Affine Units” on page 7-11.
The following operators are supported in the unit mathematical expressions:
*
Multiplication
/
Division
^
Power
+
Plus — for exponents only
-
Minus — for exponents only
()
Brackets to specify evaluation order
Metric unit prefixes, such as kilo, milli, or micro, are not supported. For example, if you
want to use milliliter as a unit of volume, you have to add it to the unit registry:
pm_addunit('ml', 0.001, 'l');
The drop-down lists next to parameter names are automatically populated by those
units that are commensurate with the unit of the parameter. If you specify the units by
typing, it is your responsibility to enter units that are commensurate with the unit of the
7-9
7
Physical Units
parameter. The unit manager performs error checking when you click Apply or OK in
the block dialog box, and issues an error if you type an incorrect unit.
In the Simulink-PS Converter and the PS-Simulink Converter block dialog boxes, the
drop-down lists are prepopulated with some common input and output units, and it is
your responsibility to select or type a unit expression commensurate with the expected
input or output units. The error checking for the converter blocks is performed at the
time of simulation. See “Model Validation” for details.
7-10
Thermal Unit Conversions
Thermal Unit Conversions
In this section...
“About Affine Units” on page 7-11
“When to Apply Affine Conversion” on page 7-11
“How to Apply Affine Conversion” on page 7-12
About Affine Units
Thermal units often require an affine conversion, that is, a conversion that performs both
multiplication and addition. To convert from the old value Told to the new value Tnew, we
need a linear conversion coefficient L and an offset O:
Tnew = L * Told + O
For example, to convert a temperature reading from degrees Celsius into degrees
Fahrenheit, the linear term equals 9/5, and the offset equals 32:
TFahr = 9 / 5 * TCels + 32
Simscape unit manager defines kelvin (K) as the fundamental temperature unit. This
makes Celsius (C) and Fahrenheit (Fh) affine units because they are both related to
kelvin with an affine conversion. Rankine (R) is defined in terms of kelvin with a zero
linear offset and, therefore, is not an affine unit.
The following are the default Simscape unit registry definitions for temperature units:
pm_adddimension('temperature', 'K'); % defines kelvin as fundamental temperature unit
pm_addunit('C', [1 273.15], 'K');
% defines Celsius in terms of kelvin
pm_addunit('Fh', [5/9 -32*5/9], 'C'); % defines Fahrenheit in terms of Celsius
pm_addunit('R', [5/9 0], 'K');
% defines rankine in terms of kelvin
When to Apply Affine Conversion
In dealing with affine units, sometimes you need to convert them using just the linear
term. Usually, this happens when the value you convert represents relative, rather than
absolute, temperature, ΔT = T1 – T2.
ΔTnew = L * ΔTold
In this case, adding the affine offset would yield incorrect conversion results.
7-11
7
Physical Units
For example, the outdoor temperature rose by 18 degrees Fahrenheit, and you need
to input this value into your model. When converting this value into kelvin, use linear
conversion
ΔTkelvin = 5 / 9 * ΔTFahr
and you get 10 K, that is, the outdoor temperature changed by 10 kelvin. If you apply
affine conversion, you will get a temperature change of approximately 265 kelvin, which
is incorrect.
This is even better illustrated if you use degrees Celsius for the input units because the
linear term for conversion between Celsius and kelvin is 1:
• If the outdoor temperature changed by 10 degrees Celsius (relative temperature
value), then it changed by 10 kelvin (do not apply affine conversion).
• If the outdoor temperature is 10 degrees Celsius (absolute temperature value), then it
is 283 kelvin (apply affine conversion).
How to Apply Affine Conversion
When you specify affine units for an input temperature signal, it is important to consider
whether you need to apply affine conversion. Usually this decision depends on whether
the signal represents absolute or relative temperature (see “When to Apply Affine
Conversion” on page 7-11).
For example, you model a house-heating system, and you need to input the outdoor
temperature. In the following diagram, the Constant source block represents the average
outdoor temperature, in degrees Celsius, and the Sine source block adds the daily
temperature variation. The average outdoor temperature, in this case, is 12 degrees
Celsius. Daily variation with an amplitude of 8 makes the input outdoor temperature
vary between 4 and 20 degrees Celsius.
7-12
Thermal Unit Conversions
This signal is an absolute temperature reading. Therefore, when the signal converts into
kelvin for further computations, you need to specify that it should use affine conversion.
Double-click the Simulink-PS Converter block, type C in the Input signal unit field, and
select the Apply affine conversion check box.
7-13
7
Physical Units
As a result, the Simulink-PS Converter block outputs a value varying between 277 K and
293 K.
7-14
Angular Units
Angular Units
Simscape implementation of angular units relies on the concept of angular units,
specifically radians, being a unit but dimensionless. The notion of angular units being
dimensionless is widely held in the metrology community. The fundamental angular unit,
radian, is defined in the Simscape unit registry as:
pm_addunit('rad', 1, 'm/m');
which corresponds to the SI and NIST definition [1]. In other words, Simscape unit
manager does not introduce a separate dimension, 'angle', with a fundamental unit
of 'rad' (similar to dimensions for length or mass), but rather defines the fundamental
angular unit in terms of meter over meter or, in effect, 1.
The additional angular units, degree and revolution, are defined respectively as:
pm_addunit('deg', pi/180, 'rad');
pm_addunit('rev', 2*pi, 'rad');
As a result, forward trigonometric functions, such as sin, cos, and tan, work directly
with arguments expressed in angular units. For example, cosinus of 90 degrees equals
the cosinus of (pi/2) radians and equals the cosinus of (pi/2). Expansion of forward
trigonometric functions works in a similar manner.
Another effect of dimensionless implementation of angular units is the convenience of
the work-energy conversion. For example, torque (in N*m) multiplied by angle (in rad)
can be added directly to energy (in J, or N*m). If you specify other commensurate units
for the components of this equation, Simscape unit manager performs the necessary unit
conversion operations and the result is the same.
References
[1] The NIST Reference on Constants, Units, and Uncertainty, http://
physics.nist.gov/cuu/Units/units.html
7-15
7
Physical Units
Units for Angular Velocity and Frequency
Angular velocity units, such as rad/s, deg/s, and rpm, can also be used to measure
frequency for cyclical processes. This is consistent with frequency defined as revolutions
per second in a mechanical context, or cycles per second in an electrical context, and lets
you write frequency-dependent equations without requiring the 2*pi conversion factor.
In the SI unit system, however, the unit of frequency is hertz (Hz), defined as 1/s.
Simscape software defines the unit hertz (Hz) as 1/s, in compliance with the SI unit
system. This definition works well when frequency refers to a nonrotational periodic
signal such as the frequency of a PWM source. For cyclical processes, however, the block
equations have to contain the 2*pi conversion factor, to convert the numerical value
specified in Hz, or s-1, to angular frequency.
As a result, frequency units (based on Hz) and angular velocity units (based on rpm) are
not directly convertible, and using one instead of the other may result in unexpected
conversion factors applied to the numerical values by the block equations. For example,
the AC Voltage Source block explicitly multiplies the value you specify for its Frequency
parameter by 2*pi, to convert it to angular frequency before calculating the sine
function.
Drop-down lists of suggested units in block dialogs reflect this distinction. For example,
if a block has a Frequency parameter with the default unit of Hz, the drop-down list
for this parameter contains only units directly convertible to Hz (such as kHz, MHz, and
GHz) and does not contain the angular velocity units. Conversely, if you define a custom
block where the Frequency parameter has the default unit of rpm, its drop-down list of
suggested units will include deg/s and rad/s, but will not contain Hz, kHz, MHz, or GHz.
When you type a unit expression in the parameter units combo box (instead of selecting
a value from the drop-down list), the Simscape unit manager considers the units of
frequency and angular velocity to be commensurate. For example, when the default
parameter unit is Hz, you are able to type not only 1/s, but also expressions such as
deg/s and rad/s. This behavior is consistent with the Simscape implementation of
angular units (see “Angular Units” on page 7-15). It is your responsibility to verify that
the unit expression you typed works correctly with the block equations and reflects your
design intent.
Note: Prior to Release R2013a, the unit definition for Hz was rev/s. For information on
how to update legacy models and custom Simscape libraries written in R2012b or earlier,
7-16
Units for Angular Velocity and Frequency
see Compatibility Considerations under “Unit definition of Hz now consistent with SI”, in
the R2013a Release Notes.
7-17
8
Add-On Product License Management
• “About the Simscape Editing Mode” on page 8-2
• “Working with Restricted and Full Modes” on page 8-9
• “Editing Mode Information” on page 8-24
8
Add-On Product License Management
About the Simscape Editing Mode
In this section...
“Suggested Workflows” on page 8-2
“What You Can Do in Restricted Mode” on page 8-3
“What You Can Do in Full Mode” on page 8-4
“Switching Between Modes” on page 8-4
“Working with Block Libraries” on page 8-7
Suggested Workflows
The Simscape Editing Mode functionality is implemented for customers who perform
physical modeling and simulation using Simscape platform and its add-on products:
SimDriveline, SimElectronics, SimHydraulics, SimMechanics, and SimPowerSystems. It
allows you to open, simulate, and save models that contain blocks from add-on products
in Restricted mode, without checking out add-on product licenses, as long as the products
are installed on your machine. It is intended to provide an economical way to distribute
simulation models throughout a team or organization.
Note Unless your organization uses concurrent licenses, see the Simscape product page
on the MathWorks Web site for specific information on how to install add-on products on
your machine, to be able to work in Restricted mode.
The Editing Mode functionality supports widespread use of Physical Modeling products
throughout an engineering organization by making it economical for one user to develop
a model and provide it to many other users.
Specifically, this feature allows a user, model developer, to build a model that uses
Simscape platform and one or more add-on products and share that model with other
users, model users. When building the model in Full mode, the model developer must
have a Simscape license and the add-on product licenses for all the blocks in the model.
For example, if a model combines Simscape, SimHydraulics, and SimDriveline blocks,
the model developer needs to check out licenses for all three products to work with it in
Full mode. Once the model is built, model users need only to check out a Simscape license
to simulate the model and fine-tune its parameters in Restricted mode. As long as no
8-2
About the Simscape Editing Mode
structural changes are made to the model, model users can work in Restricted mode and
do not need to check out add-on product licenses.
Another workflow, available with concurrent licenses only, lets multiple users, who all
have Simscape licenses, share a small number of add-on product licenses by working
mostly in Restricted mode, and temporarily switching models to Full mode only when
they need to perform a specific design task that requires being in Full mode.
Note MathWorks recommends that you save all the models in Full mode before
upgrading to a new version of Simulink or Simscape software.
If you have saved a model in Restricted mode and, upon upgrading to a new product
version, open the model and it does not run, switch it to Full mode and save. You can
then again switch to Restricted mode and work without problem.
What You Can Do in Restricted Mode
When your model is open in Restricted mode, you can:
• Simulate the model.
• Inspect parameters.
• Change certain block parameters. In general, you can change numerical parameter
values, but cannot change the block parameterization options. See the block reference
pages for specifics.
• Generate code.
• Make data logging or visualization changes.
• Add or delete regular Simulink blocks (such as sources or scopes) and appropriate
connections.
For other types of changes, listed in the following section, your model has to be in Full
mode. Some of these disallowed changes are impossible to make in Restricted mode (for
example, Restricted parameters are grayed out in block dialog boxes). Other changes, like
changing the physical topology of a model, are not explicitly disallowed, but if you make
these changes in Restricted mode, the software will issue an error message when you try
to run, compile, or save such a model.
8-3
8
Add-On Product License Management
What You Can Do in Full Mode
You need to open a model in Full mode if you need to do any of the following:
• Add or delete Physical Modeling blocks (that is, Simscape blocks or blocks from the
add-on product libraries).
• Make or break Physical connections (between Conserving or Physical Signal ports).
• Change the types of signals going into actuators or out of sensors (for example, from
velocity to torque).
• Change configuration parameters.
• Change block parameterization options and other restricted parameters.
• Change physical units of parameters.
• Protect a referenced model containing Physical Modeling blocks (for more information,
see “Protected Model”).
Switching Between Modes
The following flow chart shows what happens when you switch between modes.
8-4
About the Simscape Editing Mode
New models are always created in Full mode. You can then either save the model in Full
mode, or switch to Restricted mode and save the model in Restricted mode.
8-5
8
Add-On Product License Management
When you load an existing model, the license manager checks whether it has been saved
in Full or Restricted mode.
• If the model has been saved in Restricted mode, it opens in Restricted mode.
• If the model has been saved in Full mode, the license manager checks whether all the
add-on product licenses for this model are available and, if so, opens it in Full mode. If
a add-on product license is not available, the license manager issues an error message
and opens the model in Restricted mode. See also “Example with Multiple Add-On
Products” on page 8-6.
Note You can set a Simulink preference to specify that the models are always to open in
Restricted mode, regardless of the way they have been saved.
When a model is open, you can transition it between Full and Restricted modes at any
time, in either direction:
• When you try to switch from Restricted to Full mode, the license manager checks
whether all the add-on product licenses for this model are available. If a add-on
product license is not available, the license manager issues an error message and the
model stays in Restricted mode. See also “Example with Multiple Add-On Products”
on page 8-6.
• No checks are performed when switching from Full to Restricted mode.
Note If a add-on product license has been checked out to open a model in Full mode, it
remains checked out for the remainder of the MATLAB session. Switching to Restricted
mode does not immediately return the license.
Example with Multiple Add-On Products
When you try to open a model in Full mode or to switch from Restricted to Full mode, the
license manager scans the model and attempts to check out the required add-on product
licenses as it encounters them in the model. If a license is not available, the license
manager issues an error message and the model stays in Restricted mode. The licenses
are checked out sequentially. As a result, if a model uses blocks from multiple add-on
products, some of the add-on product licenses may have already been checked out by the
time the license manager encounters an unavailable license. In this case, these add-on
8-6
About the Simscape Editing Mode
product licenses stay checked out until you quit the MATLAB session, even though the
model is in Restricted mode.
For example, consider a model that uses blocks from SimHydraulics and SimDriveline
libraries, but the user who tries to open it has only the SimDriveline license available.
It may happen that the license manager checks out a SimDriveline license first, and
then tries to check out a SimHydraulics license, which is not available. The license
manager then issues an error message and opens the model in Restricted mode, but the
SimDriveline license stays checked out until the end of the MATLAB session.
Working with Block Libraries
This section describes the specifics of working with block libraries while using the
Editing Mode functionality. These rules are applicable to any physical modeling blocks,
that is, blocks from all Simscape libraries, including the add-on products. In general, you
need to work in Full mode when you modify a library block. However, when you open
a model that references the modified block, you may work in Restricted mode, under
certain conditions. The following summary details the Editing Mode rules for modifying
and using library blocks:
• To add physical modeling blocks to a library block, you need to work in Full mode.
• If this library block had not previously contained physical modeling blocks, you
need to work in Full mode to load a preexisting model that uses this library block
or to drag this block to a model.
• If this library block had previously contained physical modeling blocks, you can
work in Restricted mode when loading a preexisting model that uses this library
block. However, you have to work in Full mode to drag this block from the library
to a model.
• To add external physical ports to a library block, you need to work in Full mode.
• You can work in Restricted mode when loading a preexisting model that uses this
library block.
• However, to connect these additional ports, you need to work in Full mode because
you are changing the model topology.
• To delete external physical ports from a library block, you need to work in Full mode.
If these ports were connected in a model saved in Restricted mode, loading the model
causes the topology to change, so you need to switch to Full mode to save or compile
the model.
8-7
8
Add-On Product License Management
Resolving Block Library Links
All Simscape blocks in your models, including the add-on products' blocks, must have
resolved block library links. You can neither disable nor break these library links. This
is a global requirement of Simscape platform, which is necessary to enforce the Editing
Mode rules for modifying and using library blocks, listed above. A model with broken
library links will neither compile nor save. You must restore all the broken block library
links for your model to be valid.
If you want to customize certain blocks and use them in your models, you must add these
modified blocks to your own custom library, then copy the block instances that you need
to your model.
8-8
Working with Restricted and Full Modes
Working with Restricted and Full Modes
In this section...
“Set the Model Loading Preference” on page 8-9
“Save a Model in Restricted Mode” on page 8-10
“Work with a Model in Restricted Mode” on page 8-13
“Switch from Restricted to Full Mode” on page 8-22
Set the Model Loading Preference
By default, when you load an existing model, the license manager checks whether it has
been saved in Full or Restricted mode and tries to open it in this mode. However, you can
set your preferences so that the models are always open in Restricted mode, regardless of
the way they have been saved.
1
On the MATLAB Toolstrip, click Preferences. The Preferences dialog box opens.
2
In the left pane of the Preferences dialog box, select Simscape. The right pane
displays the Editing Mode group box. By default, the Load models using option is
set to Editing mode specified in models.
3
Select Restricted mode always from the drop-down list, as shown, and click OK.
8-9
8
Add-On Product License Management
Now, when you open a model, the license manager does not attempt to check out add-on
product licenses and always opens the model in Restricted mode.
Save a Model in Restricted Mode
Rather that setting your preferences so that all the models always open in Restricted
mode, you can switch an individual model to Restricted mode before saving it. Such a
model will then, by default, open in Restricted mode.
8-10
1
From the top menu bar in the model window, select Simulation > Model
Configuration Parameters. The Configuration Parameters dialog box opens.
2
In the left pane of the Configuration Parameters dialog box, select Simscape. The
right pane displays the Editing Mode option, which is by default set to Full.
3
Select Restricted from the drop-down list, as shown, and click OK.
Working with Restricted and Full Modes
4
Save the model.
Note The Simscape entry does not appear in the left pane of the Configuration
Parameters dialog box until you add at least one Physical Modeling block to your model.
If you create an additional configuration set for a model, the Simscape entry does not
appear in it until you either activate it or perform a Physical Modeling operation, such as
adding or deleting a Physical Modeling block or connection, opening a Physical Modeling
block dialog box, and so on.
Once you have switched a model to Restricted mode, working with it follows the rules
described in “Work with a Model in Restricted Mode” on page 8-13. Note, however,
that the add-on product licenses for this model stay checked out until you quit the
MATLAB session.
When you open a model that has been saved in Restricted mode, the license manager
opens it in Restricted mode and does not check out the add-on product licenses.
8-11
8
Add-On Product License Management
Example of Saving a Model in Restricted Mode
In this example, you switch a model to Restricted mode and save it.
8-12
1
Open the Simple Mechanical System example model
(ssc_simple_mechanical_system).
2
From the top menu bar in the model window, select Simulation > Model
Configuration Parameters. The Configuration Parameters dialog box opens.
3
In the left pane of the Configuration Parameters dialog box, select Simscape. The
right pane displays the Editing Mode option, which is set to Full by default.
4
Select Restricted from the drop-down list and click OK.
5
Save the model as model_test_edit_mode.
Working with Restricted and Full Modes
Work with a Model in Restricted Mode
When you open a model in Restricted mode, you can perform a variety of tasks: simulate
the model, inspect and fine-tune block parameters, add and delete basic Simulink blocks,
and so on. For a complete list of allowed operations, see “What You Can Do in Restricted
Mode” on page 8-3.
When you open a block dialog box in Restricted mode, some of the block parameters
may be grayed out. These are the so-called restricted parameters that can be modified
only in Full mode. In general, you can change numerical parameter values in Restricted
mode, but you cannot change the block parameterization options. See the block
reference pages for specifics. Note also that when a restricted parameter defines the
block parameterization schema, nonrestricted parameters available for fine-tuning in
Restricted mode depend on the value of this restricted parameter. For example, in a
Constant Volume Chamber block, the Chamber specification parameter is restricted.
If, at the time the model entered Restricted mode, this parameter was set to By volume,
then the nonrestricted parameters available for fine-tuning would be Chamber volume,
Specific heat ratio, and Initial pressure. If, however, it was set to By length and
diameter, you will have a different set of parameters available in Restricted mode.
You cannot change physical units in Restricted mode. When you open a block dialog box
in Restricted mode, the drop-down lists of units next to a parameter name and value are
grayed out. When you open a PS-Simulink Converter or Simulink-PS Converter block
dialog box, the Unit parameter is grayed out.
The following examples illustrate operations allowed and disallowed in Restricted mode:
• “How to Simulate and Fine-Tune a Model in Restricted Mode” on page 8-13
• “How to Add and Delete Simulink Blocks in Restricted Mode” on page 8-17
• “Performing an Operation Disallowed in Restricted Mode” on page 8-20
How to Simulate and Fine-Tune a Model in Restricted Mode
This example shows how you can work with a model in Restricted mode by changing
certain parameter values and observing the simulation results.
1
Open the model_test_edit_mode model, which you saved in Restricted mode in
“Example of Saving a Model in Restricted Mode” on page 8-12. The model opens
in Restricted mode.
8-13
8
Add-On Product License Management
2
8-14
Open the Joint C Position scope and simulate the model. The models runs and
simulates in Restricted mode.
Working with Restricted and Full Modes
3
Double-click the Wheel and Axle block to open its dialog box. Notice that the
Mechanism orientation parameter is grayed out, because you cannot modify the
block driving direction in Restricted mode.
4
Change the Wheel radius parameter value to 0.1.
8-15
8
Add-On Product License Management
8-16
5
Simulate the model again. Notice that the motion amplitude of node C became
smaller as a result of the wheel radius change.
6
Double-click the Mass block and change the Mass parameter value to 24.
7
Simulate the model. Notice that doubling the mass resulted in increased vibrations.
Working with Restricted and Full Modes
How to Add and Delete Simulink Blocks in Restricted Mode
This example shows how you can change the model input signal in Restricted mode by
adding and deleting basic Simulink blocks.
1
Open the model_test_edit_mode model, which you saved in Restricted mode in
“Example of Saving a Model in Restricted Mode” on page 8-12. The model opens
in Restricted mode.
2
Open the Joint C Position scope and simulate the model.
8-17
8
Add-On Product License Management
3
8-18
Delete the Signal Builder block named Force Input. Replace it with a Sine Wave
block from the Simulink Sources library, as shown below.
Working with Restricted and Full Modes
4
Simulate the model again. The model successfully compiles and simulates in
Restricted mode.
8-19
8
Add-On Product License Management
Performing an Operation Disallowed in Restricted Mode
This example shows what happens when you perform an operation that is disallowed in
Restricted mode.
8-20
1
Open the model_test_edit_mode model, which you saved in Restricted mode in
“Example of Saving a Model in Restricted Mode” on page 8-12. The model opens
in Restricted mode.
2
Double-click the MotionSensor2 block to open the subsystem.
Working with Restricted and Full Modes
3
Delete the connection line between port P of the Ideal Translational Motion Sensor
block and the PS-Simulink Converter block. Instead, connect port V of the Ideal
Translational Motion Sensor block to the input port of the PS-Simulink Converter
block, to measure the velocity on node C of the lever.
8-21
8
Add-On Product License Management
4
Try to simulate the model. An error message appears saying that the model cannot
be compiled because its topology has been changed while in Restricted mode. You
can either undo the changes, or switch to Full mode, as described in “Switch from
Restricted to Full Mode” on page 8-22.
Switch from Restricted to Full Mode
If you need to perform a task that is disallowed in Restricted mode, you can try to switch
the model to Full mode.
8-22
1
From the top menu bar in the model window, select Simulation > Model
Configuration Parameters. The Configuration Parameters dialog box opens.
2
In the left pane of the Configuration Parameters dialog box, select Simscape. The
right pane displays the Editing Mode option.
Working with Restricted and Full Modes
3
Select Full from the drop-down list, as shown, and click OK.
The license manager checks whether all the add-on product licenses for this model
are available. If yes, it checks out the add-on product licenses and switches the model
to Full mode. If a add-on product license is not available, the license manager issues
an error message and the model stays in Restricted mode.
Note If the switch to Full mode fails but some of the add-on product licenses have
already been checked out, they stay checked out until you quit the MATLAB session. For
more information, see “Example with Multiple Add-On Products” on page 8-6.
Once the model is switched to Full mode, you can perform the needed design and
simulation tasks, and then either save it in Full mode, or switch back to Restricted mode
and save it in Restricted mode.
8-23
8
Add-On Product License Management
Editing Mode Information
In this section...
“What Is the Current Mode?” on page 8-24
“Which Licenses Are Checked Out?” on page 8-24
What Is the Current Mode?
If you are unsure whether the model is currently open in Restricted or Full mode, you
can check by following these steps.
1
From the top menu bar in the model window, select Simulation > Model
Configuration Parameters. The Configuration Parameters dialog box opens.
2
In the left pane of the Configuration Parameters dialog box, select Simscape. The
right pane displays the Editing Mode option, which is either Full or Restricted.
3
At this point, you can either try switching the mode by selecting a different option
from the drop-down list, or click Cancel to stay in the current mode.
Which Licenses Are Checked Out?
Use the MATLAB license command to get a list of all the licenses currently in use. In
the MATLAB Command Window, type
license('inuse')
This command returns a list of licenses checked out in the current MATLAB session. In
the list, products are listed alphabetically by their license feature names.
8-24
Download PDF