Development and Control of Networked Servo System Srinibas Bhuyan Department of Electrical Engineering

Development and Control of Networked Servo System Srinibas Bhuyan Department of Electrical Engineering
Development and Control of
Networked Servo System
Srinibas Bhuyan
Department of Electrical Engineering
National Institute of Technology,Rourkela
Rourkela-769008, Odisha, INDIA
May 2011
Development and Control of Networked Servo
System
A thesis submitted in partial fulfillment of the
requirements for the degree of
Master of Technology by Research
in
Electrical Engineering
by
Srinibas Bhuyan
(Roll-608EE308)
Under the Guidance of
Prof. Bidyadhar Subudhi and Prof. Sandip Ghosh
Department of Electrical Engineering
National Institute of Technology,Rourkela
Rourkela-769008, Odisha, INDIA
2009-2011
Department of Electrical Engineering
National Institute of Technology, Rourkela
CERTIFICATE
This is to certify that the thesis entitled ”Development and Control of
Networked Servo System” by Mr. Srinibas Bhuyan, submitted to
the National Institute of Technology, Rourkela (Deemed University) for the
award of Master of Technology by Research in Electrical Engineering, is a
record of bonafide research work carried out by him in the Department of
Electrical Engineering , under my supervision. I believe that this thesis fulfills
part of the requirements for the award of degree of Master of Technology by
Research.The results embodied in the thesis have not been submitted for the
award of any other degree elsewhere.
Prof. Bidyadhar Subudhi
Place:Rourkela
Date:
Prof. Sandip Ghosh
To My Loving parents, my brothers Ashish, Piyush, Krish,
my sisters Arpita, Puja, Pranati and friends Bedi, Debasis
Acknowledgements
First and foremost, I am truly indebted to my supervisors Professor
Bidyadhar Subudhi and Professor Sandip Ghosh for their inspiration, excellent guidance and unwavering confidence through my study, without which
this thesis would not be in its present form. I also thank them for their
gracious encouragement throughout the work.
I express my gratitude to the members of Masters Scrutiny Committee,
Professors D. Patra, S. Das, S.S. Mohapatra and D.P. Mohapatra, for their
advise and care. I am also very much obliged to Head of the Department of
Electrical Engineering, NIT Rourkela for providing all the possible facilities
towards this work. Thanks also to other faculty members in the department.
I would like to thank Raju, Basant, Rudra, Dushmanta, Raja, Rakesh,
Abhishek, Satyam, Santanu, Kamalesh, Bikram, Debabrata and research
scholars at Center for Industrial Electronics and Robotics, NIT Rourkela,
for their enjoyable and helpful company I had with.
My wholehearted gratitude to my parents, Minakshi and Sarat Ch. Bhuyan,
my uncle, Mr.B.K Rout for their encouragement and support.
Srinibas Bhuyan
Rourkela, May 2011
v
Abstract
Control systems where the control loops are closed through a communication
network are called Networked Control System (NCS). Research on NCS has
received increased attention in recent years due to the advancement of control,
computation and communication technologies. NCS makes the design and
implementation of control systems with reduced complexity due to simpler
installation and easy maintenance. But the insertion of the communication
network in the feedback control loop introduces delay from sensor to controller
and controller to actuator, that degrades the control system performance and
also causes system instability.
This thesis focuses on development of a networked DC Servo control system using LabVIEW and Peripheral Component Interconnect (PCI) card.
The controller design for a NCS can be categorized into indirect and direct approach. An indirect approach controller design considers first without
delay followed by design a suitable delay compensation technique. A PID
controller with a Smith predictor as a compensater is implemented in realtime networked control of servo system. The above PID controller is tuned
using gain margin and phase margin specifications and Zigler-Nichols method
are implemented. A direct NCS design approach in the other hand considers the delay as well as packet loss characteristics with system dynamics at
one go.This approach gives more information about each instant of the system.It uses Lyapunov approach to design of asymptomatic stabilization of
the system, the above stabilization uses a switched approach for NCS stavi
bilization with packet loss and delay is proposed. The switched approach
divides the NCS as different subsystems considering both delay and packet
loss, then designing of controllers for each subsystem. According to packet
loss, the subsystems and controllers are switched to stabilize the NCS. In
this approach the feedback gains are calculated by solving Linear Matrix
Inequalities (LMIs).
Both direct and indirect controller design approach are simulated using
MATLAB and SIMULINK. Some Hardware in Loop simulations are also
performed on a Servo System. A real-time networked servo control system
has been developed using LabVIEW. Only indirect controller approach is
implemented in this environment to remotely control the servo system. The
results obtained by using PID controller and Smith predictor have been analyzed and it is confirmed that these controller provide good performances.
Contents
Contents
i
List of Figures
vi
List of Tables
ix
1 INTRODUCTION
1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2 Networked Control System and Its Perspectives . . . . . . . . .
3
1.2.1 Description of a Networked Control System . . . . . . . .
3
1.2.2 Networks Used in NCS . . . . . . . . . . . . . . . . . . . .
3
1.2.3 Available NCS Configurations . . . . . . . . . . . . . . . .
4
1.2.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.2.5 Control Issues . . . . . . . . . . . . . . . . . . . . . . . . .
7
1.3 A Survey on NCS design Methodology . . . . . . . . . . . . . .
9
1.4 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.5 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.6 Thesis Organisation . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 SERVO SYSTEM AND ITS MODELING
17
2.1 The System under Study . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Identification of the Servo Model
. . . . . . . . . . . . . . . . . 18
2.3 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 22
i
ii
CONTENTS
3 PID CONTROLLER DESIGN
23
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 PID Controller Design Methodologies
. . . . . . . . . . . . . . 23
3.2.1 Ziegler-Nichols PID Controller Design Methodology . . . . 25
3.2.2 A Robust PID Controller Design Methodology . . . . . . . 26
3.3 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.1 Simulation Using Artificial Delay . . . . . . . . . . . . . . 31
3.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4 SMITH PREDICTOR BASED DELAY COMPENSATION 34
4.1 Smith Predictor Based Compensation
. . . . . . . . . . . . . . 34
4.1.1 TrueTime Based Simulation . . . . . . . . . . . . . . . . . 36
4.2 Study on DC Servo Motor Setup
. . . . . . . . . . . . . . . . . 38
4.2.1 Delay Estimation . . . . . . . . . . . . . . . . . . . . . . . 38
4.2.2 Simulation of DC servo Motor Using Artificial Delay . . . 40
4.3 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5 DEVELOPMENT OF A LABVIEW BASED NCS SETUP
44
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.1.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.2 LabVIEW Based Communication Interfacing . . . . . . . . . . . 45
5.3 NCS Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.3.1 Signal Generation and Acquisition Using LabVIEW . . . . 48
5.3.2 UDP Communication Protocol in LabVIEW . . . . . . . . 50
5.3.3 Description of the Developed NCS Setup . . . . . . . . . . 55
5.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 58
5.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6 DIRECT APPROACH FOR STABILIZATION OF NCS
63
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.2 Concept of Transmission Situation . . . . . . . . . . . . . . . . . 64
iii
CONTENTS
6.3 Modeling According to Transmission Interval . . . . . . . . . . . 65
6.4 Stability Criteria and Controller Design . . . . . . . . . . . . . . 66
6.5 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.5.1 TrueTime Simulations . . . . . . . . . . . . . . . . . . . . 68
6.5.2 UDP Simulations . . . . . . . . . . . . . . . . . . . . . . . 69
6.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 71
7 CONCLUSIONS AND SCOPE FOR FUTURE WORK
72
7.1 Contributions of the Thesis . . . . . . . . . . . . . . . . . . . . . 72
7.2 Future Scope of Work
. . . . . . . . . . . . . . . . . . . . . . . 73
Bibliography
74
A Configuration wizard of DAQ Assistant VI
79
A.0.1 Steps for Signal Acquisition . . . . . . . . . . . . . . . . . 79
A.0.2 Steps for Signal Generation . . . . . . . . . . . . . . . . . 81
List of Abbreviations
Abbreviation
Description
DDC
Direct digital control
P2P
Point to Point
NCS
Networked Control System
CAN
Control Area Network
CSMA/CD
Carrier Sense Multiple Access with Collision Detection
CSMA/AMP
Carrier Sense Multiple Access with Arbitration on Message
Priority
LAN
Local Area Network
WAN
Wide Area Network
PI
Proportional-Integral
PID
Proportional-Integral-Derivative
Z-N
Ziegler-Nichols
LMI
Linear Matrix Inequalities
NS-2
Network Simulator-2
LabVIEW
Laboratory Virtual Instrumentation Engineering Workbench
PC
Personal computer
WSN
Wireless Sensor Network
LCD
Liquid Crystal Display
DVM
Digital Volt Meter
ADC
Analogue to Digital Converter
DAC
Digital to Analogue Converter
PWM
Pulse width Modulation
GUI
Graphical User Interface
NI
National Instruments
iv
v
LIST ABBREVIATIONS
Abbreviation
Description
DAQ/DAS
Data Acquisition System
SCB-68
Shielded Desktop Connector Block-68
IP
Internet Protocol
UDP
User Datagram Protocol
TCP
Transmission Control Protocol
VI
Virtual Instruments
PCI
Peripheral Component Interconnect
RCP
Rapid Control Prototyping
List of Figures
1.1 Point to point control configuration . . . . . . . . . . . . . . . . .
2
1.2 General Configuration of Networked Control System . . . . . . . .
3
1.3 Direct configuration of NCS . . . . . . . . . . . . . . . . . . . . . .
5
1.4 Hierarchical configuration of NCS
. . . . . . . . . . . . . . . . . .
6
1.5 Level-2 Configuration of NCS . . . . . . . . . . . . . . . . . . . . .
7
1.6 Closed loop Structure of PID controller with delay . . . . . . . . . 10
1.7 Effects of delay in system’s performance in closed loop . . . . . . . 11
2.1 Servo motor mechanical unit . . . . . . . . . . . . . . . . . . . . . 17
2.2 Servo motor digital unit . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 A Schematic of DC motor
. . . . . . . . . . . . . . . . . . . . . . 19
2.4 System Identification of Servo Motor . . . . . . . . . . . . . . . . . 21
3.1 Graphical determination of parameters in Ziegler-Nichols...
3.2 Block diagram of a typical PID controler
. . . . 26
. . . . . . . . . . . . . . 27
3.3 A Control system structure with a Gain-Phase Margin tester. . . . 28
3.4 User specified parameter region in parameter plane analysis . . . . 31
3.5 Closed loop control system with a PID controller . . . . . . . . . . 32
3.6 Closed loop control system response without delay . . . . . . . . . 32
3.7 Closed loop networked control system with artificial delay . . . . . 33
3.8 System response of Z-N tuned and robust PID controller with delay 33
4.1 Block diagram representation of Smith predictor . . . . . . . . . . 35
vi
LIST OF FIGURES
vii
4.2 Simulink representation of Smith Predictor . . . . . . . . . . . . . 36
4.3 Smith Predictor response with artificial delay in Simulink . . . . . 37
4.4 Networked PID controller in TrueTime Network Simulator . . . . . 37
4.5 Robust PID controller response in TrueTime Network Simulator
. 38
4.6 Networked Smith Predictor structure in TrueTime Simulator . . . 38
4.7 Response of Smith predictor in TrueTime Simulator . . . . . . . . 39
4.8 Block diagram representation of delay estimation in a LAN . . . . 39
4.9 Simulink blocks for delay estimation using UDP communication
. 40
4.10Estimated delay between two computers connected in a LAN . . . 40
4.11Rapid control prototyping with servo setup . . . . . . . . . . . . . 41
4.12PID controller without delay with servo setup . . . . . . . . . . . . 41
4.13PID controller with delay with servo setup . . . . . . . . . . . . . . 42
4.14Smith predictor without delay with servo setup . . . . . . . . . . . 42
4.15Results of Rapid control prototyping with Servo Motor . . . . . . . 43
5.1 68-pin Shielded Desktop Connector Block (SCB-68) . . . . . . . . 46
5.2 Data Acquistion Hardware (PCI-6221) . . . . . . . . . . . . . . . . 47
5.3 General Configuration of a Data Acquisition System . . . . . . . . 48
5.4 DAQmx Programming for reading the real world signal . . . . . . . 49
5.5 Signal generation and acquisition using DAQ Assistant . . . . . . . 50
5.6 UDP palette for UDP communication in LabVIEW . . . . . . . . . 52
5.7 Receiving signal from sender . . . . . . . . . . . . . . . . . . . . . 53
5.8 Writing data to the server from client . . . . . . . . . . . . . . . . 53
5.9 Closed loop signal sending unit . . . . . . . . . . . . . . . . . . . . 54
5.10Closed loop signal receiving unit . . . . . . . . . . . . . . . . . . . 54
5.11Networked Control Architecture . . . . . . . . . . . . . . . . . . . 55
5.12Networked Plant/Process configuration . . . . . . . . . . . . . . . 56
5.13Networked PID controller configuration . . . . . . . . . . . . . . . 57
5.14Networked Smith predictor configuration . . . . . . . . . . . . . . . 58
5.15Schematic diagram networked servo control . . . . . . . . . . . . . 59
5.16Generation and Acquistion of Sigal using DAQ Assiatant . . . . . . 60
viii
LIST OF FIGURES
5.17Signal Sending and Receiving Using UDP . . . . . . . . . . . . . . 60
5.18Front Panel of Networked PID controller . . . . . . . . . . . . . . . 61
5.19Front Panel of Networked Smith predictor . . . . . . . . . . . . . . 61
6.1 Illustration of packet loss, transmission interval in NCS
. . . . . . 64
6.2 TtueTime/SIMULINK block for virtual NCS configuration
. . . . 68
6.3 Response of state feedback controller in TrueTime virtual network
69
6.4 SIMULINK UDP communication-sender/plant configuration . . . . 69
6.5 SIMULINK UDP communication-receiver/controller configuration . 70
6.6 Response of state feedback controller in UDP network in SIMULINK 70
A.1 DAQ Assistant in Function palette at Block Diagram Window . . . 80
A.2 DAQ Assistant Configuration window for choosing the Express Task 81
A.3 DAQ Assistant Configuration of the Express... . . . . . . . . . . . 81
A.4 Selecting the Hardware Device and Physical Channels . . . . . . . 82
A.5 Task configuration page of DAQ Assistant . . . . . . . . . . . . . . 82
List of Tables
2.1 Symbols used for the DC motor model . . . . . . . . . . . . . . . . 19
3.1 Effects of PID parameters on a system parameters . . . . . . . . . 24
3.2 Ziegler-Nichols tuning table for PID controller. . . . . . . . . . . . 26
ix
Chapter 1
INTRODUCTION
1.1
Introduction
Digital control of systems have been received continued interest since the invention of computers. Such systems use computer as a component to quickly
modify or enhance the real-time requirement and are popularly used for supervisory control of distributed processes. Direct Digital Control (DDC)is a
class of such computer controlled systems where the analog computational
instruments are replaced by a computer.
An architecture of centralized systems may use a central computer with
sensors and actuators respective for control signal calculation, sensing and
actuation required for closed loop control. Such a scheme is shown in Fig.1.1
and also called a Point-to-Point (P2P) control system. It requires huge wiring
connected from the sensors to computer and computer to actuators and moreover becomes complicated on requirement of reconfiguring the physical setup
and functionality. Further, diagnosis and maintenance are also difficult in
such systems.
To overcome the afore mentioned difficulties posed by the centralized control, Networked Control System (NCS) has received considerable attention
with advances in control and communication technologies. In many practical
systems, the implementation is conveniently realizable if the physical plant,
its controller, sensors, and actuators are geographically distributed requiring
1
CHAPTER 1. INTRODUCTION
2
Figure 1.1: Point to point control configuration
a data to be transmitted from one location to another. When sensor and
actuator data are transmitted over a network and the network nodes are
used to work in tandem for completion of the controlling task, then we call
such system an NCS. A typical NCS configuration is shown in Fig.1.2. As
described earlier the NCS uses a common bus for information exchange.
Use of common bus network in network control system has the following
advantages.
• Connecting the control system components via a network can effectively
reduce the cost.
• In NCS the data is shared so that, it is easy to use global information to
take intelligent decisions.
• Reconfigurations e.g., adding more sensors, actuators and controllers
with very little cost and without heavy structural changes to the whole
system are possible.
This thesis first considers developing a NCS servo setup using commonly
available networks and subsequently study some control techniques to achieve
effective control performance.
CHAPTER 1. INTRODUCTION
3
Figure 1.2: General Configuration of Networked Control System
1.2
Networked Control System and Its Perspectives
NCS has evolved in the past decade through the advances in communication
technology. It has made centralized control possible with a wider range of
features and more flexibility than before.
1.2.1
Description of a Networked Control System
In general, NCSs are implemented using a network through which the feedback path is closed such that the sensors and actuators can communicate
with the controller.
1.2.2
Networks Used in NCS
In NCS a network is used to connect the system components and controller.
Broadly the networks used in NCS are classified as dedicated and nondedicated networks. A dedicated network is known as control network and
non-dedicated network as data network.A dedicated network is concerned
about the constant and frequent packets transmission among a relatively
large set of nodes. Non-dedicated networks use large data packets and relatively infrequent transmission rates, with high data rates to support the
transmission of large data files. Some of the current control networks used
for design NCS are Ethernet, Device Net and Control Net [1]. Ethernet is of
CHAPTER 1. INTRODUCTION
4
non-dedicated type while other two are dedicated networks. Ethernet is type
of local area networking solution widely used in the home, office. Ethernet
uses the Carrier Sense Multiple Access with Collision Detection (CSMA/CD)
mechanism for resolving contention on the communication medium.Ethernet
is a nondeterministic protocol and does not support any message prioritization. At high network loads, message collisions are a major problem because
they greatly affect data throughput and time delay which may be unbounded
Control Net are typical examples of token-passing bus or deterministic networks control networks. As in general token-passing buses, the node with the
token can only send data and provides excellent throughput and efficiency
at high network loads. Device Net/CAN is a serial communication protocol
developed mainly for applications in the automotive industry but also capable of offering good performance in other critical industrial applications. The
CAN protocol uses CSMA/Arbitration on Message Priority (CSMA/AMP)
medium access method.Thus the protocol is message oriented, and each message has a specifc priority that is used to arbitrate access to the bus in case
of simultaneous transmission.CAN is a deterministic protocol optimized for
short messages and very slow data rate. Apart form these there are many
network architectures for distributed control like PROFIBUS, FIELDBUS[2].
1.2.3
Available NCS Configurations
According to network used in the NCS there are two types of configuration
of NCS namely level one and level two communication configuration. Further the level one communication configuration is again classified as direct
structure and hierarchical structure. The NCS in the direct structure is the
mostly used which comprises of a controller and a system consists of sensors and actuators are connected by a common sharing network to perform
remote closed-loop control as illustrated in Fig.1.3. The control signal and
the sensor measurement are encapsulated into data packets for transmission
across the network. As shown in Fig.1.3, a controller and a remote system
CHAPTER 1. INTRODUCTION
5
Figure 1.3: Direct configuration of NCS
are in closed loop using a network. Here it shown a single sensor and actuator where, there are many sensors and actuators may present in a practical
implementation with multiple controllers. The scope of this thesis is confined
within the control methodologies for NCS in the direct structure.
The hierarchical structure consists controller and a remote closed loop system
as shown in Fig.1.4. The only difference between a direct and hierarchical
structure is the controller. Here two controller are used namely main and
remote controller. The main controller computes and sends the reference
signal in a packet via a network to the remote system. The remote system then processes the reference signal to perform local closed-loop control
and returns to the sensor measurement to the main controller for networked
closed-loop control. Similar to the direct structure, the main controller can
be implemented to handle multiple networked control loops for several remote systems. This structure is widely used in several applications including
mobile robots and tele-operation. The use of either the direct structure or
the hierarchical structure is based on application requirements and designer’s
preferences.Control and analysis methodologies for the direct structure could
also be applied for the hierarchical structure by treating the remote closed
loop system as a pure plant.
A NCS in hierarchical structure is shown in Fig.1.4, a main controller and
CHAPTER 1. INTRODUCTION
6
Figure 1.4: Hierarchical configuration of NCS
a remote system are connected by a network. Main controller calculates the
reference signal for the remote controller. The role of remote controller is to
look after the uncertainty of the system only.
A two-level communication model as its name suggests, it has two levels
are connected by communication channels as shown in Fig.1.5. Such a NCS
uses microcontrollers as intermediate communicator to communicate with the
both the channels. A system with which sensors and actuators, that are in
the closed loop with the plant through a communication network. A kind of
field bus dedicated to real-time control network used for communicating plant
to microcontroller. This communication known as level-1 communication. In
level-2 communication, the microcontrollers with a high-level computer system through another communication network. This network is typically non
dedicated networks like local area network, wide area network (WAN), or possibly the Internet. As shown in Fig.1.5 microcontrollers communicate with
system components using a dedicated network in level-1 and with a high level
controller using a non dedicated network in level-2 communication.
1.2.4
Applications
Use of networks for connecting the control system components like sensors,
controllers, and actuators in any process can effectively reduce the complex-
CHAPTER 1. INTRODUCTION
7
Figure 1.5: Level-2 Configuration of NCS
ity of systems, with nominal economical investments, eliminate unnecessary
wiring. It is easy to add more sensors, actuators and controllers with very
little cost and without heavy structural changes to the whole system. Potential applications of NCS [3], are including space explorations, terrestrial exploration, factory automation, remote diagnostics and troubleshooting, hazardous environments, experimental facilities, domestic robots, automobiles,
aircraft, manufacturing plant monitoring, nursing homes or hospitals, telerobotics and tele-operation.
1.2.5
Control Issues
The issues involved in NCS are broadly classified into two categories namely
network issues due to use of network and control performance due to presence
of network in the system. Network issues deals with bandwidth allocation,
scheduling and network security where the control problem deals with stability analysis and delay compensation.
Network Issues
As the network used is having limited bandwidth, optimizing the performance
of an NCS can be achieved by proper balancing of network sampling and
bandwidth allocation with the resulting network performance degradation.
CHAPTER 1. INTRODUCTION
8
The maximum bound of the network sampling is called a maximum allowable
delay bound, within it stability of the system is guaranteed in spite of the
performance degradation. A network scheduling method is required to reduce
a basic sampling time within the maximum allowable delay bound, while
guaranteeing real-time transmission of sporadic and periodic data, and to
minimize network utilization for non-real time message. Network security is
an another problem in a NCS which is more concern on type of network used
and network administrator. there should be provisions andpoliciesadopted
by thenetwork administrator to prevent and monitorunauthorizedaccess of
thecomputer networkand network-accessible resources.
Control Issues
Control issues involve various delays present in NCS and packet dropouts
in a network. In an NCS, various delays with variable length occur due
to sharing a common network medium[4].They are called network-induced
delays, controller processing delay and natural delay of plant. The natural
delay is the delay associated with the system itself known as transportation
lag of the system. Controller processing delay is the amount of time required
by the controller to calculate the control input. Generally these delays are
very less and mostly neglected. The delay of concern here is the networkinduced delays, it occurs when sensors, actuators, and controllers exchange
data packet across the communication network. Networked induced delay
arises from sensor to controller (backward channel delay) and controller to
actuator(forward channel delay). Packet dropouts in NCS occurs due to node
failures, improper network scheduling or data packet collisions. Due to this
Although In most network protocols a untransmitted packet only retransmit
for a limited time and after this time has expired, the packets are dropped.
Furthermore, for real-time feedback control data such as sensor measurements
and calculated control signals, it may be advantageous to discard the old
untransmitted message and transmit a new packet if it becomes available. In
this way, the controller always receives fresh data for control calculation.
CHAPTER 1. INTRODUCTION
1.3
9
A Survey on NCS design Methodology
Research interests on NCS is growing as this is of interest to research interest topic in multidisciplinary engineering. It includes the use of computer
network and control theory, with wide application in industrial automation.
Research areas of NCS are focused with networks used and classifications,
effects of network on the system and controller design for delay compensation and stabilization. Apart from above, NCS co-design is also topic of
interest for many researchers[5, 6]. A control system closed with a real-time
network in feedback form a NCS [7, 8, 9, 10]. As a large physical are requires a large interconnect wiring among components, traditional centralized
point to point control system is no longer suitable to meet this challenge.
A common bus architecture like NCS can be useful in expanding physical
set-up and functionality because of wires connected between central control
computer with each sensor or actuator. In this section, a brief discussion on
focused topics of research on NCS is presented. Networks are the backbones
of a NCS, there are many literatures on communication networks used for
NCS [1]. Mostly ethernet, device net or control net [10] are used in a NCS.
Recent interest is to use wireless network in NCS [11]. Wireless sensor networks (WSN) have been extensively researched for over a decade, because
they provide appealing possibilities for distributed, flexible and ubiquitous
sensing applications, where each node in the network performs sensing, data
processing and communication functions. The highly distributed nature of
WSN makes them fault tolerant and adaptive to dynamically changing environments [12]. Even though one node in the network experiences problems
and is shut down, networking protocols and both sensing and data processing
algorithms could adapt to the changed situation. Hence packets would not
be delivered through the faulty node, routes would be reestablished and data
processing would adapt to a missing source of measurements. Based on the
communication channels used in a NCS architecture, it is divided into class A
10
CHAPTER 1. INTRODUCTION
and class [7]. A NCS using single communication channel is treated as a class
A and two level communication channel is known as class B. Further class A,
divided according to use of controller in the system like direct structure and
hierarchical structure [8]. More on this described in section 1.2. In both the
class there is a network and due to insertion of this communication network,
delays in control loop from controller to actuator and sensor to controller are
introduced along with controller processing delay and natural delay as shown
in Fig.1.2. Apart from delay there are issues like packet droputs, jitters [4]
are also present. A delay is the source of performance degradation and destabilization [8] of a stable system by decreasing the system’s phase margin by
the amount of delay. For example, consider a second order system given by
PID
num
den
Step Input
(Reference signal)
CONTROLLER
PLANT
Delay
Figure 1.6: Closed loop Structure of PID controller with delay
Gp (s) =
5.928
s3 + 3.994s + 0.09181
and a PID (Proportional-Integral-Derivative) controller as,
Gc (s) = Kp (1 +
Ki
+ Kd s)
s
and by using the SIMULINK’s Response Optimization Tool for PID controller tuning, the tuned gains of PID found to be, Kd ,Ki and Kp as 1.5692,
0.5222, and 0.3799 respectively. The delays (sum of both networked induced
delays) are varied from 0 sec to 0.5 sec and the corresponding closed loop
step responses are shown in above Fig.1.7. It is observed that with increase
of delay the system’s overall performance gradually degrades. Time delay in
a system is modeled by transfer function e−τd s . The delay causes a decreased
phase margin which implies a lower damping ratio and a more oscillatory
CHAPTER 1. INTRODUCTION
11
response for the closed-loop system and hence deteriorate the system performance and cause the system instability. Therefore, it is necessary to design a
controller which can compensate the effect of time delays, stabilize the system
and improve the control performance of the NCS.
Figure 1.7: Effects of delay in system’s performance in closed loop
System stability is of vital issue in the system analysis and control design.
Many results have appeared in the literature to analyze the closed-loop stability in the presence several NCS issues. In general, these approaches can be
classified into two types: indirect and direct . Controller design in indirect
approaches assume that there is no delay associated in the system, followed
by a suitable dead time compensator for delay compensation. A direct approach is quite simpler as it takes the delay in account at the time of controller
design. The PID controller is mostly used in indirect approach along with a
suitable dead time compensator like smith predictor.The objective of a PID
controller design only depends upon fine tuning of its parameter gains. The
concept of tunning method for PID controller was brought by Zigler-Nicols in
1942. They proposed a tuning method as step response and sustain oscillation method [13, 14]. The ZN tuning method is not a good choice for higher
order systems [15] so many advanced tuning methods like analytical tuning,
CHAPTER 1. INTRODUCTION
12
prediction approach tuning[16], optimized tuning , auto-tuning[17] and tuning based on system gain and phase margin specifications[18, 19, 20, 21] has
been developed. Phase margin and gain margin based PID controller tuning makes the system robust by bounding the system margins in between
a predefined value. Manually tuning procedure is very tedious and time
consuming, and the resultant system performance mainly depends on the experience and the process knowledge the engineers. To avoid this the relay
feedback auto-tuning method proposed by Astrom and Hugglund. a method
which enables the controller to be tuned automatically on demand from an
operator or an external signal. A well defined survey is presented on [22].
To evaluate the stability of a PID controlled system with uncertainties, such
as varying time-delays, robust control techniques can be used. For example,
the robustness of different PID tuning methods for a case process with parameter uncertainties has been investigated in [23]. A PID controller itself is
not sufficient for NCS [24] , a delay compensator must be incorporated. A
detailed survey on deadtime compensators are presented in [25]. Smith predictor is the most commonly used dead time compensators used in industrial
applications [26, 24], the befit lies in that the structural simplicity and easy
implementation.
As the use of network, which is a source of delay and packet loss. There are
literatures, which are considered NCS as an application of time delayed systems and designed controller [27]. However the indirect method uses transfer
function method for control design and does not explain the internal system
behavior i.e. the states of the system in every instance of time. It deals with
the tracking control of the system, to follow a desired reference path given
by a reference input. But in contrast direct method indicates the system
behavior clearly and deals with stabilization of the system with delay and
packet losses in NCS.
The direct approach used to determine the controller gain to stabilize
the system or to find out the maximum delay bound for system, that can
CHAPTER 1. INTRODUCTION
13
be tolerated to guarantee the stability using Lyapunov stability criterion
[28, 29, 30]. A stability condition in direct approach is formulated by linear
matrix inequalities (LMI). In [5] a survey of stability of NCS is described
which introduces many directions of stability analysis.
NCS analysis using switched system approach is described in [30, 29, 31].
A switch system divides the whole systems as several subsystems according
to delays in a transmission interval. Then, designing a suitable controller for
each subsystems, as a whole stabilize the systems. The controller may be in
designed by state feedback [31], output feedback [29] approach.
The NCS may consider as a sampled data system as a continuous plant
dynamics interacting with the discrete nature of the network. Designing of
digital controllers for a sampled data system is done by using lifting technique
[32, 33]. Lifting techniques provide a equivalent characterization of sampled
data system with delay. This technique also takes the inter sample behavior
into account as well as the effect of performance of the system by sampling
frequency [34].
A networked predictive control scheme is proposed by Liu et al. [35]. This
scheme having two main units: the control prediction generator, to generate
a set of future control predictions and the network delay compensator, used
to compensate the effect of unknown random network delay.
A optimal cost control of NCS with uncertainty is communicated in [36],
which provide an upper bound on a given performance index and thus design a controller so that, the system performance degradation occur by the
uncertainties is guaranteed to be less than this bound.
In [37],conditions of asymptotic stability for networked control system with
long time delay are presented. Modeling of delay and packet loss are described
in [30]. A discrete time model of NCS incorporating all network phenomenon
is presented in [38]. There are methods like sliding mode control and Kalman
filter [39]based estimator are also some topics of interest in NCS
Model-based networked control systems, an explicit model of the plant is
CHAPTER 1. INTRODUCTION
14
used to produce an estimate of the plant state behavior between transmission
times. This control architecture has as its main objective the reduction of
the data packets transmitted over the network. In this way, the amount of
bandwidth necessary for feedback control to maintain certain stability and
performance criteria is minimized
The control and communication co-design [6, 40, 41]is a new and interesting research. In the co-design approach, network issues such as time delay,
packet dropout, and bandwidth limitation will be considered simultaneously
with control system issues such as stability and control performance. Generally, the network scheduling in NCSs is to assign a transmission schedule to
each transmission entity (sensor, controller, actuator) based on a scheduling
algorithm
The NS-2 network simulator is a network simulation package developed at
the Information Sciences Institute at the University of Southern California
[42]. NS-2 provides many powerful objects to simulate different types of
networks and network architectures, as well as different types of nodes and
traffic patterns.
TrueTime is a MATLAB-SIMULINK based simulator facilitates co-simulation
of controller task execution in real-time kernels, network transmissions and
continuous plant dynamics for NCS [43]. The simulator software consists
of a SIMULINK block library . The various network blocks allow nodes to
communicate over simulated wired or wireless networks [11].
1.4
Motivations
The insertion of the communication network in the feedback control loop
makes the analysis and design of a networked control system more complex
and induces some issues that degrade the control system’s performance and
even cause system instability. Some fundamental issues that influence performance of an NCS respectively: network-induced delays, sampling period,
jitter, data packet dropout, network scheduling and stability. Above all the
CHAPTER 1. INTRODUCTION
15
major issues raised in NCSs is the unreliable transmission paths because of
limited bandwidth and large amount of data packet transmitted over one line,
which may result in transmission delays and data packet dropout. Because
of the variability of network-induced time delays, NCSs may be time-varying
systems, making analysis and design more challenging.
This thesis presents a development framework for design of a real-time
networked servo control system for investigation of issues due to use of communication channel.
1.5
Objectives
The salient objectives of the thesis are:
i. Development of a real-time networked control system using LABVIEW.
ii. Implementation of PID controller and Smith predictor for control and
delay compensation induced by the communication network.
iii. Discrete time analysis for controller design for stabilization of control
system in presence of networked delays and packet dropouts.
1.6
Thesis Organisation
The thesis is organized as follows.
• In chapter 2, description and modeling of the Servo setup is presented.
• Chapter 3 depicts PID controller design and its tuning algorithms. Studies on the Servo system using an artificial delay are also presented.
• In Chapter 4, Smith predictor compensation design and implementation
in Servo system are discussed.
• Chapter 5 presents development of a LabVIEW based real-time NCS
environment including implementation of PID controller and Smith predictor.
CHAPTER 1. INTRODUCTION
16
• In chapter 6, a direct approach using discrete time system analysis for
controller design using Lyapunov stability criteria is described.
• Chapter 7 concludes the thesis. Extensions of the present work and
future scopes for further work are also discussed therein.
Chapter 2
SERVO SYSTEM AND ITS MODELING
2.1
The System under Study
A servo is an error feedback system used to achieve the desired speed or position used in many industrial applications. Here, we consider a position servo
system based on DC motor. It is a laboratory based setup manufactured
by Feedback Instruments Ltd (Model No. 33-100). This servo motor have
two main parts one is mechanical unit and another one is digital unit, which
are shown in Fig.2.1 and Fig.2.2 respectively. The mechanical unit of servo
Figure 2.1: Servo motor mechanical unit
setup[44] consists of electro-mechanical components comprising of a DC motor, an analogue tachogenerator, analogue input and output potentiometers,
absolute and incremental digital encoders and magnetic brake and some sup17
CHAPTER 2. SERVO SYSTEM AND ITS MODELING
18
porting electronics comprises like power amplification, a low frequency sine,
square and triangle waveform generator for testing purposes, encoder reading
circuitry and Liquid Crystal Display (LCD) and Digital Volt Meter (DVM).
A separate power supplied unit is connected to this unit.
Figure 2.2: Servo motor digital unit
The digital unit[44] is the interface between the mechanical unit and a
computer(PC). It contains Analog to Digital Converter(ADC) and Digital to
Analog Converter (DAC) circuits for signal conversion, Pulse Width Modulation (PWM) motor drive, input and output potentiometers or digital encoders. Connection to the mechanical unit is by way of a ribbon cable which
also supplies power to the unit.
2.2
Identification of the Servo Model
Mathematical Modeling of DC servo motor
DC motors are most widely used actuators in servo position, speed regulation
control systems. Basically DC motors are torque transducers, converting
electrical energy to rotational mechanical energy. For analysis of control
system we require a mathematical model of a system. Equivalent circuit of a
DC motor is shown in Fig.2.3. The control input of the motor is applied as
the input voltage ( va (t)) of the armature terminals.
19
CHAPTER 2. SERVO SYSTEM AND ITS MODELING
Table 2.1: Symbols used for the DC motor model
Ra
La
ia (t)
if (t)
va (t)
eb (t)
Tm (t)
θm (t)
jm
Bm
ϕ
Armature resistance (ohm)
Armature inductance (H)
Armature current (Ampere)
Field current (Ampere)
Applied Armature voltage (volts)
Back emf (volts)
Torque developed by motor (Nm)
Angular displacement of the motor shaft (rad)
Moment of inertia of motor shaft (kg − m2 )
Nm
Viscous friction of motor shaft ( rad/s
)
Magnetic flux
Figure 2.3: A Schematic of DC motor
In servo applications, the DC motor are generally used in [13] linear range,
so we assume that the torque developed by motor (Tm (t)) proportional to the
flux (ϕ) and armature current (ia (t))
Tm (t) = km (t) ϕ ia (t)
(2.1)
As the flux is constant, the above (2.1) can be written as
Tm (t) = ki ia (t)
(2.2)
The motor back emf is proportional to speed of the motor is described as
eb (t) = kb
dθm (t)
dt
(2.3)
where ki is motor torque constant and kb is the back emf constant. The
20
CHAPTER 2. SERVO SYSTEM AND ITS MODELING
differential equation for the DC motor circuit (no-load) is
La
dia (t)
+ Ra ia (t) + eb (t = va (t)
dt
(2.4)
and the torque equation is using (2.4)
d2 θm (t)
dθm (t)
jm
+
B
= Tm = ki ia (t)
m
dt2
dt
(2.5)
Laplace transformation of (2.3,2.4,2.5) with zero initial conditions we get
Eb (s) = Ki sθ(s)
(2.6a)
(La s + Ra )Ia (s) = Va (s) − Eb (s)
(2.6b)
(jm s2 + Bm s)θ(s) = Ki Ia (s)
(2.6c)
substituting the value of (2.6a) and (2.6b) in (2.6c), we get the transfer
function(input voltage Va (s) and output position θm (s)) of the DC motor as
a third order equation
θm (s)
Ki
=
Va (s)
(jm s2 + Bm s)(La s + Ra ) + Ki Kb s
(2.7)
Assuming armature circuit inductance La to be very small, is usually negligible. So the above equitation becomes a second order transfer function
as
θm (s)
Ki
=
Va (s)
Ra jm s2 + Ra Bm s + Ki Kb s
(2.8)
The servo motor is equipped with A/D, D/A converters, PWM converters and others (see chapter-3 Sec.5.2). So, identification of each individual
component is a bulky procedure. Hence we tried to identify the system as a
whole including all the components. For this we use the system identification
toolbox of MATLAB. Providing input voltage to the servo motor and obtain
the corresponding position as output, and by using these input and output
data model of the servo system is identified. The procedures for the system
identification using MATLAB are described in following section.
CHAPTER 2. SERVO SYSTEM AND ITS MODELING
21
System identification using MATLAB
System identification using system identification toolbox provides users to
calculate and observe the progress of process identification. A typical workflow in the System Identification Tool GUI includes the following steps:
• Running the system with some known input. The input and its corresponding output are stored in MATLAB workspace.
• A new System Identification toolbox session can be obtained by typing
”ident” in MATLAB command window.
• Importing the input/output data from MATLAB workspace to System
Identification GUI.
• System Identification GUI consists of 4 different parts - Data Views,
Operations, Model Views and Validate data.
• Data View palette shows the data set on which the identification process
is to be carried out.
Figure 2.4: System Identification of Servo Motor
CHAPTER 2. SERVO SYSTEM AND ITS MODELING
22
• Operations palette is again sub divided into 3 parts as Preprocessors (filtering),working data (current data used for identification) and Estimate
(to identify the type of model).
• After importing the data to operation palette, choose the process model
option under estimate menu.
• Choose the order and type of model you want to identify.
• After the above step, Go to Validate palette and choose the model output option. This shows a graph between measured and simulate model
response with best fit in percentage. The maximum best fit percentage
will give better accuracy for model matching.
As shown in Fig.2.4, where P3(third order model response) has best fit percentage of 93.61 and P3(second order model response) has 91.49. So we
choose the model as a third order model. After performing the above identification procedure the transfer function of the servo system is given by.
θ(s)
53.2718
= 3
V (s) s + 9.481s2 + 36.1855s + 0.8211
(2.9)
where θ(s)is the output angular position of the servo and V (s)is the applied
voltage to the servo system.
2.3
Chapter Summary
A simple way for system identification using MATLAB system identification
tool-box is presented. Although a Servo system can be modeled as DC motor,
but use of some digital circuits here makes the identification procedure very
complex so a simple procedure is carried out to perform the identification. A
third order model is identified as it matches with the original response of the
servo system.
Chapter 3
PID CONTROLLER DESIGN
3.1
Introduction
The Proportional-Integral-Derivative (PID) controller [45, 14]is the most
widely used controller structure in many industrial applications due to its
following advantages.
• structural simplicity and sufficient ability of solving many practical control problems
• reduced number of parameters to be tuned
• simple, robust and familiar to the field operator
3.1.1
Objectives
This chapter focus on some well known PID controller tuning formulas and
verification of these in simulation. The simulation are done with MATLAB/SIMULINK. Real time experimentation shown in following chapter.
3.2
PID Controller Design Methodologies
PID controllers are used extensively in the industry and having longest history and most vigorous development[17, 18, 46]. The structure of a PID
23
24
CHAPTER 3. PID CONTROLLER DESIGN
controller in time domain is
u(t) = Kp (e(t) +
1
Ti
Zt
e(t)dτ + Td
0
de(t)
)
dt
(3.1)
where
u(t)=The Control Input
e(t)=The difference between reference signal yr (t) and output signal y(t)
The Complete structure of PID controller is shown in Fig.3.2
C(s) =
1
Ki
U (s)
= Kp (1 +
+ sTd )E(s) = Kp +
+ Kd (s)
E(s)
sTi
s
(3.2)
whereTi is called the integral time constant or reset time andTd is called the
derivative time constant or rate time. The coefficients Kp Ki Kd and Ti , Td
related by.
Proportional Gain =Kp
Integral Gain(Ki ) = KTPi
Derivative Gain(Kd ) = Kp Td
The controller has three parameters to be tuned for the desired control response. These parameters has different effects on system parameters as shown
in Table3.1.
Parameter
Proportional Gain
Integral Gain
Derivative Gain
Rise Time
Decrease
Decrease
Increase
Overshoot
Increase
Increase
Reduce
Steady-State Error
Decrease
Remove
No Effect
Settling Time
Small Change
Increase
Decrease
Table 3.1: Effects of PID parameters on a system parameters
The parameters of a PID controller can be tuned by various methods, such
as trial and error tuning, empirical tuning like the well-known ZieglerNichols
method[14], analytical tuning, prediction approach tuning[16], optimized tuning and auto-tuning[17].
CHAPTER 3. PID CONTROLLER DESIGN
3.2.1
25
Ziegler-Nichols PID Controller Design Methodology
The Ziegler-Nichols(Z-N) tuning methods can be carried out on open-loop
step response or closed-loop frequency response tests and according to Table3.2 one can obtain the tuned parameters of P, P-I or P-I-D controller.
Open-Loop Step Response Method
The Ziegler-Nichols step response method is an experimental tuning method
for open-loop plants. Procedures for this method are follows :
• Apply a step signal on the open-loop system.
• The point on the step response curve with the maximum slope is (inflection point)determined and the tangent is drawn.
• Two terms A and L are determined graphically from the measurement
of the step response of the plant as illustrated in Fig:a of Fig.3.1.
• The intersection of the tangent with the vertical axis gives A, while the
intersection of the tangent with the horizontal axis gives L.
• Once L and L are determined, the PID controller parameters are then
given in terms of L and L by the formulas shown in Table3.2
Closed Loop Frequency Response Method
In the frequency response method the loop is closed and a pure gain controller
is used.In this method, the two parameters to be calculated are the ultimate
gain Ku and the ultimate period Tu which can be calculated experimentally in
the following way:
• The gain is increased to the ultimate gain Ku when the system exhibits
a sustain oscillation.
• The oscillation period is measured Tu .
The sustain oscillatory response is shown in Fig:b of Fig.3.1 and the PID tuning is calculated from the Z-N tuning Table3.2. P,P-I and P-I-d controllers
26
CHAPTER 3. PID CONTROLLER DESIGN
have separate tuning rules.
Tuning Method/Parameter
Ziegler-Nichols Step Response
(Proportional-Integral-Derivative)
Ziegler-Nichols Frequency Response
(Proportional-Integral)
(Proportional-Integral-Derivative)
(Proportional)
KP
Ti
Td
1.2
A
0.6
AL
0.6L
A
0.6Ku
0.45Ku
0.5Ku
0.5
Tu
0.833
Tu
∗
0.125Tu
∗
∗
Table 3.2: Ziegler-Nichols tuning table for PID controller.
The Z-N tuning is usually for first order systems. For higher order systems
some modifications needed in Z-N method to improve the performance[15].
Figure 3.1: Graphical determination of parameters in Ziegler-Nichols tuning step response test
(Fig:a) and frequency response test(Fig:b)
3.2.2
A Robust PID Controller Design Methodology
The delay in NCS causes a decreased phase margin which implies a lower
damping ratio and a more oscillatory response for the closed-loop system
performance. In this section a robust PID controller design scheme is illustrated by using Gain and Phase margin method.
The objective of this PID tuning is to keep the phase and gain margin of
a delayed system fixed at a certain value so that change in delay variation
couldn’t change this parameters hence the system will be stable in presence
of delay. This method of PID tunning [20, 19, 18] is known as frequency
27
CHAPTER 3. PID CONTROLLER DESIGN
domain/parameter plane tuning method.Consider a servo system which contains a time delay element, its transfer function is shown as follows.
53.2718
Gp (s) = 3
e−τ s
(3.3)
2
s + 9.481s + 36.18s + 0.8211
where ”τ ” is the delay time of the system. Using a second-order approximation, the time domain and frequency domain specifications are approximately
converted into interval gain margins and phase margins. Fig.3.2 shows the
Distrubance D(s)
R(s)
Refereence
Input
Gc (s)
Controller
Gp (s)
Plant
Figure 3.2: Block diagram of a typical PID controler
block diagram of the considered system where the transfer functions of the
process and the controller are denoted as Gp (s) and Gc (s), respectively.D(s)is
the external disturbance. An error actuated PID controller has the transfer
function.
Ki
+ Kd s
(3.4)
s
The forward open-loop transfer function of the control system shown in Fig.
Gc (s) = Kp +
3.2 is,
GO (s) = GC (S) GP (S) =
N (S)
D (S)
(3.5)
i.e.
1
N (s) = 0
(3.6)
D (s)
By letting s = jω, and Re [G0 (jω)]and Im [G0 (jω)]be the real part and
G0 (s) −
imaginary part of the G0 (jω), respectively, one has
GO (jω) = |GO (jω) |ejφ
where
(3.7)
q
|GO (jω) | =
Re [GO (jω)]2 + Im[GO (jω)]2
(3.8)
28
CHAPTER 3. PID CONTROLLER DESIGN
and
Im[GO (jω)
}
(3.9)
Re[GO (jω)
and θ = ϕ + 180, as when θ = 0, A is the gain margin
φ = ∠GO (jω) = tan−1 tan−1 {
Assuming A =
1
GO (jω)
of the system, and when A = 1, θ is the corresponding phase margin. In
view of the above, a gain-phase margin tester function may be defined as.
F (jω) = D(jω) + Ae−jω N (jω)
(3.10)
It can be seen thatF (jω) = 0, ∀ω. The open loop transfer function can be
rewritten using the controller structure(3.4) as,
53.2718
kp s + ki + kd s2
)×( 3
e−T s )
(
2
s
s + 9.481s + 36.18s + 0.8211
(3.11)
puttings = jω, and Ae−jθ = Acosθ − jAsinθ, the numerator of (3.11) will
be.
Figure 3.3: A Control system structure with a Gain-Phase Margin tester.
³
2
´
N (jω) = kp jω+ ki + kd (jω) × 53.27 × e−T jω
¡
¢
= 53.27 (cos ωT − jsinωT) × jkpω + ki − kdω2
¡
¢
= 53.27[cos cos ωT ki − kdω2 + sin ωT (kpω) + j{cos{cos ωT (kpω)
¡
¢
− sin sin ωT ki − kdω2 }
(3.12)
Let us define
¡
¢
XN = cos cos ωT ki − kdω2 + sin ωT (kpω) and YN = cos cos ωT (kpω) −
¡
¢
sin sin ωT ki − kdω2
Aejθ N (jω) = (A cosθ − j A sinθ) (53.27XN + j53.27YN )
CHAPTER 3. PID CONTROLLER DESIGN
= 53.27 [(AcosθXN + AsinθYN ) + j (AcosθYN − AsinθXN )]
29
(3.13)
and the denominator of (3.11) will be.
³
´
3
2
D (jω) = jω (jω) + 9.481(jω) + 36.18jω + 0.8211
¡
¢
= ω 4 − j36.18ω 4 − j 9.481ω 3 − 0.8211ω
(3.14)
¡
¢
¡
¢
XD = ω 4 − 36.18ω 2 andYD = 9.481ω 3 − 0.8211ω
(3.15)
Let us define
Combining real parts of (3.14) and (3.13)
¡ 4
©
¡
ª
¢
¢
ω − 36.18ω 2 + 53.27A cos cos θ cos cos ωT ki − kdω2 + sin ωT (kpω)
©
¡
¢ª
+53.27A sin sin θ cos ωT (kpω) − sin ωT ki − kdω2
Define
B1 = (53.27Acosθ × sin ωT × ω) + (53.27Asinθ × cos ωT × ω)
(3.16)
C1 = (53.27(Acosθ × cos ωT) − (53.27Asinθ × sin ωT)
(3.17)
D1 = ω 4 − 36.18ω 2 − 53.27Aω 2 kd cos (θ + ωT )
(3.18)
Then from (3.16),(3.17),(3.18) we have,
kp B1 + ki C1 + D1 = 0
(3.19)
The imaginary parts are,
¡
¢
£
¡
¢¤
9.481ω 3 − 0.8211ω +53.27(Acosθ cos cos ωT (kp ω) − sin sin ωT ki − kd ω 2
¡
£
¡
¢
¤¢
− Asinθ cos cos ωT ki − kd ω 2 + sin sin ωT (kp ω)
Defining,
B2 = (53.27A cos θ × cos ωt × ω) − (53.27A sin θ × sin ωt × ω)
= 53.27Aω cos(θ + ωt)
(3.20)
CHAPTER 3. PID CONTROLLER DESIGN
30
C2 = −53.27(A cos θ ×sin ωt)−(53.27A sin θ ×cos ωt) = 53.27A sin(θ +sin ωt)
(3.21)
D2 = (−9.481ω 3 + 0.8211) + 53.27A cos θ × sin ωT × ω 2 kd + 53.27A cos ω 2 kd
(3.22)
Then we can write from (3.20),(3.21),(3.22)
kp B2 + ki C2 + D2 = 0
(3.23)
Solving the equations(3.19) and (3.23) we can find
kp =
C 1 × D2 − D1 × C 2
B1 × C2 − C1 × B2
(3.24)
and
B2 × D1 − B1 × D2
B1 × C2 − C1 × B2
Parameter plane analysis
ki =
(3.25)
As discussed above, if A = 1 and θ=0 then setting Kd to a constant, for
different values of ω, a locus representing the stability boundary of the system
without the gain-phase margin tester can be plotted in the Kp -Ki plane. By
choosing A as a constant value and θ=0, the locus in the plane is a boundary
of the constant gain margin. By setting A=1, and θ is assumed equal to a
constant value, then the locus in the plane is a boundary of constant phase
margin. By varying one of the parameters, A, θ and ω, and fixing the others,
it suffices to plot the constant gain margin boundary and the constant phase
margin boundary in the parameter plane. The boundary obtained shows a
useful relationship between the three parameters, Kp -Ki and Kd of the PID
controller.
A = 10(
GainM arg in
)
20
and assuming the delay time of the system is fixed at
τ = 0.50. Keeping Kd = 0.02, the constant phase margin boundaries for
θ = 30and 60◦ can be plotted as in Fig.3.4. Similarly, for A = 5 and 10dB,
the constant gain margin boundaries can also be plotted.
31
CHAPTER 3. PID CONTROLLER DESIGN
7
GM=0;PM=0;
GM=5;PM=0;
GM=10;PM=0;
GM=0;PM=40;
GM=0;PM=20
6
Ki (integral gain)
5
4
3
2
1
0
0
1
2
3
4
Kp (proportional gain)
5
6
7
Figure 3.4: User specified parameter region in parameter plane analysis
3.3
Simulation Studies
In this section, we presented some simulation results with MATLAB/ SIMULINK.
As NCS uses a shared network which is the source of delay using artificial
delay blocks of SIMULINK and assuming that as to be a network.
3.3.1
Simulation Using Artificial Delay
An artificial delay block refers to transport delay block in SIMULINK. We
started with a basic simulation of a closed loop system as shown in Fig.3.2.
Below in Fig.3.5 represents the SIMULINK model of a basic closed loop
control system and Fig.3.7 shows the networked control system (presence of
a artificial delay block).
Responses of Fig.3.5 and Fig.3.7 are shown in Fig.3.6 and Fig.3.8 respectively. It can be concluded that in the absence of delay in system Fig.3.5 ,
PID controller tuned by Z-N method shows a satisfactory response with high
overshoot, good rise time and settling time where in the gain margin/phase
margin tuning method the response is better that Z-N tuned PID controler
CHAPTER 3. PID CONTROLLER DESIGN
32
Figure 3.5: Closed loop control system with a PID controller
Figure 3.6: Closed loop control system response without delay
shown in Fig.3.6. Considering 0.03sec delay in both channels as shown in
Fig.3.7 , the reposes of systems under different tuned PID controller is shown
in Fig.3.8. The Z-N tuned PID controller could not incorporate the delay as
the response shows very high oscillation drives the systems to become unstable where in gain margin/phase margin tuning method, as we consider the
delay at the time of design it shows a better time response with good rise
time, less oscillation result as compared to Z-N tuned PID controller.
CHAPTER 3. PID CONTROLLER DESIGN
33
Figure 3.7: Closed loop networked control system with artificial delay
Figure 3.8: System response of Z-N tuned and robust PID controller with delay
3.4
Chapter Summary
A detailed description of PID controller tuning using Zigler-Nichols and a
Robust PID tuning method using gain margin and phase margin specification
is presented. Some simulation studies is also carried out with artificial delay
in the loop with the servo system model. It has found that the PID controller
tuned by gain margin and phase margin specification makes the system robust
with delay.
Chapter 4
SMITH PREDICTOR BASED
COMPENSATING CONTROL FOR NCS
As discussed, PID controller alone is not a good choice for NCS, there should
be a suitable delay compensation techniques associated with for efficient control. A Smith predictor[26] has been known as an effective controller to
overcome dead time.It creates a virtual environment using the plant model
and estimated delay which are used to compensate the effect of delay.More
details is described in below Section.4.1.
4.1
Smith Predictor Based Compensation
Probably the simplest dead time compensator used in industrial application
is the Smith predictor [26]. Developed in 1950 by O.J Smith to compensate
process time delay as so named as Smith Predictor. The Smith predictor
structure shown below in Fig.4.1 contains model of the actual process to
be controlled and an estimated delay of the actual control loop. It creates
a virtual environment where the plant model and estimated delay used to
compensate the effect of delay in the loop. There are two loops working in
a Smith predictor. The outer loop is the actual feedback loop of the process
which is always affected by delays and an inner loop is a virtual loop that
consists of process model series with estimated delay. The outputs of inner
34
CHAPTER 4. SMITH PREDICTOR BASED DELAY COMPENSATION
35
and outer loop are subtracted in order to cancel the delay effect in the control
loop.
Figure 4.1: Block diagram representation of Smith predictor
Consider a process model described by G(s) = G0 (s)e−τ s ,where G0 (s) is
the delay free part of the system, and C(s)is the controller for this, then the
close loop transfer function H(s) will be
H(s) =
C(s)G0 (s)
1 + C(s)G0 (s)
(4.1)
Again consider the delayed plant G(s)and a controller Cdelay (s) , then the
close loop transfer function Hdelay (s) will be
Hdelay (s) =
Cdelay (s)G(s)
1 + Cdelay (s)G(s)
(4.2)
As the (4.1) is having no delay(τ ),so the response of close loop H(s) is satisfactory under proper design of controller. The objective of Smith predictor is
to eliminate the delay effects in (4.2) by designing a suitable controller Cdelay .
It can be stated as
Hdelay (s) = e−τ s H(s)
then
Cdelay (s)G(s)
C(s)G0 (s)
= e−τ s
1 + Cdelay (s)G(s)
1 + C(s)G0 (s)
(4.3)
36
CHAPTER 4. SMITH PREDICTOR BASED DELAY COMPENSATION
In above (4.3), it is not possible to use the actual plant(G(s)) and delay
e
in the actual closed loop (τ ) ,so replacing it with a model as (G(s))
of actual
plant and estimated closed loop delay as (e
τ ). Then (4.3) becomes
e
Cdelay (s)G(s)
−e
τ s C(s)G0 (s)
=e
e0 (s)
1 + Cdelay (s)G(s)
1 + C(s)G
(4.4)
Solving(4.4), one can find the value of Cdelay which is shown in the inner loop
of Fig.4.1.
Cdelay (s) =
C(s)
e0 (s)e−eτ s
1 + C(s) − C(s)G
Simulink diagram of Smith predictor is shown Fig.4.2 and the corresponding response is shown in Fig.4.3.
Figure 4.2: Simulink representation of Smith Predictor
4.1.1
TrueTime Based Simulation
Co-design in NCS [40, 41]is necessary for utilization of system resources, to
achieve the optimized system performance and for better understanding of
the system. TrueTime is a MATLAB/SIMULINK-based simulator [43] for
networked and embedded control systems that has been developed at Lund
University since 1999 which facilitates co-simulation of networked system.
CHAPTER 4. SMITH PREDICTOR BASED DELAY COMPENSATION
37
Figure 4.3: Smith Predictor response with artificial delay in Simulink
Figure 4.4: Networked PID controller in TrueTime Network Simulator
TrueTime Network is used as a communication channel between controller
and plant.A networked architecture using TrueTime Network is shown in
Fig.4.4 and Fig.4.6 with PID controller and smith predictor respectively and
the corresponding response is shown in Fig.4.5 and Fig.4.7.
CHAPTER 4. SMITH PREDICTOR BASED DELAY COMPENSATION
38
Figure 4.5: Robust PID controller response in TrueTime Network Simulator
Figure 4.6: Networked Smith Predictor structure in TrueTime Simulator
4.2
Study on DC Servo Motor Setup
For experimental purpose we use a laboratory based DC servo motor setup. A
rapid control prototyping process is developed with this where, PID controller
and Smith predictor structure is verified.
4.2.1
Delay Estimation
As discussed in section.4.1, Smith predictor requires exact model of the system to be control and the estimated delay in closed loop.For Delay estimation,
CHAPTER 4. SMITH PREDICTOR BASED DELAY COMPENSATION
39
Figure 4.7: Response of Smith predictor with robust PID controller in TrueTime Simulator
we used two PC’s named as PC-1 and PC-2 are connected with a Local Area
Network(LAN). The process starts with sending a sinusoidal signal from PC1 to PC-2 then receiving the same from PC-2 to PC-1 as shown in Fig.4.8.
Difference of time between the amplitude of signal sent from PC-1 to PC-1
(reference) and received by PC-1 from PC-2 (delayed) will give the amount
of delay. We used UDP communication blocks of XPC target in Simulink
Figure 4.8: Block diagram representation of delay estimation in a LAN
library for this experiment and Fig.4.9 shows the configuration of PC-1 and
PC-2.
Fig.4.10 shows the reference signal and delayed signal. Performing
the delay estimation procedure, the estimated delay found to be 0.06sec.
CHAPTER 4. SMITH PREDICTOR BASED DELAY COMPENSATION
40
Figure 4.9: Simulink blocks for delay estimation using UDP communication
Figure 4.10: Estimated delay between two computers connected in a LAN
4.2.2
Simulation of DC servo Motor Using Artificial Delay
Simulink models for rapid control prototyping with servo motor is shown in
Fig.4.12,Fig.4.13 and Fig.4.14. The responses of these models are shown in
Fig.4.15. The servo setup has two parts a mechanical and digital part. Digital
part is the intermediate between computer algorithm and mechanical part.
Fig4.11 shows the rapid control prototyping structure with DC servo system.
The ADC converts the real physical measurements to digital data so that a
software(MATLAB) based controller can utilize to generate a control signal
to DAC and this analog signal drives the servo system again to generate a
physical measurement. Details of the servo system is explained in chapter 3.
CHAPTER 4. SMITH PREDICTOR BASED DELAY COMPENSATION
41
Figure 4.11: Rapid control prototyping with servo setup
Figure 4.12: PID controller without delay with servo setup
A rapid control prototyping structure with the servo system and a PID
controller without delay in control loops is shown in Fig.4.12, a PID controller
with consideration of delay in both channels is shown in Fig.4.13 and in
Fig.4.14, it shows Smith predictor structure. Delays considered here are
artificial delay block of SIMULINK.
CHAPTER 4. SMITH PREDICTOR BASED DELAY COMPENSATION
Figure 4.13: PID controller with delay with servo setup
Figure 4.14: Smith predictor without delay with servo setup
42
CHAPTER 4. SMITH PREDICTOR BASED DELAY COMPENSATION
43
Figure 4.15: Results of Rapid control prototyping with Servo Motor
Fig.4.15 shows the responses of Rapid control prototyping with Servo Motor with an input of square wave (amplitude =30v and frequency=0.001
hz). The response of PID controller shown in (Fig.a) of Fig.4.15 is good
with less oscillation and overshoot when there is no delay but as we increase
the delay the response deteriorates and tends to unstable (Fig.b and Fig.c)
of Fig.4.15. The Smith Predictor response with delay=0.06sec is shown in
(Fig.d) of Fig.4.15which compensates the delay effects like as Fig.a.
4.3
Chapter Summary
Smith Predictor method to compensate time delay systems has been analyzed
with different PID controllers and compared. We have found that the smith
predictor method gives better results than the PID Controllers. An simple
experimental delay measurement is presented and used in Smith predictor .It
can be concluded that Smith predictor gives the best result in presence of
delay.
Chapter 5
DEVELOPMENT OF A LABVIEW
BASED REAL-TIME NCS SETUP
5.1
Introduction
In this chapter, we demonstrate a networked servo position control system using National Instrument’s (NI) data acquisition (DAQ) card (Model
PCI 6221), LabVIEW software package, and DAQ signal accessory(SCB 68)
board. LabVIEW is a graphical programming environment based on the
concept of data flow programming[47],[48] . It is widely used for data acquisition[49],[50] and instrumentation based control. It also facilitates development of automated instrumentation systems using the PC plug-in Data
Acquisition (DAQ) interfaces.
In view of the above, we attempt to develop a LabVIEW based networked
servo control system for studying
1. How to develop such a network control system.
2. The effects of involvement of networks in a closed loop control system
and,
3. To observe the performance of the PID controller designed in the last
chapter.
44
CHAPTER 5. DEVELOPMENT OF A LABVIEW BASED NCS SETUP
45
This chapter describes the different hardware used for the development
and how the whole set up can be brought into reality by using discretely
available components.
5.1.1
Objective
A networked based position control system is A laboratory based servo setup
is used for this purpose to develop a networked based position control system.
A networked platform is being developed in remote and host architecture
where a remote PC equipped with a Feedback servo motor to be controlled
by a host PC using PI controller. At remote the VI reads the current motor
position of the motor and send to host via LAN using UDP Communication.
The host generates a control input using the received measurement and send
it again to remote via the same network thus creating a closed loop networked
system. Reading the motor position and sending voltage to the motor circuit
are accomplished via the DAQ’s input and output ports respectively.
5.2
LabVIEW Based Communication Interfacing
The PC-Based data acquisition and control[51],[52] is now increasingly recognized as an open and powerful hardware platform, which can provide effective
and reliable control, with no requirement for additional processors or complex hardware additions. Data Acquisition Systems (abbreviated with the
acronym DAS or DAQ) is a process of acquisition of real world analog signal,
conditioning it into a suitable such as voltage or current. The elements of a
PC based data acquisition system are of follows
1. Physical Components
Data acquisition begins with the physical system to be measured. This
physical phenomenon could be the room temperature,the position of
servo motor, the intensity of a light source, the pressure inside a chamber, the force applied to an object, or many other things. A transducer
or sensor is a device that converts a physical phenomenon into a mea-
CHAPTER 5. DEVELOPMENT OF A LABVIEW BASED NCS SETUP
46
surable electrical signal, such as voltage or current. The servo system
described in chapter2 is used as the physical component here.
2. Signal Handling and Noise Reduction
Sometimes transducers generate signals too difficult or too dangerous
to measure directly with a data acquisition device. For instance, when
working with high voltages, noisy environments, or extreme high and low
signals, signal conditioning is essential for an effective data acquisition
system. Signal conditioning maximizes the accuracy of a system, gives
sensors the ability to operate properly, and guarantees safety. The digital unit of the servo setup along with SCB 68 (I/O connector) acts as
the Signal conditioning element. The SCB(Shielded Desktop Connector
Block)-68 is a noise rejecting, shielded I/O connector block as shown in
Fig.5.1. It is the actual interface between the servo digital unit and a
PC. It contains the analog input, analog output, and digital input/output
terminals ports by which it sends a software generated analog signals,
acquires signals to and from the servo setup along with PC.
Figure 5.1: 68-pin Shielded Desktop Connector Block (SCB-68)
3. Data Acquisition Hardware
Data acquisition hardware(PCI-6221) acts as the interface between the
computer and the outside world. It primarily functions as a device that
CHAPTER 5. DEVELOPMENT OF A LABVIEW BASED NCS SETUP
47
digitizes incoming analog signals so the computer can interpret them.
Other data acquisition hardware functionality includes analog output,
digital I/O, counter/timers, and triggering and synchronization circuitry.
Figure 5.2: Data Acquistion Hardware (PCI-6221)
4. Driver and Application Software
Software transforms the PC and data acquisition hardware into a complete data acquisition, analysis, and data visualization tool. There are
two layers of software in a data acquisition system: driver software and
application software. Driver software is the communication layer between the application software and the hardware. The application layer
can be either a development environment in which you build a custom
application that meets specific criteria or a configuration-based program
with preset functionality. Application software adds analysis and visualization capabilities to driver software.
Complete structure of a data acquisition is shown in Fig.5.3 where the mechanical unit acts a the physical process to be control, the digital unit and
SCB 68 both acts as signal condition element for noise reduction and better
signal processing, PCI 6221 is the data acquisition hardware and NI DAQmx
and LabVIEW are the driver and application software receptively .The DAQ
process starts with providing some analog input(reference input) to the motor
CHAPTER 5. DEVELOPMENT OF A LABVIEW BASED NCS SETUP
48
input terminal and acquire the corresponding response from the tachometer
output terminal using LabVIEW DAQ Assistant, both at digital unit.Here
the objective is to match the input and servo response.
Figure 5.3: General Configuration of a Data Acquisition System
5.3
NCS Setup
In this section we’ll discuss about the use LabVIEW application software for
development of NCS setup. LabVIEW is a virtual instrumentation platform
for developing sophisticated measurement, test, and control systems using
intuitive graphical icons and wires. It has two Windows namely Block Diagram window and Front Panel Window. Block Diagram window is meant
for graphical programming where the Front Panel window shows the output. There are three types of choice namely control, constant and indicator.
Control and Constant used for input and indicator for output. We are using
LabVIEW 8.2 provided by National Institute of Technology, Rourkela.
5.3.1
Signal Generation and Acquisition Using LabVIEW
Data Acquisition using LabVIEW an be done by two different ways - one
using DAQmx programming in Measurement I/O palette and another is using
DAQ Assistant in Express VI palette. DAQmx is a graphical programming
CHAPTER 5. DEVELOPMENT OF A LABVIEW BASED NCS SETUP
49
way for data acquisition where DAQ Assistant is a configuration wizard type
set up.A DAQmx based programming for signal acquistion is shown in Fig.5.4
DAQmx programming includes the following steps.
Figure 5.4: DAQmx Programming for reading the real world signal
• Go to Measurement I/O palette under Function palette and choose DAQmx
icon.
• Drag and drop DAQmx Create Virtual Channel to Block Diagram window
– Create control/constant for a physical channel. Choosing a physical
channel activates an analog or digital port in data acquisition hardware, through which signal can generated to and acquired from the
physical component to DAQ hardware.
– Create control/constant for a maximum and minimum value. It
makes the hardware to generate and acquire the measured signal
between a maximum and minimum value. Every DAQ hardware
has a predefined maximum and minimum value e.g. PCI 6221 can
generate and acquire ± 10 volt
• Choose DAQmx Timming to block diagram window. The NI-DAQmx
Timing function configures the timing for hardware-timed data acquisition operations. This includes specifying whether the operation will
be continuous or finite, selecting the number of samples to acquire or
generate for finite operations, and creating a buffer when needed.
CHAPTER 5. DEVELOPMENT OF A LABVIEW BASED NCS SETUP
50
• Choose DAQmx start task to block diagram window.The NI-DAQmx
Start Task function explicitly transitions a task to the running state
• Choose DAQmx read/write to block diagram window.The NI-DAQmx
Read/Write function reads/writes samples from the specified acquisition
task. The different instances of the function allow for the type of acquisition (analog, digital, or counter), the number of virtual channels, the
number of samples, and the data type to be selected.
• Choose DAQmx clear Task to block diagram window.The NI-DAQmx
Clear Task function clears the specified task. If the task is currently
running, the function first stops the task and then releases all of its
resources. Once a task has been cleared, it cannot be used unless it is
recreated
Another way for data acquisition is to use of DAQ Assistant function which is
a easier method than DAQmx Programming.It is wizard based configuration
described in Appendix-A. A complete block diagram of signal generation and
acquisition is shown in Fig.5.5.
Figure 5.5: Signal generation and acquisition using DAQ Assistant
5.3.2
UDP Communication Protocol in LabVIEW
Internet Protocol (IP), User Datagram Protocol (UDP), and Transmission
Control Protocol (TCP) are the basic tools for network communication.UDP
is a minimal message-oriented transport layer that uses ports to provide
CHAPTER 5. DEVELOPMENT OF A LABVIEW BASED NCS SETUP
51
packet application-to-application communication over a network.UDP protocol does not have much in the way of communication control, no explicit
connection to the other side of communication is necessary in order to send
or receive data. A client must simply listen on a specified UDP port, and
send any data to that port of that client is received.
Reasons for choosing UDP over TCP
• UDP is faster than TCP is because there is no form of flow control or
error correction. Which will behave like a time driven sensor and will
send the last received data to plant as actuator.
• It provides a best-effort datagram service to an end system (IP host).
• The simplicity of UDP, however, reduces the overhead from using the
protocol and the services therefore are adequate in many cases.
• UDP is only concerned with speed so it is better to use UDP in an
application sending data from a fast acquisition
• A computer may send UDP packets without first establishing a connection to the recipient.
UDP Communication in LabVIEW
UDP communication provides a simple user interface that conceals the complexities of ensuring faster network communications. There are two PCs
named receiver and sender required for UDP communication. The sender who
sends the signal and receiver who receives the same. To use the UDP protocol
in LabVIEW go to Functions =⇒ Data Communications =⇒ Protocol =⇒
UDP palette for UDP communication in LabVIEW . UDP communication
can be utilized in every applications in LabVIEW with a standard process
which involves opening the connection, reading and writing the information,
and closing the connection see Fig.5.6.
CHAPTER 5. DEVELOPMENT OF A LABVIEW BASED NCS SETUP
52
Figure 5.6: UDP palette for UDP communication in LabVIEW
Basic Steps for Developing UDP Communication Applications
• The UDP open vi opens a UDP socket on the specified port. Create
a control for port and IP address of the another computer. The post
number sould be a local port where the IP address is of another PC with
which you want to create a UDP application.
• UDP Read vi/UDP Write vi used for reading/ writing data from the
server or to the host.UDP Read vi has two attributes, max size is the
maximum number of bytes to read and Time out is the maximum time
limit for a byte transmission above the limit it returns an error.UDP
Write vi has two important attributes IP Address and Port Address.
IP address is same as UDP open. Port Address is the port of another
computer to which you want to write/send some data.
• UDP Close vi Closes a UDP socket.
Each blocks of UDP palette are interconnected with a Connection ID wire
from UDP open vi to UDP close vi that uniquely identifies about the UDP
socket.A complete UDP palette for UDP communication in LabVIEW is
shown in Fig.5.6.
Description of a Open loop UDP communication using LabVIEW
• A ”UDP open vi” for opening a UDP task in a specified port of the
computer.
CHAPTER 5. DEVELOPMENT OF A LABVIEW BASED NCS SETUP
53
• A ”simulate signal vi” (see Fig.5.8) that will generate the required signal
to be transmitted.
• A ”UDP write vi” (see Fig.5.8) and ”UDP read vi” (see Fig.5.7) inside a
while loop for continuously sending and reading the signal respectively.
• A ”UDP close vi” for stop a UDP task.
Figure 5.7: Receiving signal from sender
Figure 5.8: Writing data to the server from client
Fig.5.7 and Fig.5.8 are the receiver and sender respectively in open loop
UDP communication. Fig.5.7 consists of a UDP read vi which reads the
signal that is sent by Fig.5.8 using UDP write vi.
CHAPTER 5. DEVELOPMENT OF A LABVIEW BASED NCS SETUP
54
Description of a Closed loop UDP communication using LabVIEW
Fig.5.7 and Fig.5.8 show one way transmission of signal from host to server.
A complete networked behavior is presented in Fig.5.9 and Fig.5.10 where
there is a closed loop between host hand server.In Fig.5.9 and Fig.5.10 there
is a parallel structure of UDP read and UDP write inside a while loop for
continuous generation and acquisition of signals at the both end in a closed
loop manner. The steps are described as follows.
Figure 5.9: Closed loop signal sending unit
Figure 5.10: Closed loop signal receiving unit
CHAPTER 5. DEVELOPMENT OF A LABVIEW BASED NCS SETUP
55
• Select a simulate signal vi, which generates the signal to be sent.
• Connect the output of the simulate signal vi to the UDP write vi, (see
Fig.5.9)with which will send the generated signal to the receiver.
• This signal received at receiver by a read vi and again send back to
sender unit using (see Fig.5.9) write vi.
5.3.3
Description of the Developed NCS Setup
A networked control system architecture consists of two attributes namely a
plant that is to be controlled by a controller as shown in Fig.5.11.
Figure 5.11: Networked Control Architecture
Developing Networked Plant Block Diagram
Server part is also can be named as process where there is at least a physical
process to be controlled. As shown in Fig.5.11, a servo is the server which acts
as a physical process here. Actuator and Sensor are other elements except
the plant at server. Basic functions to perform by a server are (a)Actuator to
CHAPTER 5. DEVELOPMENT OF A LABVIEW BASED NCS SETUP
56
receive the control input and drive the process, (b)Sensor to sense the process
parameters and send to controller or host. The Plant side configuration is
shown in Fig.5.12 and the procedure is described below.
• Setup a data acquisition VI as described in Appendix-A, for closed loop
data acquisition and generation using LABVIEW DAQ Assistant VI.
• Connect the UDP read to the input of DAQ Assistant VI as controller
input. The DAQ Assistant VI here will act as an actuator.
• The servo position is acquired by using another DAQ Assistant which
acts as a sensor which is connected to UDP write. So the measurement
signal will transmitted to controller unit. The plant unit will remain
same for any controller used.
Figure 5.12: Networked Plant/Process configuration
Developing Networked Block Diagram for Controller
Controller unit where a operator will visualize the plant response. The basic
function at controller is to receives the sensor measurement and calculate the
control input which is again sent to actuator.
CHAPTER 5. DEVELOPMENT OF A LABVIEW BASED NCS SETUP
57
Figure 5.13: Networked PID controller configuration
Configuration of Networked PID controller
• A PID controller for networked application is shown in Fig.5.13 which
can be obtained from Fig.5.10, with some modification.
• Inserting a ”PID controller vi” in it and connecting the output of ”UDP
read vi” and simulate signal as measurement and reference signal of PID
controller respectively .
• The output of ”PID controller vi” is connected to ”UDP write vi”, for
sending control signal to plant.
Configuration of Networked Smith predictor
• Insert a Simulation Loop present in Control design and Simulation palette
of LabVIEW. Insert a transfer function, transport delay PID controller
VI and a summing point into this simulation loop.
• In the transfer function enter the numerator and denominator as per
plant transfer function. This will act as model of the servo plant.
• The summing point has three inputs, reference input, the original servo
response from UDP read and the response of the model plant.
CHAPTER 5. DEVELOPMENT OF A LABVIEW BASED NCS SETUP
58
Figure 5.14: Networked Smith predictor configuration
• The response of actual plant and model plant is subtracted to eliminate
the delay effect and added with output of Simulate signal
• The resultant signal is input to the PID controller.
A networked Smith predictor structure is shown in Fig.5.14
5.4
Experimental Results
A Rapid Prototyping Control (RPC) process involves developing simulation models or generate application code, then using some interfacing device
(DAQ) to run and test this software in real time on a PC connected to the
physical hardware.The benefits of rapid prototyping are.
• It decrease development time.
• It decrease costly mistakes.
• It minimize sustaining engineering changes.
A complete diagram for RCP for networked servo system, is shown in Fig.5.15,
which includes two steps, sigal Generation and Acquistion using DAQ Assistant in closed loop and UDP communication between two PC. The Front
CHAPTER 5. DEVELOPMENT OF A LABVIEW BASED NCS SETUP
59
panel of the closed loop data acquisition is shown in Fig.5.16 whose block
diagram is shown in Fig.5.5.
Figure 5.15: Schematic diagram networked servo control
As shown in Fig.5.16, A square wave (6V amplitude and 1.5 Hz) is generated using LabVIEW and fed to the servo motor. Corresponding position of
the servo is acquired and shown in below of the figure.
The front panel of the UDP communication between two PC is shown
in Fig.5.17. A sine wave (5V amplitude and 0.1 Hz frequency) is sent and
received at the sender side.
In this experiment we used a laboratory based servo motor setup as a real
process and a remote PID controller designed in LabVIEW. A PID controller
is used for the purpose of controlling position of the servo system, whose
response is shown in Fig.5.18 and having a response of high overshoots, whose
block diagram is shown in Fig.5.13.
Fig.5.14 shows the LabVIEW block diagram of the smith predictor and the
response is shown in Fig.5.19. This is clear from that the response in Fig.5.19,
that the overshoots present in PID controller response are eliminated.
CHAPTER 5. DEVELOPMENT OF A LABVIEW BASED NCS SETUP
Figure 5.16: Front panel of Generation and Acquistion of Sigal using DAQ Assiatant
Figure 5.17: Front Panel of Signal Sending and Receiving Using UDP Protocol
60
CHAPTER 5. DEVELOPMENT OF A LABVIEW BASED NCS SETUP
Figure 5.18: Front Panel of Networked PID controller
Figure 5.19: Front Panel of Networked Smith predictor
61
CHAPTER 5. DEVELOPMENT OF A LABVIEW BASED NCS SETUP
5.5
62
Chapter Summary
In this chapter, a real time networked servo control platform is developed by
using LabVIEW. A remote Servo Setup connected by a PC is controlled by
a PID controller using another PC connected by a LAN. A Smith predictor
is also used to compensate the delay in the loop.
Chapter 6
DIRECT APPROACH FOR
STABILIZATION OF NCS
6.1
Introduction
Approaches to delay compensation discussed in earlier are indirect, as they
involve two step controller design. As communication is in discrete, so analysis in continuous is difficult. So a discrete domain approach where the NCS
is stabilized with a feedback controller is discussed in this chapter. The
discrete approach divides the whole system in number of subsystems and
a feedback stabilization involves to finding appropriate switching signals as
well as state/output feedback controllers [29] to make the closed-loop systems (asymptotically) stable. Once the feedback controllers are given, the
closed loop systems are force free, and the switching signal design can then
be carried out using the packet loss in the network channel.
There are difficulties to deal with the modeling, analysis and synthesis
for the NCSs with both delay and packet dropout and is more difficult for
modeling, especially, when the controlled plant is continuous one. So, the
discrete switched system model [31, 28] are introduced.
63
CHAPTER 6. DIRECT APPROACH FOR STABILIZATION OF NCS
64
Figure 6.1: Illustration of packet loss, transmission interval in NCS
6.2
Concept of Transmission Situation
Direct approach for controller design uses the concept of packet transmission.
It models the whole system in terms of packet loss and delay in the control
loop and design a suitable feedback controller for stabilization of the system.
In a NCS there is equally possible cases of packet loss and delay. Delays
arise in two situations, one when there is signal is transmitting from sensor
to controller, another from controller to actuator. A transmission situation
includes the many transmission intervals, a transmission interval is defined
as the time period between two consecutive successful transmissions. A successful transmission in NCS refers to no packet loss and no delay, in between
generation of data packets at sensor and reception of the same at actuator
through a communication channel.
A typical transmission situation is shown Fig.6.1.The state information
at the sensor end are sampled with constant time-interval although due to
information losses in the sensor-to-controller communication all these state
information does not reach the controller. Similarly, there are further infor-
CHAPTER 6. DIRECT APPROACH FOR STABILIZATION OF NCS
65
mation losses in the controller-to-actuator channel and the control input at
the actuator end is updated whenever new control information is received
therein. Dark bars at sensor as shown in Fig.6.1 represents the packet generation. Dark bars at controller end represents the received packets and dotted
bars are the lost packets so the same at the actuator. Consecutive dark bars
at sensor, controller and actuator will considered as a successful transmission. The time period between two consecutive successful transmission is
the transmission interval, and which will provide the information about the
packet loss and delay. Each arbitrary packet loss condition will be treated
as a subsystem. A switch system approach consider each subsystem for controller design. The direct approach for controller design includes the following
process. (a) Modelling of NCS into different subsystems according to transmission interval. (b) Formulation of Linear matrix inequalities (LMI) for
designing a controller for each subsystem.
6.3
Modeling According to Transmission Interval
A discrete-time plant sampled with constant time-period may be represented
at k th time-instant as:
x(k + 1) = Ax(k) + Bu(k)
(6.1)
where x(k) ∈ Rn is the states and u(k) ∈ Rm the plant input; A, B are known
matrices. The objective is to stabilize the system using feedback closed via
a communication network. Considering the static feedback-gain controller
the control input can be written as: u(k) = Kx(k − l) : l ∈ [1, 2, ...L],
where K is an appropriate dimensional matrix required to be suitably designed so as the system is stabilized even if there are arbitrary information
losses in the feedback channel represented by the arbitrarily delayed state
x(k − l). Transmission interval (tk ) refers to the time duration between two
successful transmissions of data packets from sensor to actuator via communication channel and controller.It means at a time-instant when a packet
66
CHAPTER 6. DIRECT APPROACH FOR STABILIZATION OF NCS
generated from sensor it should reach at actuator through controller at the
same time-instant and the difference between two such transmission is termed
as a transmission interval as illustrated in Fig.6.1. Successive transmission
intervals are denoted as {0, t1 , ...tk , tk+1 , tk+2 ...} ∈ N .
Considering a transmission interval from tk to tk+1 , and assuming the
initial condition (x(m) ) is transmitted successfully then.
x(m + 1) = Ax(m) + BKx(m)
(6.2)
For the next time instant, for successful transmission the above (6.2) becomes
x(m + 1) = Ax(m + 1) + BKx(m + 1)
(6.3)
x(m + 2) = A2 x(m) + ABKx(m) + BKx(m)
(6.4)
Otherwise,
If there are consecutive L1 packet loss, in-between these interval tk+1 and tk ,
assuming the final state is(x(n) ) then,(6.4) becomes.
X(n−m)−1
n−m
x(n) = (A
+
Al1 BK)x(m))
l=0
(6.5)
This can be written as.
XL1 −1
XL1 −1
(tk+1 −tk )
l1
L1
x(tk+1 ) = (A
+
A BK)x(tk )) = (A +
Al1 BK)x(tk ))
l1 =0
l1 =0
(6.6)
Eq.(6.6), gives the system model incorporating the packet loss information
of the system.
6.4
Stability Criteria and Controller Design
Lemma-1
Given the symmetric matrixS =
"
S11 S12
#
where S11 is r × rthen
T
S12
S22
the following three statements are true [29].
Statement 1:S < 0;
Statement 2:S11 < 0; S22 − S12 T S11 −1 S1 2 < 0
Statement 3:S2 2 < 0; S1 1 − S1 2 S22 −1 S12 T < 0;
67
CHAPTER 6. DIRECT APPROACH FOR STABILIZATION OF NCS
Here the time interval between tk and tk+1 is referred as one transmission
interval and tk+1 − tk = L1 is the maximum packet loss in that transmission
interval. Assuming
AK 1 = (AL1 +
XL1 −1
l=1
Al BK)
, (6.6) can be written as.
x(tk+1 ) = Ak1 x(tk )
(6.7)
Defining a switched function that will consists of all the packet loss information up to a successful transmission. z(0) = x(0),z(1) = x(t1 ), ...z(k) =
x(tk ), ..., Then (6.7) can be written as.
z(k + 1) = Ak1 z(k)
(6.8)
The discrete NCS described in (6.1) with packet loss will be stabilized, if (6.8).
is stable. For stabilization adopting a Lyapunov function for the switched
system as.
V (k, z(k)) = z T (k)P z(k)
(6.9)
where P is the parameter to be designed such that the system will be
asymptotically stable. The difference of (6.9) along the switched system is.
∆V (z(k)) = z T (k + 1)P z(k + 1) − z T (k)P z(k)
T
XL1 −1
XL1 −1
T
L1
l1
= z (k)[A +
A BK] P [AL1 +
Al1 BK]z(k) − z T (k)P z(k)
l1 =0
l1 =0
The stability condition will be
[AL1 +
XL1 −1
l1 =0
T
Al1 BK] P P −1 P [AL1 +
XL1 −1
l1 =0
Al1 BK] − P < 0
and using lemma-1 can be written as.
"
P −1 l1
T #
−P
[AL1 + Ll11=0
A BK] P
<0
P −1 l1
P [AL1 + Ll11=0
A BK]
−P
(6.10)
68
CHAPTER 6. DIRECT APPROACH FOR STABILIZATION OF NCS
Post and pre-multiplying the above (6.10) by diag P −1 , P −1 , and assuming (
P −1 = X) the final LMI formulated as "
PL1 −1 l1
T#
L1
−X X[A + l1 =0 A BK]
∗
−X
<0
(6.11)
Eq.(6.11), is the desired LMI for controller design. This LMI will give the
controller gain after solving for asymptomatically stabilization.
6.5
Simulation Studies
Simulation studies of NCS is performed in TrueTime co-design tool and real
time using UDP protocol in SIMULINK.
6.5.1
TrueTime Simulations
Data
1: 1
Trigger
ACTUATOR
y(n)=Cx(n)+Du(n)
x(n+1)=Ax(n)+Bu(n)
In1
Data
Out1
1: 1
PACKET LOSS
SWITCH
PLANY DYNAMICS
IN DISCRETE TIME
Trigger
TRIGGER
SENSOR
1 Schedule
TRUETIME NETWORK
Data
K
1: 1
Data
1: 1
Trigger
Trigger
CONTROLLER
SEND
RECEIVE
Figure 6.2: TtueTime/SIMULINK block for virtual NCS configuration
Fig.6.2, shows the TrueTime virtual NCS environment for controller implementation. A discrete time statespace block in SIMULINK acts as a model
of plant. TrueTime Network acts as network and TrueTime send block and
TrueTime receive block at plant side acts as sensor and actuator respectively.
A packet loss switch will generate random packet loss for the system. The
response of the controller design for consecutive 7 packet loss is shown in
69
CHAPTER 6. DIRECT APPROACH FOR STABILIZATION OF NCS
RESPONSE IN TRUETIME VIRTUAL NETWORKED ENVIRONMENT
5
StateX
1
StateX
2
4
StateX
3
3
State Values
2
1
0
-1
-2
0
50
100
150
200
250
300
350
400
450
500
Time
Figure 6.3: Response of state feedback controller in TrueTime virtual network
Fig.6.3, which stabilize the system as the states of the system (X1 ,X2 ,X3 )
are approaching towards the equilibrium point.
6.5.2
UDP Simulations
ACTUATOR
UDP
Receive
Binary
y(n)=Cx(n)+Du(n)
x(n+1)=Ax(n)+Bu(n)
Unpack
Unpack
SYSTEM DYANMICS IN
DISCRETE STATE-SPACE
RECEIVE FROM
CONTROLLER
PLANT CONFIGURATION
CLRCV
SEND
SENSOR
UDP
Send
Binary
SEND TO
CONTROLLER
Pack
Out1
Pack
PACKET LOSS
GENERATOR
In1
Figure 6.4: SIMULINK UDP communication-sender/plant configuration
UDP protocol requires a sender and a receiver, here two PCs named as
plant and controller will act as sender(shown in Fig.6.4) and receiver(shown
in Fig.6.5,) respectively. These PCs are separated, but connected to a shar-
70
CHAPTER 6. DIRECT APPROACH FOR STABILIZATION OF NCS
ing network. Plant with sensor and actuator communicating with controller
with this network. The controller response in UDP communication is shown
in Fig.6.6.It is clear that the controller successfully stabilize the system in
presence of real-time uncertainties and packet losses as the states are approaching to equilibrium point.
UDP
Receive
Binary
Unpack
[K]
Unpack
Gain
RECEIVE
FROM PLANT
RCV
CONTROLLER CONFIGURATION
To Workspace
UDP
Send
Binary
Pack
SEND TO PLANT
Pack
Figure 6.5: SIMULINK UDP communication-receiver/controller configuration
RESPONSE IN REALTIME UDP COMMUNICATION
5
State X
1
State X
2
4
State X
3
State Values
3
2
1
0
-1
-2
0
50
100
150
200
250
Time
300
350
400
450
Figure 6.6: Response of state feedback controller in UDP network in SIMULINK
500
CHAPTER 6. DIRECT APPROACH FOR STABILIZATION OF NCS
6.6
71
Chapter Summary
A direct approach for NCS stabilization using state feedback controller design
based on packet loss information modeling and Lyapunov stability criteria is
presented. Stabilization criteria is carried out by use of LMI. As this is
a discrete domain and state space approach it describes the each state of
the system unlike form the indirect method. The designed controller for
maximum 7 consecutive packet loss in a single transmission is examined in
NCS co-design and real-time environment using TrueTime and MATLAB
respectively.
Chapter 7
CONCLUSIONS AND SCOPE FOR
FUTURE WORK
NCS are distributed control systems that uses communication networks in
implementing feedback control strategies. Use of such networks induces delay
and packet loss in the closed loop. This thesis deals with development of
a real-time networked servo system using LabVIEW for understanding the
concept of NCS. PID controller and Smith predictor are implemented for the
NCS. The discrete approach for stabilization of the NCS also discussed.
7.1
Contributions of the Thesis
The following are the salient contributions of the thesis.
• An identification of the Servo system using system identification tool box
of MATLAB is described.
• A real-time networked servo platform for studying NCS characteristics
is developed. This uses LabVIEW as application software, PCI 6221 as
DAQ card, SCB-68 as a connector cable between PC and PCI 6221 with
the driver software.
• PID controller using Z-N tuning and Gain margin phase margin specification based tuning is performed and implemented in real-time for servo
72
CHAPTER 7. CONCLUSIONS AND SCOPE FOR FUTURE WORK
73
position control. Smith predictor used for delay compensation in the
feedback loop.
• The packet dropouts in NCS occurs during data transmission from one
network component to the other. A discrete time approach is discussed
to match with the discrete nature of the network and the PC-based
control system. A Lyapunov stability criteria of NCS is derived and
studies on the design have been made using TrueTime virtual network
and SIMULINK.
7.2
Future Scope of Work
• Controller used here are not adaptive to match with the stochastic behavior of network characteristics, an adaptive or predictive controller
implementation may be the next work.
• The networked servo control system developed here is confined to a LAN.
This may be extended to, Internet based servo control system.
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Appendices
78
Appendix A
Configuration wizard of DAQ Assistant
VI
A brief introduction to LabVIEW and LabVIEW based VI is described in
Sec.5.1 and Sec.5.2. This Appendix-A describes about the modern way to
communicate with real world instruments using LabVIEW DAQ Assistant.
DAQ Assistant can be found by left click in block diagram window then
Function =⇒ Express palette =⇒ Input =⇒ DAQ Assistant VI as shown
in Fig.A.1.For data acquisition the DAQ Assistant wizard involves two basic
Express Tasks,these are signal generation and signal acquisition. The basic
requirement for a DAQ Assistant is that you have installed National Instruments DAQ hardware device (PCI 6221) and a latest version of DAQmx
Device Driver software.
A.0.1
Steps for Signal Acquisition
1. Place the DAQ Assistant VI on the block diagram window.A pop up
window will appear as Fig.A.2 allowing you to configure your Express
Task.
2. Choose the required task (Acquire or Generate Signals) and also the type
of signal that you want to perform. Here we choose the an voltage type
analog input as in Fig.A.3
79
APPENDIX A. CONFIGURATION WIZARD OF DAQ ASSISTANT VI
80
Figure A.1: DAQ Assistant in Function palette at Block Diagram Window
3. Once you completed the Step-2 ,you’ll have the option to select from
which device(if there are more than one hardware device are installed)
and physical channels (depending upon the DAQ hardware device) you
want to acquire from see FigA.4.
4. After completing the Step-3,click the Finish button.This will bring up
the analog input task configuration page where you can set up your task
like The Signal Input Range, Acquisition Mode, Samples to read Rate
to acquire data exactly the way you want as shown in Fig.A.5
5. Click the OK button after completing Step-1 to 4.All the settings are
stored in DAQ Assistant VI,and the data will be available on the data
output. Wiring this output to an analysis VI, file I/O VI, directly to an
indicator for analysis and visualize.
APPENDIX A. CONFIGURATION WIZARD OF DAQ ASSISTANT VI
81
Figure A.2: DAQ Assistant Configuration window for choosing the Express Task
Figure A.3: DAQ Assistant Configuration of the Express Task for acquisition of voltage type analog
input
A.0.2
Steps for Signal Generation
1. The procedure for Signal Generation is same as Signal Acquisition, if
we choose Signal Generation instead of Signal Acquisition at Step-1 of
above procedure in Sec.A.0.1, which is shown in Fig.A.2
APPENDIX A. CONFIGURATION WIZARD OF DAQ ASSISTANT VI
82
Figure A.4: DAQ Assistant Configuration of the Express Task for Selecting the Hardware Device
and Physical Channels
Figure A.5: Task configuration page of DAQ Assistant
Publications From This Thesis
• B.Subudhi, S.Ghosh, S.Bhuyan, B.Raju and M.M.Gupta. Smith Predictor Based Delay Compensation in Networked Control of Digital Servo
Motor, chapter Innovations and Advances in Communications, Information and Network security. Macmillan Publishers India, 2010.
• B.Subudhi, S.Ghosh, S.Bhuyan, B.Raju and M.M.Gupta, ”Smith predictor based delay compensation in networked control of digital servo
motor”, In International Conference on Data Management, Gaziabad,
pp.123-134, March, 2010
• B Subudhi, S Ghosh and S.Bhuyan. Learning networked control system
using labview submitted to IEEE Trans. on Education.
83
Authors Biography
Srinibas Bhuyan was born to Sri Sarat Chandra Bhuyan and Smt. Minakshi
Bhuyan on 15th May, 1986 at Kendrapara, Odisha, India. He obtained a
Bachelors degree in Applied Electronics and Instrumentation Engineering
from Biju Patanaik University of Technology (B.P.U.T), Rourkela, Odisha in
2007. He joined the Department of Electrical Engineering, National Institute
of Technology, Rourkela in January 2009 as an Institute Research Scholar to
pursue M.Tech by Research.
84
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