implementation of mrac, svmpc and pid control...

IMPLEMENTATION OF MRAC, SVMPC AND PID CONTROL BASED ON

DIRECT DIGITAL CONTROL APPLICATION FOR DC SERVOMOTOR

SALEHA BTE MOHAMAD SALEH

A project report submitted in partial fulfillment

of the requirement for the award of the degree of

Master of Engineering

(Electrical - Mechatronics & Automatic Control)

Faculty of Electrical Engineering

Universiti Teknologi Malaysia

NOVEMBER, 2005

iii

To my husband, Zairulazha.

Thanks for your tremendous love and support.

I owe a lot to you.

iv

ACKNOWLEDGEMENT

Alhamdulillah, a lot of praise and ‘syukur’ to ALLAH. I wish to express my sincere

gratitude and appreciation to my supervisor, Associate Professor Dr. Mohd. Fua’ad

bin Haji Rahmat for giving me a chance to handle this project. Without his never-

ending guidance, patience and encouragement throughout this project, I would never

finish the thesis as it is. Thank you very much! Not forget to the laboratory assistant,

Mr. Fazli, who spends time to help my researches in the lab.

I would like to thank the Kolej Universiti Teknikal Kebangsaan Malaysia

(KUTKM) for sponsoring my study in the form of a scholarship. I also would like to

thank Mr. Mohd. Ariff Mat Hanafiah and Mr. Syed Najib Syed Salim, to whom I

owe thanks for helping me, secure the scholarship.

A very special thanks to my beloved parents, Mariah Abdullah and Mohamad

Saleh Ahmad, for their enduring patience, understanding and for all the pray.

Without both of you, I do not think that I can get through this. Last but not least, I

would like to use this opportunity to say thank you to my beloved brother and his

wife, Mohamad Nor, for taking care of our mum and dad. Finally, I would like to

express my appreciation to all my friends, especially to Zuraida and Herdawati,

thanks for your love and constant moral support.

Thank you to all of you

Assalamualaikum.

v

ABSTRACT

The project focused on speed control of DC servomotor under load variation

using Direct Digital Control technique. The main objective is to design and develop

GUI software for speed control experiment, where Single Variable Model Predictive

Control (SVMPC), Model Reference Adaptive Control (MRAC) and PID

controllers’ design approaches has been applied. The main purpose of using the

SVMPC is to achieve perfect control using an Internal Model Control (IMC) strategy.

The desired behavior of the adaptive controller is expressed by utilizing reference

model, and the algorithms have been realized using the Lyapunov method and MIT

rules.

The Direct Digital Control approach is selected to replace the conventional

method regarding on controlling the speed of DC motor because of its advantages in

terms of cost reduction, simplicity, flexibility and give better performance than

previous one. The original speed control experiment is conducted and data is

recorded. Based on the information that been gathered, the controllers have been

designed and the system is simulated using MATLAB to analyze their initial

performance. The computer is connected to MS150 Modular Servo System via

AX5412 data acquisition card and Microsoft Visual Basic 6.0 is used to conduct the

experiment. Field-testing is implemented to compare the results between the original

and modified system within three types of controller. Finally, the performance of the

system is analyzed and validation is done in terms of time response, robustness and

percentage of error.

vi

ABSTRAK

Projek ini memfokuskan kepada sistem kawalan halaju bagi motor servo arus terus

yang dikenakan pelbagai beban dengan menggunakan teknik kawalan digital secara

langsung. Objektif utama projek ini adalah untuk merekabentuk dan membangunkan

perisian interaktif komputer untuk ujikaji sistem kawalan halaju, di mana teknik

Kawalan Model Ramalan bagi satu pembolehubah, Kawalan Adaptasi Model

Rujukan dan Kawalan PID diaplikasikan bagi rekabentuk sistem kawalan untuk

motor tersebut. Matlamat utama menggunakan Kawalan Model Ramalan bagi satu

pembolehubah adalah untuk mendapatkan kawalan sempurna dengan menggunakan

strategi Kawalan Model Dalaman (IMC). Manakala sifat kawalan yang dikehendaki

diterjemahkan dalam bentuk model rujukan dengan menggunakan kaedah Lyapunov

dan aturan MIT.

Teknik kawalan digital secara langsung dipilih untuk menggantikan kaedah

lama dalam pengawalan halaju bagi motor arus terus kerana kelebihan-kelebihannya

iaitu dari aspek pengurangan kos, fleksible, mudah dan memberikan prestasi yang

lebih baik dari kaedah terdahulu. Eksperimen asal bagi kawalan halaju telah

dijalankan dan data-datanya telah direkodkan. Berdasarkan daripada maklumat yang

didapati, sistem kawalan telah direkabentuk dan simulasi bagi sistem dilakukan

untuk menilai prestasi asal dengan menggunakan perisian MATLAB. Komputer

telah disambungkan kepada sistem servo MS150 menerusi kad DAQ dan perisian

Microsoft Visual Basic 6.0 telah digunakan untuk menjalankan eksperimen. Ujian

terhadap sistem dijalankan untuk tujuan perbandingan di antara sistem asal dengan

sistem yang telah diubahsuai. Prestasi sistem dianalisa dan pengesahan telah dibuat

dari aspek tindakbalas masa, ketegapannya dan peratus sisihan dengan nilai yang

dikehendaki.

vii

TABLE OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES xi

LIST OF FIGURES xii

LIST OF APPENDICES xvi

LIST OF ABBREVIATIONS xvii

viii

1 INTRODUCTION 1

1.1 Direct Digital Control Overview

1.2 The benefit of Direct Digital Control

1.3 Objectives

1.4 Scopes of Work

1.5 Research Methodology

1.6 Thesis Outline

1

4

5

5

5

8

2 LITERATURE REVIEW 10

2.1 The Virtual Laboratory

2.2 Enhancing Electrical Engineering Teaching

Method

2.3 Design of PID controller for speed control

10

13

15

3 SPEED CONTROL OF DC SERVOMOTOR 19

3.1 Introduction

3.2 Power Supply Unit 150E

3.3 Motor Unit 150F

3.4 Servo Amplifier 150D

3.5 Attenuator Unit 150B

3.6 Reduction Gear Tacho Unit

3.7 Operational Amplifier Unit 150A

3.8 Loading Unit 150L

3.9 Armature Control

19

19

20

21

21

22

23

23

24

4 METHOD OF ANALYSIS 26

4.1 Modeling of the system

4.2 System Identification

4.3 Controller Design for DC Servomotor System

4.3.1 PID controller

4.3.1.1 Ziegler-Nichols Methods

4.3.1.2 Controller Modes

26

31

33

33

35

37

ix

4.3.2 Model Reference Adaptive Control

(MRAC)

4.3.2.1 The MIT rule

4.3.2.2 Lyapunov stability theorem

4.3.3 Single Variable Model Predictive

Control (SVMPC)

4.3.3.1 Internal Model Control

4.3.3.2 The IMC Strategy

4.3.3.3 Practical Design of IMC

41

42

45

46

47

48

51

5 DIRECT DIGITAL CONTROL 53

5.1 Introduction

5.2 Device Driver Installation

5.3 AXIOM’s Hardware Device Setup

5.4 Connection

5.5 Creating Graphical Interface Forms

53

54

55

57

59

6 RESULT AND ANALYSIS 63

6.1 Introduction

6.2 Original Experiment

6.2.1 Experiment 1: Determination of

Tachometer Gain

6.2.2 Experiment 2: Speed – input voltage

curve at no load

6.2.3 Experiment 3: Open Loop Speed

Control System

6.2.4 6.2.4 Experiment 4: Gain effect on speed

when load varies

63

64

64

67

69

72

x

6.3 Simulation Result using MATLAB Simulink

6.3.1 Experiment 5: MRAC controller on

speed control

6.3.2 Experiment 6: IMC controller on speed

control

6.4 Interactive Learning

6.4.1 Graphical User Interface (GUI)

6.4.2 Experimental Result via DDC

Technique

6.4.2.1 Experiment 1 – To determine

tachometer gain

6.4.2.2 Experiment 2 – To determine speed-

input voltage curve

6.4.2.3 Experiment 3 – Open-loop speed

control system

6.4.2.4 Experiment 4 – Gain effect on speed

when load varies

6.4.2.5 Experiment 5 – MRAC controller on

speed control

6.4.2.6 Experiment 6 – IMC controller on

speed control

6.5 Comment on Performance of Controllers

75

75

77

77

78

84

84

85

86

86

88

91

92

7 CONCLUSION 94

7.1 Conclusion

7.2 Future Work

94

95

REFERENCES 97

APPENDIX A 99

APPENDIX B 158

xi

LIST OF TABLES

TABLE DESCRIPTION PAGE

2.1 Advantages of a Virtual Laboratory 11

4.1 Ziegler Nichols Rules 36

5.1 Action between modules 62

6.1 Result for Experiment 1 66

6.2 Result for Experiment 2 68

6.3 Result for Experiment 3 (Attenuator at position ‘10’;

Vin = 14.41V)

70

6.4 Result for Experiment 3 (Attenuator at position ‘1’;

Vin = 0.8V)

70

6.5 Result for Experiment 4 (Gain = 1 (Attenuator at

position 10))

73

6.6 Table for Experiment 4 (Gain = 5 (Attenuator at position

1))

73

6.7 Comparison regarding on the performances among P,

PD, PI and PID controllers

87

6.8 Comparison regarding on the controller’s performance 92

xii

LIST OF FIGURES

FIGURE DESCRIPTION PAGE

1.1 Equipment Setup 2

1.2 Block Diagram Comparison (a) The Original Closed

Loop Speed Control System (b) The Modified Closed

Loop Speed Control System

3

1.3 Components that been eliminated (a) attenuator (b)

operational amplifier (c) oscilloscope

4

1.4 Design flow 7

2.1 Hardware structure of the virtual laboratory 12

2.2 PID controller 16

2.3 Control system block diagram 18

3.1 Power Supply Unit 20

3.2 DC Motor Unit 20

3.3 Servo Amplifier Unit 21

3.4 Attenuator Unit 22

3.5 Tachogenerator Unit 22

3.6 Operational Amplifier Unit 23

3.7 Loading Unit 24

3.8 Equipments of speed control of dc servomotor 24

3.9 Armature Control 25

3.10 Speed vs. Voltage 25

3.11 Speed vs. Torque 25

xiii

4.1 Armature-controlled dc motor with load 26

4.2 Block diagram of a dc motor (armature-controlled)

system

28

4.3 Block diagram of the system (a) Open loop system

(b) Closed loop system

30

4.4 Input output form 31

4.5 Identification of the system 32

4.6 S-shape response curve 36

4.7 P-controller algorithm (with sampling period is about

50 ms)

37

4.8 PI-controller algorithm (with sampling period is

about 50 ms, Ti = 50 ms and KI = KP * Ts/Ti)

38

4.9 PD-controller algorithm (with sampling period is

about 50 ms, Td = 50 ms and KD = KP * Td/Ts)

39

4.10 PID-controller algorithm (with sampling period is

about 50 ms, Td = 50 ms, Td = 50 ms, KI = KP *

Ts/Ti and KD = KP * Td/Ts)

40

4.11 Block diagram of an adaptive system 41

4.12 Block diagram of a model reference adaptive control 42

4.13 MRAC using the MIT rule’s algorithm 44

4.14 MRAC using the Lyapunov’s stability theory 46

4.15 Open loop control strategy 47

4.16 Schematic of the IMC scheme 48

4.17 Internal Model Control (IMC) algorithm 52

5.1 AX5412 Data Acquisition Card 54

5.2 Device Manager Window 55

5.3 Device setting 56

5.4 Base Address Switch Setting 54

5.5 AX5412 (CN1) Pin Assignment 58

5.6 Hardware connection 59

5.7 Communication between modules 61

6.1 Overall Project 64

6.2 Connection for Experiment 1 65

xiv

6.3 Graph of motor speed vs. tachometer voltage 66

6.4 Graph of motor speed vs. input voltage 68

6.5 Graph of motor speed vs. brake position 71

6.6 Connection for Experiment 4 72

6.7 Graph of motor speed vs. brake position 74

6.8 Simulation result for Experiment 5 (a) MRAC using

Lyapunov stability theory (b) MRAC using MIT rule

76

6.9 Simulation result for IMC controller 77

6.10 Graphical User Interface for Speed Control of DC

Servomotor (Setting)

78

6.11 Graphical User interface for Speed Control of DC

Servomotor (Run the Experiment)

80


Servomotor (Result)

81


Servomotor (MRAC)

82


Servomotor (IMC)

83

6.15 Result for Experiment 1 (a) Speed vs. tachometer

voltage (b) Tachometer gain

84

6.16 Result for Experiment 2 (a) Speed vs. input voltage

(b) Speed motor and input voltage’s ratio

85

6.17 Result for Experiment 3 (Speed vs., Position of the

Magnetic Brake)

86

6.18 Result for Experiment 4 (a) P and PD controller (b)

PI and PID controller

87

6.19 Graph of the Speed via PID controller (at no-load) 88

6.20 Result for Experiment 5 using Lyapunov method (a)

Reference model and actual output response (b)

Current output voltage

89

6.21 Result for Experiment 5 using MIT rule (a)

Reference model and actual output response (b)

Current output voltage

90

xv

6.22 Result for Experiment 6 (a) Reference model and

actual output response (b) Desired output (c)

Current output

91

xvi

LIST OF APPENDICES

APPENDIX DESCRIPTION PAGE

Appendix A Software Source Code 99

Appendix B Formula Derivation 158

xvii

LIST OF ABBREVIATIONS

ADC - Analog-Digital Converter

API - Application Program Interface

DAC - Digital-Analog Converter

CD - Compact Disc

CN - Connector

CV - Control Variable

DAS - Data Acquisition System

DAQ - Data Acquisition

DC - Direct Current

DDC - Direct Digital Control

Err - Error

GPIB - General Purpose Interface Bus

GUI - Graphical User Interface

IMC - Internal Model Control

I/O - Input / Output

J - Loss function

LSLNR - Linear System Learner

MIMO - Multi Input Multi Output

MIT - Massachusetts Institute of Technology

MPC - Model Predictive Control

MRAC - Model Reference Adaptive Control

OS - Overshoot; operating system

PC - Personal Computer

PCI - Peripheral Component Interface

PI - Proportional-Integral

PID - Proportional-Integral-Derivative

xviii

PLC - Programmable Logic Control

PV - Process Variable

OOP - Object-Oriented Programming

O/P - Output

ISA - Integrated System Architecture

SP - Set point

SVMPC - Single Variable Model Predictive Control

tp - Peak Time

ts - Settling Time

VB - Visual Basic

Ve - Error Voltage

Vg - Tachometer voltage

Vin - Input voltage

rpm - rotation per minute

CHAPTER I

INTRODUCTION

1.2 Direct Digital Control Overview

The major change occurring at the present is the increasing number of user

friendly software that make it possible for student to experience new and fast ways of

learning. In minutes, simulation, controller and real world interfacing can be created.

The software package is developed to help students to learn and explore the

experiment with an interesting way. A picture worth a thousand words.

In DDC, the control laws are implemented in a digital computer as a

computer programs. In realizing a real time computer controlled system in which a

digital computer, specifically a microcomputer or PC is one of the major component

that acts as a controller in the control loop [1]. The computer must be connected

somehow to the external event and the program instructions are necessary to direct

the interaction between the computer and the external activity.

2

There are two major parts:

Hardware Interfacing – connecting the computer to external equipment.

Figure 1.1 shows the equipment setup for this project

Software Design – programming the computer to carry out its control

calculation (control laws) while interacting with external components. Visual

Basic will be used to program the DAS board since this program is easy to

learn it’s code programming and user friendly

Figure 1.1: Equipment Setup

ure 1.2 sh ws the comparis the original and modified closed

loop speed control system. The system (pl a continuous-time

system. The ‘heart’ of the controller is a di ital computer. The problem of realizing a

digital controller is mainly one of developing a com .

(a)

Fig o on between

ant) under control is

g

puter program

Input speed

AttenuatorServomplifierA Motor

Tachometer

Summingfier

-

Ampli+

Rotatiospeed

nal output

3

res.

g controllers, any change in the characteristics of the controller is

sually laborious and expensive, since it requires changes in the structure and the

lements of the controller. In digital controller, the designer has the flexibility to use

e same hardware equipment to realize and test different control algorithms. This

an be done because only the program that realizes the control algorithm has to be

hanged for every controller realization. However, the performance of the digital

control is strongly dependent on many fact rs, among which are the sampling period,

possible computational, the word length in the microprocessor and the interface

devices used [2].

ut speed

(b)

Figure 1.2: Block Diagram Comparison (a) The Original Closed Loop Speed Control

System (b) The Modified Closed Loop Speed Control System

Digital controllers present significant advantages over classical analog

controllers. One of them is a greater flexibility in modifying the controller’s featu

For classical analo

u

e

th

c

c

o

Inp

Computer ServoAmplifier

Motor

Tachometer

AX5412DAS board

Rotationaloutput speed

4

1.2

enefit of using DDC are listed below:

Performance

t is

will not be exactly the nominal values. Meanwhile, by

using DDC technique the controller gain is exactly the value set by user

ii.

iii.

he number of hardware will be redu e contro

lace in software. Figure 1.3 shows the components that will be eliminated in

losed-loop speed control system and replace by software. It permits fast and

ce the

associated control law can simply be programmed.

(c)

Figure 1.3: Co ts that been eliminated (a) attenuator (b) operational amplifier

(c) oscilloscope

The benefit of Direct Digital Control

B

i. Improve Accuracy and

The gain provided by connecting operational amplifier and attenuator uni

different with the gain calculated because the tolerance of the gain defining

resistor values, which

Improve Effectiveness

By using DDC method, it is more flexible in changing set points and the

overall control logic. Students are able to see system response through the

virtual oscilloscope

Reduce Cost

T ced since th ller function takes

p

c

low cost implementation of even more sophisticated control system sin

(a) (b)

mponen

5

1.3 Object

The ob

i. To apply Direct Digital Control technique on the speed control of DC

motor.

ii. To improve the system performance through designing and tuning of

the controllers.

aphical user interface (GUI) for speed control

experiment and analyze the system response.

1.4 Scopes

i. trol method towards controlling speed

of DC motor.

ii. Implementing the proposed controller: MRAC, SVMPC and PID.

iii. Designing the programming structure for controller via Microsoft

Visual Basic 6.0.

cquisition Board to interface between the

computer and DC Servomotor.

1.5 Research Methodology

. Also

e theory of conventional controllers.

ives

jectives of this project are as follows:

iii. To design a gr

of Work

Applying the Direct Digital Con

iv. Using AX5412 Data A

Literature review to understand the concept and identify the

techniques, problems and current works.

ii. Define the modeling and the method will be used for the system

understand th

6

iii. n and MATLAB simulation of the system.

v. s.

vi. Design and writing program to modify the system using DDC

application.

through DAS card.

viii. Field-testing is conducted to compare the results between the original

and modified system. Analyze the system’s performance.

esign steps of work methodology can be simplified as shown in Figure 1.4.

System identificatio

iv. Conducting the procedures of the original system and get the results.

Learn up VB programming and the Axiom driver function

vii. Interface with hardware between computer and DC servomotor

D

7

Figure 1.4: Design flow

ConclusionC& Analysisomparison

Objective

OriginalExperiment

Writing VB program

Visual Basic Software

Study / Review

Integration with Hardware

Hardware Connection & DAQ Card Installation

Simulation using MATLAB

Previous Works from others

Theory

Identify the system

FulfillSpec?

Yes

No

8

hapter 1: Introduction

introduction to the project report, objectives, scope of

works a ftware

hapter 2: Literature Review

w on the Virtual Laboratory,

Enh

hapter 3: Speed Control of DC Servomotor

explained through this chapter. The DC servomotor

prin

hapter 4: Method of Analysis

l be introduced in this chapter. Starting with

modeli s

hapter 5: Direct Digital Control

This chapter will explain how the Direct Digital Control application will be

luding the installation and connection of the devices.

1.6 Thesis Outline

C

This chapter gives the

nd methodology taken. It also described briefly the hardware and so

used in completing this project.

C

This chapter covers the literature revie

ancing Electrical Engineering Teaching Method and Design of PID controller for

speed control, how it works and its components.

C

DC Servomotor devices are

ciple of operation is discussed. Device characteristics and functions are also

included.

C

There are several concepts wil

ng of the system, discretize the analog controller and parameter tuning proces

of PID. MRAC and IMC controller design implementation.

C

implemented in this project. Inc

9

he results are determined through the original experiments of the speed

control, simulation and through the experiment where the used apparatus has been

been an

Chapter 7: Conclusion

his last chapter presented the overall conclusion for the project. For the

future work, some suggestions have been included in order to improve the work that

has been conducted.

Chapter 6: Result & Analysis

T

modified. Analysis regarding on the performance of the controller design also has

alyzed and validated.

T

98

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[1] Control System. Holt, Rinehart and Winston, INC,

[2] Digital Control Systems. Prentice Hall, 1996

[3] Horton and Thomas Agayoff. Teaching Power

boratory. IEEE, 2001

[4] n, Jianping Chen, Yuan Zhuang and Kay Chen Tan.

evelopment of a Web-Based Laboratory for Control Experiments on a

d Tank Apparatus. IEEE Transactions on Education, Vol 44, No.1,

[5] ntation on the Internet. Engineering Science

[6] onnie. Enhancing Classical Control Education via

EE Control System, 1999

[7] asilio, S. R. Matos. Design of PI and PID Controllers with Transient

ion, Vol 45, No.4,

[8] zotto. Speed Control of an Autonomous Mobile

obot – Comparison between a PID Control and a Control using Fuzzy Logic.

z. Soc. Mech. Sci. Vol 24, No.2, 2002

Benjamin C. Kuo. Digital

1980

P. N. Paraskevopoulos.

Saul Goldberg, William F.

Conversion in a Virtual La

C.C.Ko, Ben M. Che

D

Couple

2001

K.K.Tan and C.Y.Soh. Instrume

and Educational Journal, 2001

Raymond C. Garcia and B

Interactive GUI Design. IE

J. C. B

Performance Specification. IEEE Transactions on Educat

2002

P. E. Silveira, Souza, Bia

R

J. Bra

99

[9] Modular Servo System MS150Mk2 DC, Synchro, &

[10] M. pal. Control Systems – Principle and Design. McGraw Hill, Second

002

[11] ystems Engineering. John Wiley & Sons, 2000

[12] Katsuhiko Ogata. Discrete-Time Control System. Prentice Hall, 1995

[13] D. Johnson. Process Control Instrumentation Technology. Prentice

all, 2000

[14] arl Johan Astrom and Bjorn Wittenmark. Adaptive Control. Addison-

Second Edition, 1995

[15] . Bordons. Model Predictive Control. Springer, Second

dition, 2004

[16] ntrol – Designing Processes and Control

ic Performance. Second Edition, 2000

[17] o., Ltd. AX 5412 High Speed Data Acquisition Board

nual

[18] – How to program. Prentice Hall, 1999

[19] Robert H. Bishop. Modern Control Systems. Prentice

5

Feedback Instrument Ltd.

AC Basic Experiments. Book 1

Go

Edition, 2

Norman S. Nise. Control S

Curtis

H

K

Wesley Publishing Company, Inc,

E. F. Camacho and C

E

Thomas E. Marlin. Process Co

Systems for Dynam

Axiom Technology C

User’s Ma

Deitel, T. R. Nieto. Visual Basic 6

Richard C. Dorf and

Hall, Tenth Edition, 200

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