UNIVERSITI PUTRA MALAYSIA

BASHEER NOAMAN HUSSEIN

FK 2010 52

DESIGN OF ROBUST PARTICLE SWARM OPTIMIZATION - TUNED FUZZY CONTROLLER FOR A SINGLE AXIS SMALL MAGNETIC

LEVITATION SYSTEM

© COPYRIG

HT UPM

DESIGN OF ROBUST PARTICLE SWARM OPTIMIZATION - TUNED

FUZZY CONTROLLER FOR A SINGLE AXIS SMALL MAGNETIC

LEVITATION SYSTEM

By

BASHEER NOAMAN HUSSEIN

Thesis submitted to the School of Graduate Studies of University Putra Malaysia in

the fulfilment of the requirements for the Degree of Master of Science

OCTOBER 2010

© COPYRIG

HT UPM

ii

DEDICATION

This thesis is dedicated to

My dearest Parents, Brother and Sisters, and Grandmother

The understanding and encouragement they provided during all these years of

study

Also, this thesis is dedicated to

My fiancée Sara Ali and the memory of my cousin Yasir Kahtan

I love you

© COPYRIG

HT UPM

iii

Abstract of the thesis presented to the School of Graduate Studies of University Putra

Malaysia in the fulfilment of the requirement for the degree of Master of science

DESIGN OF ROBUST PARTICLE SWARM OPTIMIZATION - TUNED

FUZZY CONTROLLER FOR A SINGLE AXIS SMALL MAGNETIC

LEVITATION SYSTEM

By

BASHEER NOAMAN HUSSEIN

October 2010

Chairman: Nasri bin Sulaiman, PhD

Faculty: Engineering

A control system is robust when it has low sensitivity, it is stable over the range of

parameter variations and the performance continues to meet the specification in the

presence of a set of changes in the system parameters and disturbances.

In this work the design of the robust linear and nonlinear controllers for Single Axis

Magnetic Levitation System are presented. These controllers must overcome the

problems of the high steady state error and robustness in the magnetic levitation

system. The design of H∞ robust controller is presented first and the system

dynamics are linearized to be suitable for applying the H∞ robust control technique.

The magnetic force is regulated using this controller to achieve robust stability and

performance, disturbance/noise rejection and asymptotic tracking with zero steady

© COPYRIG

HT UPM

iv

state error. The plant with structured uncertainty is expressed in terms of

unstructured multiplicative uncertainty to cover the overall change in system

parameters. The unstructured multiplicative uncertainty is determined using curve

fitting method.

The designed H∞ controller has assured robust stability and robust performance of

the single axis magnetic levitation system with parametric uncertainty. The

parameters of the performance and control weighting functions that are obtained

using trial and error lead to obtain a robust controller that achieves force control of

magnetic levitation system.

The design of PD like fuzzy robust controller is presented secondly in this work. The

Particle Swarm Optimization method (PSO) is used to find the optimal values of the

Scalar gains and the membership functions subject to the robust control and

minimum error constraints. The designed PD like fuzzy controller has assured robust

stability and robust performance of the nonlinear model of single axis magnetic

levitation system. This controller minimizes the rules from 64 rules to 16 rules and

achieved zero steady state error without using the integral.

Finally, a comparison between the performances of the H∞ controller and the optimal

fuzzy logic controller has been made. It shows that the nonlinear optimal fuzzy logic

controller achieve better performance than the linear H∞ controller.

© COPYRIG

HT UPM

v

Abstrak tesis yang dikemukakan kepada Senat Universiti Putra Malaysia sebagai

memenuhi keperluan untuk ijazah Master Sains

REKABENTUK DARI TEGAP KAWANAN ZARAH PENGOPTIMUMAN

PENYESUAIAN KAWALAN SAMAR BAGI SUATU UNTUK KECIL

SISTEM MAGNET PENGANGKATAN

Oleh

BASHEER NOAMAN HUSSEIN

Oktober 2010

Pengerusi: Nasri bin Sulaiman, PhD

Fakulti: Kejuruteraan

Sistem kawalan adalah tegap apabila ia mempunyai kepekaan yang rendah,

keseimbangan di dalam julat variasi pembolehubah dan mempunyai prestasi yang

menepati spesifikasi walaupun terdapat perubahan pembolehubah dan gangguan di

dalam sistem.

Di dalam kajian ini, rekaan alat kawalan lelurus dan tidak lelurus yang tegap untuk

sistem magnet pengangkatan satu paksi dibentangkan. Alat kawalan ini mencapai

tahap ketegapan untuk variasi di dalam pembolehubah sistem dalam julat yang luas.

Rekaan alat kawalan yang kuat lagi tegap H∞ dibentangkan dan dinamik sistem

dileluruskan supaya teknik H∞ sesuai diaplikasikan. Daya magnet diaturkan

menggunakan alat kawalan ini untuk mencapai kekuatan dan ketegapan dari segi

keseimbangan dan prestasi, menolak gangguan dan menjejak isyarat rujukan. Kilang

© COPYRIG

HT UPM

vi

dengan ketidakpastian berstruktur dilahirkan dalam bentuk ketidakpastian

pendaraban tidak berstruktur untuk melitupi perubahan keseluruhan di dalam

pembolehubah sistem. Ketidakpastian pendaraban berstruktur diperolehi melalui

kaedah garisan lengkungan yang sesuai.

Alat kawalan H∞ dapat memastikan kekuatan dan ketegapan dari segi keseimbangan

dan prestasi untuk sistem magnet pengangkatan satu paksi dengan ketidakpastian.

Pembolehubah fungsi pemberat diperolehi kaedah cuba jaya seterusnya mendorong

untuk mencapai alat kawalan yang kuat lagi tegap untuk system kawalan daya

magnet pengangkatan.

Di samping itu, rekaan alat kawalan samar seperti PD turut dibentangkan di dalam

penyelidikan ini. Kaedah yang dikenali sebagai Particle Swarm Optimization (PSO)

digunakan untuk mendapatkan nilai keuntungan dan fungsi keahlian yang optimum,

tertakluk pada kawalan yang kuat lagi tegap dan ralat yang kecil. Rekaan alat

kawalan samar seperti PD memastikan kekuatan dan ketegapan dari segi

keseimbangan dan prestasi bagi model sistem magnet pengangkatan satu paksi yang

tidak lelurus. Alat kawalan ini meringkaskan peraturan dari 64 ke 16 peraturan.

Akhir sekali, perbandingan di antara alat kawalan H∞ dan kawalan samar optimal

dibuat. Ia menunjukkan alat kawalan samar optimal mencapai prestasi yang lebih

baik berbanding alat kawalan H∞.

© COPYRIG

HT UPM

vii

ACKNOWLEDGEMENT

In the name of Allah SWT, the Most Gracious and the Most Merciful, I offer my

humble thank gratitude You for giving me the strength to complete this thesis.

First and foremost, my sincere gratitude and appreciation goes to my supervisor, Dr.

Nasri Sulaiman, and to my co-supervisors Dr. Raja Mohd Kamil and Associate

Professor Dr. Mohammad Hamiruce for their constructive ideas, criticism, guidance

and patience throughout the long duration of preparing this thesis. They have

successfully guided me through some stressful times and were always willing to

sharpen my understanding of this thesis and other academic activities.

I am also greatly indebted to Hazem I. Ali for his valuable insights, comments, ideas

and suggestions in the course of improving and completing this thesis. I wish to

thank Zeyad Assi Obaid for his kind assistance rendered to me in my study.

I wish to mention my beloved father, Noaman Hussein Ali who was instrumental in

this accomplishment. My greatest pleasure would be to share this moment with him.

Due appreciation is also extended to my mother, Amal Abed Shakir, my sisters and

brother who have given me their prayers, encouragement, and unfailing support for

me to go throughout this long journey.

Finally, I would like to extend my gratitude and affection to my Fiancée Sara Ali.

Thank you for providing me the support with your patience, love, encouragement,

and inspiration that has greatly facilitated the completion of this challenging effort.

© COPYRIG

HT UPM

viii

I certify that a Thesis Examination Committee has met on __11/10/2010__ to

conduct the final examination of Basheer Noaman Hussein on his thesis entitled

“Design of Robust Particle Swarm Optimization – Tuned Fuzzy Controller for

Single Axis Small Magnetic Levitation System " in accordance with the

Universities and University Colleges Act 1971 and the Constitution of the University

Putra Malaysia [P.U.(A)] 15 March 1998. The Committee recommends that the

Student be awarded the relevant Master of Science.

Members of the Thesis Examination Committee were as follows:

Norhisam b. Misron, PhD

Associate Professor

Faculty of Engineering

Universiti Putra Malaysia

(Chairman)

Samsul Bahari b. Mohd. Noor, PhD

Senior Lecturer

Faculty of Engineering

Universiti Putra Malaysia

(Internal Examiner)

Roslina bt. Mohd. Sidek, PhD

Associate Professor

Faculty of Engineering

Universiti Putra Malaysia

(Internal Examiner)

Mohd. Nasir Taib, PhD

Professor

Faculty of Electrical Engineering

Universiti Teknologi MARA

(External Examiner)

BUJANG KIM HUAT, PhD

Professor and Deputy Dean

School of Graduate Studies

Universiti Putra Malaysia

Date:

© COPYRIG

HT UPM

ix

This thesis was submitted to the Senate of Universiti Putra Malaysia and has been

accepted as fulfilment of the requirement for the degree of Master of Science. The

members of the Supervisory Committee were as follows:

Nasri bin Sulaiman, PhD

Senior Lecturer

Faculty of Engineering

Universiti Putra Malaysia

(Chairman)

Mohammad Hamiruce Marhaban, PhD

Associate Professor

Faculty of Engineering

Universiti Putra Malaysia

(Member)

Raja Mohd Kamil bin Raja Ahmed, PhD

Senior Lecturer

Faculty of Engineering

Universiti Putra Malaysia

(Member)

HASANAH MOHD GHAZALI, PhD Professor and Dean

School of Graduate Studies

Universiti Putra Malaysia

Date: December / 2010

© COPYRIG

HT UPM

x

DECLARATION

I declare that the thesis is my original work except for quotations and citations,

which have been duly acknowledged. I also declare that it has not been previously,

and is not concurrently, submitted for any other degree at Universiti Putra Malaysia

or at any other institution.

BASHEER NOAMAN HUSSEIN

Date: 11 / 10 / 2010

© COPYRIG

HT UPM

xi

TABLE OF CONTENTS

Page

DEDICATION ii

ABSTRACT iii

ABSTRAK v

ACKNOWLEDGEMENT vii

APPROVAL viii

DECLARATION x

LIST OF TABLES xiii

LIST OF FIGURES xiv

LIST OF ABBREVIATIONS xvii

LIST OF SYMBOLS xx

CHAPTER

1 INTRODUCTION

1.1 Introduction 1

1.2 History of Magnetic Levitation 2

1.3 Principle of Magnetic Levitation 3

1.3.1 Types of Levitation 7

1.3.2 Categories of Magnetic Levitation Systems 8

1.4 Problem Statement 8

1.5 Objectives 9

1.6 Thesis Contributions 10

1.7 Scope of the Work 10

1.8 Thesis Outline 11

2 LITERATURE REVIEW

2.1 Introduction 13

2.2 Overview on Magnetic Levitation Systems 13

2.3 Heavy-Current MLS (Magnetic Levitation Vehicles) 14

2.4 Light-Current MLS Used in Micro-Machines 15

2.5 Applications of Magnetic Levitation 16

2.6 System Description 17

2.7 Modelling and Control Approaches 18

2.8 Controller 34

2.9 Optimal Fuzzy Logic Controller 37

2.10 Summary 40

3 METHODOLOGY

3.1 Introduction 41

3.2 System Model and Dynamics 43

© COPYRIG

HT UPM

xii

3.2.1 Nonlinear Model 43

3.2.2 Runge-Kutta 4th Order Method 46

3.2.3 Linear Model 47

3.2.4 System Discretization 55

3.3 Uncertainty Model Construction 57

3.4 Controller Design 61

3.5 PD like Fuzzy Controller Design 64

3.6 Particle Swarm Optimization (PSO) 68

3.7 Optimal PD like Fuzzy Controller Design 73

3.7.1 Fuzzy Controller with Gain Tuning using

PSO

73

3.7.2 PSO-Based Fuzzy Robust Controller Design 74

3.8 Summary 76

4 RESULTS AND DISCUSSION

4.1 Introduction 77

4.2 Controller Design 77

4.3 Robust PD like Fuzzy Controller Design 86

4.3.1 Application to Linear Model 86

4.3.2 Application to Nonlinear Model 96

4.4 Results Comparison and Discussion 103

4.5 Summary 104

5 CONCLUSION AND FUTURE WORK

5.1 Conclusion 105

5.2 Suggestions for Future Work 106

REFERENCES 107

APPENDIX A 117

APPENDIX B 119

BIODATA OF STUDENT 120

LIST OF PUBLICATIONS 121