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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
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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
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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
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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
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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.
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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
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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∞.
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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.
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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:
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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
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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
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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
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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
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