UNIVERSITI PUTRA MALAYSIA FARZIN PILTAN FK 2011 162 METHODOLOGY OF FUZZY-BASED TUNING FOR SLIDING MODE CONTROLLER
UNIVERSITI PUTRA MALAYSIA
FARZIN PILTAN
FK 2011 162
METHODOLOGY OF FUZZY-BASED TUNING FOR SLIDING MODE CONTROLLER
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METHODOLOGY OF FUZZY-BASED TUNING FOR SLIDING MODE CONTROLLER
By
FARZIN PILTAN
Thesis Submitted to the School of Graduate Studies, Universiti Putra Malaysia, in Fulfillment of the Requirements for the Degree of Master of Science
November 2011
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DEDICATION
I dedicate this dissertation to:
My wife, Nazi for all lovely support in these years,
My dearest daughter Pantea who is the aim of my life,
My Mother; My Moon
and
My Father; My Sun
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Abstract of thesis to be presented to the Senate of Universiti Putra Malaysia in fulfillment of the requirements for the degree of Master of Science
METHODOLOGY OF FUZZY-BASED TUNING FOR SLIDING MODE CONTROLLER
By
FARZIN PILTAN
November 2011
Chairman: Nasri. B. Sulaiman, PhD
Faculty: Engineering
Design a nonlinear controller for second order nonlinear uncertain dynamical systems is one of
the most important challenging works. This thesis focuses on the design, implementation and
analysis of a chattering free Mamdani’s fuzzy-based tuning error-based fuzzy sliding mode
controller for highly nonlinear dynamic PUMA robot manipulator, in presence of uncertainties.
In order to provide high performance nonlinear methodology, sliding mode controller is selected.
Pure sliding mode controller can be used to control of partly known nonlinear dynamic
parameters of robot manipulator. Conversely, pure sliding mode controller is used in many
applications; it has two important drawbacks namely; chattering phenomenon which it can
causes some problems such as saturation and heat the mechanical parts of robot manipulators or
drivers and nonlinear equivalent dynamic formulation in uncertain dynamic parameter.
In order to reduce the chattering this research is used the linear saturation function boundary
layer method instead of switching function method in pure sliding mode controller and fuzzy
sliding mode controller. In order to solve the uncertain nonlinear dynamic parameters, implement
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easily and avoid mathematical model base controller, Mamdani’s performance/error-based fuzzy
logic methodology with two inputs and one output and 49 rules is applied to pure sliding mode
controller. The results demonstrate that the error-based fuzzy sliding mode controller with
saturation function is a model-free controllers which works well in certain and partly uncertain
system. Pure sliding mode controller with saturation function and error-based fuzzy sliding mode
controller with saturation function have difficulty in handling unstructured model uncertainties.
To solve this problem applied fuzzy-based tuning method to error-based fuzzy sliding mode
controller for adjusting the sliding surface gain (𝜆𝜆 ). Since the sliding surface gain (𝜆𝜆) is adjusted
by fuzzy-based tuning method, it is nonlinear and continuous. In this research new 𝜆𝜆 is obtained
by the previous 𝜆𝜆 multiple sliding surface slopes updating factor (𝛼𝛼) which is a coefficient varies
between half to one. Fuzzy-based tuning error-based fuzzy sliding mode controller is stable
model-free controller which eliminates the chattering phenomenon without to use the boundary
layer saturation function. Lyapunov stability is proved in fuzzy-based tuning fuzzy sliding mode
controller based on switching (sign) function. This controller has acceptable performance in
presence of uncertainty (e.g., overshoot=0%, rise time=0.8 second, steady state error = 1e-9 and
RMS error=1.8e-12). Fuzzy-based tuning error-based fuzzy sliding mode controller and Guo and
Woo adaptive fuzzy sliding mode controller have been comparatively evaluated through
simulation, for robotic manipulator. Most of nonlinear controllers need real time mobility
operation so one of the most important devices which can be used to solve this challenge is Field
Programmable Gate Array (FPGA). FPGA can be used to design a controller in a single chip
Integrated Circuit (IC). To have higher implementation speed with good performance SMC is
implemented on Spartan 3E FPGA using Xilinx software (controller computation time=30.2 ns,
Max frequency=63.7 MHz and controller action frequency=33 MHZ).
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Abstrak tesis yang dikemukakan kepada Senat Universiti Putra Malaysia sebagai memenuhi sebahagian keperluan untuk ijazah Master Sains
KAEDAH PENALAAN SAMAR-BERASASKAN UNTUK PENGAWAL MOD GELANGSAR
Oleh
FARZIN PILTAN
November 2011
Pengerusi: Nasri. B. Sulaiman, PhD
Fakulti: Kejuruteraan
Merekabentuk pengawal tak linear untuk sistem dinamik tertib kedua yang tidak menentu
merupakan salah satu daripada kerja-kerja terpenting yang mencabar. Tesis ini memberi tumpuan
kepada rekabentuk, pelaksanaan dan analisis kabur-penalaan berasaskan gelugutan percuma
Mamdani berasaskan kesilapan kabur pengawal mod gelangsar bagi pengolah dinamik robot
PUMA yang sangat tak linear, dengan kehadiran ketidaktentuan. Pengawal mod gelangsar yang
tulen boleh digunakan untuk mengawal sebahagian parameter dinamik tak linear yang diketahui
untuk pengolah robot. Dalam usaha untuk mengurangkan gelugutan, kajian ini menggunakan
kaedah lapisan sempadan ketepuan fungsi linear bukan fungsi menukar kaedah pengawal mod
tulen gelongsor dan pengawal mod gelangsar kabur. Untuk menyelesaikan parameter-parameter
dinamik tak linear yang tidak menentu, melaksanakan dengan mudah dan mengelakkan model
pengawal asas matematik, prestasi Mamdani / kesilapan berasaskan kaedah logik kabur dengan
dua masukan dan satu keluaran dan 49 peraturan digunakan kepada pengawal mod gelangsar
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tulen. Keputusan menunjukkan bahawa mod berasaskan kesilapan pengawal gelongsor kabur
dengan fungsi tepu adalah pengawal model bebas yang berfungsi dengan baik dalam sistem
tertentu dan sebahagiannya tidak menentu. Untuk menyelesaikan masalah ini kaedah penalaan
kabur berasaskan kepada kesilapan kabur pengawal mod gelangsar dengan penyesuaian gandaan
permukaan gelangsar (λ) digunakan. Oleh kerana gandaan permukaan gelangsar (λ) diselaraskan
oleh kaedah penalaan berasaskan kabur, ianya tak linear dan berterusan. Dalam penyelidikan ini
nilai baru λ diperolehi oleh nilai λ sebelumnya yang mempunyai berbilang cerun permukaan
gelangsar yang mengemas kini faktor (α) iaitu satu pekali yang berubah di antara setengah
hingga satu. Berdasarkan kepada penalaan kesilapan-kabur pengawal mod gelangsar yang
merupakan pengawal bebas model yang stabil yang menghapuskan fenomena gelugutan tanpa
menggunakan fungsi lapisan sempadan tepu. Kestabilan Lyapunov dibuktikan dalam penalaan
kabur berasaskan pengawal mod gelangsar kabur berdasarkan pensuisan (tanda) fungsi.
Pengawal ini mempunyai prestasi yang boleh diterima dengan kehadiran keadaan yang tidak
menentu (contohnya, terlajak = 0%, masa naik = 0.8 saat, ralat keadaan mantap = 1E-9 dan ralat
RMS = 1.8e-12). Kebanyakan pengawal tak linear memerlukan masa operasi mobiliti sebenar
jadi salah satu peranti yang paling penting yang boleh digunakan untuk menyelesaikan cabaran
ini adalah tatasusunan get boleh aturcara medan (FPGA). FPGA boleh digunakan untuk
merekabentuk satu pengawal dalam satu cip tunggal litar bersepadu (IC). Untuk mempunyai
kelajuan yang yang lebih tinggi dalam pelaksanaan dengan prestasi SMC yang baik dilaksanakan
pada Spartan 3E FPGA menggunakan perisian Xilinx (masa pengiraan pengawal = 30.2 ns,
frekuensi maximum = 63,7 MHz dan pengawal tindakan kekerapan = 33 MHZ).
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ACKNOWLEDGEMENT
I would like to express sincere gratitude to my supervisor Dr. Nasri B. Sulaiman for all
his faithful guidance and also his inestimable comments to complete the thesis on related
research.
I would like to express my appreciation to Assoc. Prof. Dr. Mohammad Hamiruce
Marhaban for his great help also for providing me a deep thinking of control and artificial
intelligence.
I would like to thank Assoc. Prof. Dr. Rahman Ramli for his plentiful supports in robotic science.
I really owe my sincere thanks to my family specially my wife and my daughter for their
great help, lovely support in these years and understanding of their time lost during my studies.
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This thesis was submitted to the Senate of Universiti Putra Malaysia and has been
accepted as fulfillment of the requirement for the degree of Master of Science.
The members of the Supervisory Committee are as follows:
Nasri b. sulaiman, PhD Lecturer
Faculty of Engineering
Universiti Putra Malaysia
(Chairman)
Mohammad Hamiruce b. Marhaban, Assoc. Prof. Dr Lecturer
Faculty of Engineering
Universiti Putra Malaysia
(Member)
Abdul Rahman b. Ramli, Assoc. Prof. Dr Lecturer
Faculty of Engineering
Universiti Putra Malaysia
(Member)
HASANAH MOHD GHAZALI, PhD
Professor and Dean School of Graduate Studies Universiti Putra Malaysia Date:
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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 it has not been previously, and is not concurrently submitted
for any other degree at Universiti Putra Malaysia or other institutions.
FARZIN PILTAN
Date: 25 July 2011
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TABLE OF CONTENTS ABSTRACT II
ABSTRAK IV
ACKNOWLEDGEMENTS VI
APPROVAL VII
DECLARATION
LIST OF TABLES
LIST OF FIGURES
IX
XIII
XV
LIST OF ABBREVIATIONS XIX
CHAPTER
1) INTRODUCTION 1
1.1 Motivation and Background 1
1.2 Problem Statements 5
1.3 Objectives 7
1.4 Scope of Work 8
1.5 Contributions 8
1.5 Thesis Outline 9
2) LITERATURE REVIEW 11
2.1 Introduction 11
2.2 Robot Manipulators 12
2.2.1 History and Application of Robotics 13
2.2.2 Classification of robot manipulators and its effect on the design
controllers
14
2.2.3 Rigid-Body Kinematics 15
2.2.4 Dynamic of Robotic Manipulator 21
2.3 Control Historical Review 24
2.4 Linear Control of Robot Manipulators 25
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2.4.1 Joint space control Vs. Operational Space Control 26
2.4.2 Independent-Joint Space Control 27
2.5 Nonlinear Control of Robotic Manipulator 27
2.5.1 Inverse Dynamics Control 28
2.5.2 Passivity-Based Control 28
2.5.3 Feed-back Linearization (Computed-Torque Control) and the robot
manipulator’s (PUMA 560) applications
29
2.5.4 Sliding Mode Control (Variable Structure Control) and the robot
manipulator’s (PUMA 560) applications
33
2.5.5 Fuzzy logic methodology and its application to SMC 39
2.5.5.1 Foundation and basic definitions of fuzzy logic 42
2.5.5.2 Fuzzy Controller Structure 48
2.5.6 Adaptive Control Methodology 49
2.6 Field Programmable Gate Arrays (FPGAs) 52
2.6.1 Xilinx Spartan 3EArchitectureal overview 54
2.7 Summary 55
3) METHODOLOGY
58
3.1 Introduction 58
3.2 Reduce the chattering in pure sliding mode controller 61
3.3 Design of error-based fuzzy sliding mode controller 63
3.4 Design of position fuzzy-based tuning error-based fuzzy sliding mode controller 75
3.4.1 Proof of stability in fuzzy-based tuning error-based fuzzy sliding mode
controller
86
3.4.2 Comparison of fuzzy-based tuning error-based fuzzy sliding mode
controller and Guo &Woo adaptive fuzzy sliding mode controller 89
3.5 Design of FPGA-based PD Sliding Mode controller for PUMA Robot
Manipulator and implementation in (Xilinx ISE)
93
3.6 Modeling of PUMA 560 Robotic Manipulator 99
3.6.1 Kinematics of PUMA 560 Robot Manipulator 99
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3.6.2 Dynamics of PUMA560 Robot Manipulator 102
3.7 Summary 110
4) RESULT AND DISCUSSION
112
4.1 Introduction 112
4.2 Results 113
4.2.1 Comparison of computed torque controller and sliding mode controller:
with switching function and with boundary layer
113
4.2.2 Comparison of the PD-SMC with boundary layer and PID-SMC with
boundary layer
136
4.2.3 Error-based fuzzy Sliding Mode Controller 146
4.2.4 Fuzzy-based tuning error-based fuzzy Sliding Mode Controller 154
4.2.5 Comparison of fuzzy-based tuning error-based fuzzy sliding mode
controller and Guo &Woo adaptive fuzzy sliding mode controller
166
4.2.5 FPGA-based PD Sliding Mode Controller to control of PUMA-560 robot
manipulator (Xilinx ISE 9.1)
172
4.4 Summary 178
5) CONCLUSION AND RECOMMENDATION
181
5.1 Conclusion 181
5.2 Recommendation 183
REFERENCE
184
APPENDIX A 189
APPENDIX B 191
LIST OF PUBLICATIONS 192
BIODATA OF STUDENT 197