UNIVERSITI PUTRA MALAYSIA

FARZIN PILTAN

FK 2011 162

METHODOLOGY OF FUZZY-BASED TUNING FOR SLIDING MODE CONTROLLER

© COPYRIG

HT UPM

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

© COPYRIG

HT UPM

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

© COPYRIG

HT UPM

II

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

© COPYRIG

HT UPM

III

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).

© COPYRIG

HT UPM

IV

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

© COPYRIG

HT UPM

V

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).

© COPYRIG

HT UPM

VI

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.

© COPYRIG

HT UPM

VII

© COPYRIG

HT UPM

VIII

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:

© COPYRIG

HT UPM

IX

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

© COPYRIG

HT UPM

X

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

© COPYRIG

HT UPM

XI

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

© COPYRIG

HT UPM

XII

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