UNIVERSITI PUTRA MALAYSIA METHODOLOGY OF FUZZY-BASED TUNING FOR SLIDING MODE CONTROLLER FARZIN PILTAN FK 2011 162
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
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
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 Chairman: Nasri. B. Sulaiman, PhD Faculty: Engineering By FARZIN PILTAN November 2011 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 II
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). III
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 Pengerusi: Nasri. B. Sulaiman, PhD Fakulti: Kejuruteraan Oleh FARZIN PILTAN November 2011 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 IV
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). V
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. VI
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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: VIII
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 IX
ABSTRACT ABSTRAK ACKNOWLEDGEMENTS APPROVAL DECLARATION LIST OF TABLES LIST OF FIGURES LIST OF ABBREVIATIONS CHAPTER TABLE OF CONTENTS 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 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 II IV VI VII IX XIII XV XIX 14 X
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 2.5.4 Sliding Mode Control (Variable Structure Control) and the robot manipulator s (PUMA 560) applications 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 3.4.2 Comparison of fuzzy-based tuning error-based fuzzy sliding mode controller and Guo &Woo adaptive fuzzy sliding mode controller 3.5 Design of FPGA-based PD Sliding Mode controller for PUMA Robot Manipulator and implementation in (Xilinx ISE) 3.6 Modeling of PUMA 560 Robotic Manipulator 99 3.6.1 Kinematics of PUMA 560 Robot Manipulator 99 29 33 86 89 93 XI
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 4.2.2 Comparison of the PD-SMC with boundary layer and PID-SMC with boundary layer 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 4.2.5 FPGA-based PD Sliding Mode Controller to control of PUMA-560 robot manipulator (Xilinx ISE 9.1) 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 197 113 136 166 172 XII