Fractional Order Motion Controls

Ying Luo, South China University of Technology, China. Currently Assistant Professor in the Department of Automatic Control and Engineering, South China University of Technology, Dr Luo joined the? BS-Ph.D program? in 2004. He went to Utah State University, Logan, UT, USA, as a visiting scholar/exchange PhD?from September 2007 to February 2009 and received the PhD degree in Automation Science and Engineering from South China University of Technology, Guangzhou, China, in July 2009. Dr Luo has been based at Utah State University, Logan, UT, USA, as a postdoctoral fellow from September 2009. He has worked on several patents and has published research in some key journals. YangQuan Chen, Utah State University, USA. Dr Chen is Associate Professor in the Department of Electrical & Computer Engineering as well as Director at the Center for Self-Organizing & Intelligent Systems (CSOIS) of Utah State University, Logan. Prior to this he has held positions at Seagate Tech. Int., Singapore, National University of Singapore and Nanyang Technological University. He is the owner of 14 patents and Senior Member of the IEEE.

Acronyms xix Foreword xxiii Preface xxv Acknowledgments xxix PART I FUNDAMENTALS OF FRACTIONAL CONTROLS 1 Introduction 3 1.1 Fractional Calculus 3 1.2 Fractional Order Controls 9 1.3 Fractional Order Motion Controls 20 1.4 Contributions 22 1.5 Organization 22 PART II FRACTIONAL ORDER VELOCITY SERVO 2 Fractional Order PI Controller Designs for Velocity Servo Systems 25 2.1 Introduction 25 2.2 FOPTD Systems and Three Controllers Considered 27 2.3 Design Specifications 27 2.4 Fractional Order PI and [PI] Controller Designs 28 2.5 Simulation 38 2.6 Chapter Summary 39 3 Tuning Fractional Order PI Controllers for Fractional Order Velocity Systems with Experimental Validation 41 3.1 Introduction 41 3.2 Three Controllers to Be Designed and Tuning Specifications 42 3.3 Tuning Three Controllers for FOVS 42 3.4 Illustrative Examples and Design Procedure Summaries 43 3.5 Simulation Illustration 45 3.6 Experimental Validation 49 3.7 Chapter Summary 54 4 Relay Feedback Tuning of Robust PID Controllers 59 4.1 Introduction 59 4.2 Slope Adjustment of the Phase Bode Plot 62 4.3 The New PID Controller Design Formulae 65 4.4 Phase and Magnitude Measurement Via Relay Feedback Tests 66 4.5 Illustrative Examples 67 4.6 Chapter Summary 72 5 Auto-Tuning of Fractional Order Controllers with Iso-Damping 73 5.1 Introduction 73 5.2 FOPI and FO[PI] Controllers Design Formulae 75 5.3 Measurements for Auto-Tuning 80 5.4 Simulation Illustration 80 5.5 Chapter Summary 87 PART III FRACTIONAL ORDER POSITION SERVO 6 Fractional Order PD Controller Tuning for Position Systems 91 6.1 Introduction 91 6.2 Fractional Order PD Controller Design for Position Servos 92 6.3 Design Procedures 94 6.4 Simulation Example 95 6.5 Experiments 99 6.6 Chapter Summary 101 7 Fractional Order [PD] Controller Synthesis for Position Servo Systems 105 7.1 Introduction 105 7.2 Position Control Plants and Design Specifications 106 7.3 Fractional Order [PD] Controller Design 106 7.4 Parameter Design Examples and Bode Plot Validations 108 7.5 Implementation of Two Fractional Order Operators 110 7.6 Simulation 111 7.7 Experiment 120 7.8 Chapter Summary 122 8 Time-Constant Robust Analysis and Design of Fractional Order [PD] Controller 123 8.1 Introduction 123 8.2 Problem Statement 124 8.3 FO[PD] Tuning Specifications and Rules 125 8.4 The Solution Existence Range and An Online Computation Method 127 8.5 Experiment 135 8.6 Chapter Summary 136 9 Experimental Study of Fractional OrderPDController Synthesis for Fractional Order Position Servo Systems 139 9.1 Introduction 139 9.2 Fractional Order Systems and Fractional Order Controller Considered 140 9.3 FOPD Controller Design Procedure for the Fractional Order Position Servo Systems 141 9.4 Simulation Illustration 144 9.5 Experimental Study 148 9.6 Chapter Summary 153 10 Fractional Order [PD] Controller Design and Comparison for Fractional Order Position Servo Systems 155 10.1 Introduction 155 10.2 Fractional Order Position Servo Systems and Fractional Order Controllers 156 10.3 Fractional Order [PD] Controller Design 156 10.4 Integer Order PID Controller and Fractional Order PD Controller Designs 159 10.5 Simulation Comparisons 160 10.6 Chapter Summary 162 PART IV STABILITY AND FEASIBILITY FOR FOPID DESIGN 11 Stability and Design Feasibility of Robust PID Controllers for FOPTD Systems 165 11.1 Introduction 165 11.2 Stability Region and Flat Phase Tuning Rule for the Robust PID Controller Design 168 11.3 PID Controller Design with Pre-Specifications on Am and !c 171 11.4 Simulation Illustration 180 11.5 Chapter Summary 185 12 Stability and Design Feasibility of Robust FOPI Controllers for FOPTD Systems 187 12.1 Introduction 187 12.2 Stabilizing and Robust FOPI Controller Design for FOPTD Systems 188 12.3 Design Procedures Summary with An Illustrative Example 194 12.4 Complete Information Collection for Achievable Region of wc and m 197 12.5 Simulation Illustration 201 12.6 Chapter Summary 207 PART V FRACTIONAL ORDER DISTURBANCE COMPENSATORS 13 Fractional Order Disturbance Observer 211 13.1 Introduction 211 13.2 Disturbance Observer (DOB) 212 13.3 Actual Design Parameters In DOB and Their Effects 213 13.4 Loss of The Phase Margin With DOB 215 13.5 Solution One: Rule-Based Switched Low Pass Filtering With Varying Relative Degree 216 13.6 The Proposed Solution: Guaranteed Phase Margin Method Using Fractional Order Low Pass Filtering 216 13.7 Implementation Issues: Stable Minimum-Phase Frequency Domain Fitting 218 13.8 Chapter Summary 222 14 Fractional Order Adaptive Feed-forward Cancellation 223 14.1 Introduction 223 14.2 Fractional Order Adaptive Feed-forward Cancellation 225 14.3 Equivalence Between Fractional Order Internal Model Principle and Fractional Order Adaptive Feed-Forward Cancellation 229 14.4 Frequency-domain analysis of the FOAFC performance for the periodic disturbance 231 14.5 Simulation Illustration 233 14.6 Experiment Validation 237 14.7 Chapter Summary 241 15 Fractional Order Robust Control for Cogging Effect 243 15.1 Introduction 243 15.2 Fractional Order Robust Control of Cogging Effect Compensation 244 15.3 Simulation Illustration 252 15.4 Experiments on A Lab Testbed - Dynamometer 258 15.5 Chapter Summary 264 16 Fractional Order Periodic Adaptive Learning Compensation 275 16.1 Introduction 275 16.2 Fractional Order Periodic Adaptive learning Compensation for the State-dependent Periodic Disturbance 276 16.3 Simulation Illustrations 282 16.4 Experimental Validation 284 16.5 Chapter Summary 288 PART VI EFFECTS OF FRACTIONAL ORDER CONTROLS ON NONLINEARITIES 17 Fractional Order PID Control of A DC-Motor with Elastic Shaft 293 17.1 Introduction 293 17.2 The Benchmark Position Servo System 294 17.3 A Modified Approximate Realization Method 295 17.4 Comparative Simulations 297 17.5 Chapter Summary 305 18 Fractional Order Ultra Low-Speed Position Servo 313 18.1 Introduction 313 18.2 Ultra Low-Speed Position Tracking using Designed FOPD and Optimized IOPI 314 18.3 Static and Dynamic Models of Friction and DescribingFunctions for Friction Models 316 18.4 Simulation Analysis with IOPI and FOPD Controllers Using Describing Function 321 18.5 Extended Experimental Demonstration 324 18.6 Chapter Summary 325 19 Optimized Fractional Order Conditional Integrator 329 19.1 Introduction 329 19.2 Clegg Conditional Integrator 330 19.3 Intelligent Conditional Integrator 331 19.4 The Optimized Fractional Order Conditional Integrator 332 19.5 Simulation Validation 340 19.6 Chapter Summary 342 PART VII FRACTIONAL ORDER CONTROL APPLICATIONS 20 Lateral Directional Fractional Order Control of A Small Fixed-Wing UAV 345 20.1 Introduction 345 20.2 Flight Control System of Small Fixed-Wing UAV 346 20.3 Integer/Fractional Order Controller Designs 351 20.4 Modified Ziegler-Nichols PI Controller Design 352 20.5 Fractional Order (PI)¸ Controller Design 353 20.6 Fractional Order PI Controller Design 355 20.7 Integer Order PID Controller Design 356 20.8 Simulation Illustration 357 20.9 Flight Experiments 363 20.10 Chapter Summary 367 21 Fractional Order PD Controller Synthesis and Implementation for HDD Servo System 369 21.1 Introduction 369 21.2 Fractional Order Controller Design with Flat Phase 370 21.3 Implementation of the Fractional Order Controller 372 21.4 Readjustment for the Designed FOPD Controller 377 21.5 Experiment 380 21.6 Chapter Summary 383 References 385 Index 403