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Fractional Order Motion Controls

Ying Luo (Original Author), YangQuan Chen (Original Author)
ISBN: 978-1-119-94455-3
454 pages
December 2012
Fractional Order Motion Controls (1119944554) cover image

Description

Covering fractional order theory, simulation and experiments, this book explains how fractional order modelling and fractional order controller design compares favourably with traditional velocity and position control systems. The authors systematically compare the two approaches using applied fractional calculus. Stability theory in fractional order controllers design is also analysed.

  •  Presents material suitable for a variety of real-world applications, including hard disk drives, vehicular controls, robot control and micropositioners in DNA microarray analysis
  • Includes extensive experimental results from both lab bench level tests and industrial level, mass-production-ready implementations
  • Covers detailed derivations and numerical simulations for each case
  • Discusses feasible design specifications, ideal for practicing engineers

The book also covers key topics including: fractional order disturbance cancellation and adaptive learning control studies for external disturbances; optimization approaches for nonlinear system control and design schemes with backlash and friction. Illustrations and experimental validations are included for each of the proposed control schemes to enable readers to develop a clear understanding of the approaches covered, and move on to apply them in real-world scenarios.

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Table of Contents

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 Ám 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 Φm 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

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