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.

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.

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.

Acronyms xix

Foreword xxiii

Preface xxv

Acknowledgments xxix

PART I FUNDAMENTALS OF FRACTIONAL CONTROLS

1 Introduction 3

1.1 Fractional Calculus 3

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

2.6 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

3.6 Experimental Validation 49

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

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

5.4 Simulation Illustration 80

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

6.4 Simulation Example 95

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

7.5 Implementation of Two Fractional Order Operators 110

7.7 Experiment 120

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

8.5 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

9.5 Experimental Study 148

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

10.5 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