Fractional Order Motion Controls E-Book

Ying Luo

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 439

Veröffentlichungsjahr: 2012

Beschreibung

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.

Leseprobe

Contents

Cover

Title Page

Copyright

Dedication

Foreword

Preface

Acknowledgments

Acronyms

Part I: Fundamentals of Fractional Order Controls

Chapter 1: Introduction

1.1 Fractional Calculus

1.2 Fractional Order Controls

1.3 Fractional Order Motion Controls

1.4 Contributions

1.5 Organization

Part II: Fractional Order Velocity Controls

Chapter 2: Fractional Order PI Controller Designs for Velocity Systems

2.1 Introduction

2.2 The FOPTD System and Three Controllers Considered

2.3 Design Specifications

2.4 Fractional Order PI and [PI] Controller Designs

2.5 Simulation

2.6 Chapter Summary

Chapter 3: Tuning Fractional Order PI Controllers for Fractional Order Velocity Systems with Experimental Validation

3.1 Introduction

3.2 Three Controllers to be Designed and Tuning Specifications

3.3 Tuning Three Controllers for FOVS

3.4 Illustrative Examples and Design Procedure Summaries

3.5 Simulation Illustration

3.6 Experimental Validation

3.7 Chapter Summary

Chapter 4: Relay Feedback Tuning of Robust PID Controllers

4.1 Introduction

4.2 Slope Adjustment of the Phase Bode Plot

4.3 The New PID Controller Design Formulae

4.4 Phase and Magnitude Measurement via Relay Feedback Tests

4.5 Illustrative Examples

4.6 Chapter Summary

Chapter 5: Auto-Tuning of Fractional Order Controllers with Iso-Damping

5.1 Introduction

5.2 FOPI and FO[PI] Controller Design Formulae

5.3 Measurements for Auto-Tuning

5.4 Simulation Illustration

5.5 Chapter Summary

Part III: Fractional Order Position Controls

Chapter 6: Fractional Order PD Controller Tuning for Position Systems

6.1 Introduction

6.2 Fractional Order PD Controller Design for Position Systems

6.3 Design Procedures

6.4 Simulation Illustration

6.5 Experimental Validation

6.6 Chapter Summary

Chapter 7: Fractional Order [PD] Controller Synthesis for Position Systems

7.1 Introduction

7.2 Position Systems and Design Specifications

7.3 Fractional Order [PD] Controller Design

7.4 Controller Design Examples and Bode Plot Validations

7.5 Implementation of Two Fractional Order Operators

7.6 Simulation Illustration

7.7 Experimental Validation

7.8 Chapter Summary

Chapter 8: Time-Constant Robust Analysis and Design of Fractional Order [PD] Controller

8.1 Introduction

8.2 Problem Statement

8.3 FO[PD] Tuning Specifications and Rules

8.4 The Solution Existence Range and An Online Computation Method

8.5 Experimental Validation

8.6 Chapter Summary

Chapter 9: Experimental Study of Fractional Order PD Controller Design for Fractional Order Position Systems

9.1 Introduction

9.2 Fractional Order Systems and Fractional Order Controller Considered

9.3 FOPD Controller Design Procedure for the Fractional Order Position Systems

9.4 Simulation Illustration

9.5 Experimental Validation

9.6 Chapter Summary

Chapter 10: Fractional Order [PD] Controller Design and Comparison for Fractional Order Position Systems

10.1 Introduction

10.2 Fractional Order Position Systems and Fractional Order Controllers

10.3 Fractional Order [PD] Controller Design

10.4 Integer Order PID Controller and Fractional Order PD Controller Designs

10.5 Simulation Comparisons

10.6 Chapter Summary

Part IV: Stability and Feasibility

Chapter 11: Stability and Design Feasibility of Robust PID Controllers for FOPTD Systems

11.1 Introduction

11.2 Stability Region and Flat Phase Tuning Rule for the Robust PID Controller Design

11.3 PID Controller Design with Pre-Specifications on and ωC

11.4 Simulation Illustration

11.5 Chapter Summary

Chapter 12: Stability and Design Feasibility of Robust FOPI Controllers for FOPTD Systems

12.1 Introduction

12.2 Stabilizing and Robust FOPI Controller Design for FOPTD Systems

12.3 Design Procedures Summary with an Illustrative Example

12.4 Complete Information Collection for Achievable Region of ωc and

12.5 Simulation Illustration

12.6 Chapter Summary

Part V: Fractional Order Disturbance Compensations

Chapter 13: Fractional Order Disturbance Observer

13.1 Introduction

13.2 Disturbance Observer

13.3 Actual Design Parameters in DOB and their Effects

13.4 Loss of the Phase Margin with DOB

13.5 Solution One: Rule-Based Switched Low Pass Filtering with Varying Relative Degree

13.6 The Proposed Solution: Guaranteed Phase Margin Method using Fractional Order Low Pass Filtering

13.7 Implementation Issues: Stable Minimum-Phase Frequency Domain Fitting

13.8 Chapter Summary

Chapter 14: Fractional Order Adaptive Feed-Forward Cancellation

14.1 Introduction

14.2 Fractional Order Adaptive Feed-Forward Cancellation

14.3 Equivalence Between Fractional Order Internal Model Principle and Fractional Order Adaptive Feed-Forward Cancellation

14.4 Frequency-Domain Analysis of the FOAFC Performance for the Periodic Disturbance

14.5 Simulation Illustration

14.6 Experiment Validation

14.7 Chapter Summary

Chapter 15: Fractional Order Adaptive Compensation for Cogging Effect

15.1 Introduction

15.2 Fractional Order Adaptive Compensation of Cogging Effect

15.3 Simulation Illustration

15.4 Experimental Validation

15.5 Chapter Summary

Chapter 16: Fractional Order Periodic Adaptive Learning Compensation

16.1 Introduction

16.2 Fractional Order Periodic Adaptive Learning Compensation for State-Dependent Periodic Disturbances

16.3 Simulation Illustration

16.4 Experimental Validation

16.5 Chapter Summary

Part VI: Effects of Fractional Order Controls on Nonlinearities

Chapter 17: Fractional Order PID Control of a DC-Motor with Elastic Shaft

17.1 Introduction

17.2 The Benchmark Position System

17.3 A Modified Approximate Realization Method

17.4 Comparative Simulations

17.5 Chapter Summary

Chapter 18: Fractional Order Ultra Low-Speed Position Control

18.1 Introduction

18.2 Ultra Low-Speed Position Tracking using Designed FOPD and Optimized IOPI

18.3 Static and Dynamic Models of Friction and Describing Functions for Friction Models

18.4 Simulation Analysis with IOPI and FOPD Controllers using Describing Function

18.5 Extended Experimental Demonstration

18.6 Chapter Summary

Chapter 19: Optimized Fractional Order Conditional Integrator

19.1 Introduction

19.2 Clegg Conditional Integrator

19.3 Intelligent Conditional Integrator

19.4 The Optimized Fractional Order Conditional Integrator

19.5 Simulation Illustration

19.6 Chapter Summary

Part VII: Fractional Order Motion Control Applications

Chapter 20: Lateral Directional Fractional Order Control of a Small Fixed-Wing UAV

20.1 Introduction

20.2 Flight Control System of Small Fixed-Wing UAVs

20.3 Integer/Fractional Order Controller Designs

20.4 Modified Ziegler-Nichols PI Controller Design

20.5 Fractional Order (PI)λ Controller Design

20.6 Fractional Order PI Controller Design

20.7 Integer Order PID Controller Design

20.8 Simulation Illustration

20.9 Flight Experiments

20.10 Chapter Summary

Chapter 21: Fractional Order PD Controller Synthesis and Implementation for an HDD Servo System

21.1 Introduction

21.2 Fractional Order Controller Design with “Flat Phase”

21.3 Implementation of the Fractional Order Controller

21.4 Adjustment of the Designed FOPD Controller

21.5 Experiment

21.6 Chapter Summary

References

Index

This edition first published 2013

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Library of Congress Cataloging-in-Publication Data

Luo, Ying, 1973– Fractional order motion controls / Ying Luo, YangQuan Chen. pages cm Includes bibliographical references and index. ISBN 978-1-119-94455-3 (cloth) 1. Motion control devices. 2. Incremental motion control. I. Chen, YangQuan, 1966– II. Title. TJ214.5.L86 2012 629.8–dc23 2012020586

A catalogue record for this book is available from the British Library.

Print ISBN: 9781119944553

To my father XianShu Luo and my mother Gui’E Xiong – Ying Luo

To my family, my mentors and my colleagues – YangQuan Chen

Preface

There is increasing interest in dynamic systems and controls of non-integer orders or fractional orders. Traditional calculus is based on integer order differentiation and integration. The concept of fractional calculus has tremendous potential to change the way we model and control the world around us. Rejecting fractional derivatives is like saying that zero, fractional, or irrational numbers do not exist. Fractional calculus has a firm and enduring theoretical foundation. However, the fractional calculus concept was not widely applied in control engineering for hundreds of years, because the idea was unfamiliar and the fractional operators were limited in their realization. In the past few decades, with the rapid development of computer technology and better understanding of the potential of fractional calculus, the realization of fractional order control systems became much easier and fractional calculus is becoming more and more useful in various science and engineering areas. The present book focuses on fractional order control of motion systems.

Motion control is a sub-field of automation, in which the velocity and position of machines are controlled using certain types of actuation devices such as a hydraulic actuator, a linear actuator, or an electric motor, generally called a servo. Motion control is an important part of robotics and Computerized Numerical Control (CNC) machine tools, and is widely used in packaging, printing, textile, semiconductor production, and the assembly industries. In motion control systems, the control strategies should be stabilizing, fast and precise. In real-time applications, high performance motion control systems must be immune to any kind of disturbance. Thus, motion control research explores enhancement of both performance following command and disturbance rejection. The aim of this book is to introduce fractional calculus-based control methods in motion control applications and to illustrate the advantages and importance of using fractional order controls.

In order to improve the performance following command of motion control, fractional order PID controllers are proposed and designed in a systematic way for integer/fractional order velocity and position systems in this work. With the “flat phase” tuning constraint and other specifications, the motion control systems based on fractional calculus can achieve better robust performances with respect to loop gain variations or time constant variations than using traditionally optimized integer order controllers. From our extensive simulation and experimental efforts, we demonstrated the desirable control performance with faster response and smaller overshoot using properly designed fractional order controllers over those using optimized integer order controllers. In terms of systematic design schemes for fractional order PID controllers satisfying the desired specifications, stability is the minimum requirement for the controller design, and it is better to obtain a feasible region to check the complete set of specifications before the controller is designed and tuned. Therefore, the complete stability regions of the fractional order PID controller parameters, and the achievable regions of the specifications to obtain stabilizing and the desired fractional order PID controllers are discussed in detail in this book. Impressively, the achievable regions of specifications using fractional order PID controllers are significantly larger than those using an integer order PID controller for certain types of systems.

Motion control systems are usually influenced by various disturbances. In high performance motion control systems, maintaining a stable and robust operation by attenuating the influence of disturbances is required. A fractional order disturbance observer (DOB) based on the fractional order Q-filter is presented. A nice feature of this is that the traditional DOB is extended to the fractional order DOB (FO-DOB) with the advantage that the FO-DOB design will no longer be conservative nor aggressive. In addition, a fractional order adaptive feedforward cancellation (FO-AFC) scheme is proposed to cancel periodic disturbances. This FO-AFC method is much more flexible than the integer order AFC in preventing periodic disturbance and suppressing the harmonics or the noise. Meanwhile, a fractional order robust control method is devised for cogging effect compensation on the permanent magnetic synchronous motor position and the velocity systems. Also presented is a fractional order periodic adaptive learning compensation method to reject general state-dependent periodic disturbances.

In this book, nonlinear motion control systems are also considered for fractional calculus applications. A fractional order PID controller design scheme is presented for a DC motor control system with an elastic shaft. Under the same optimization conditions, the best fractional order PID controller outperforms the best integer order PID controller for the motion control system with nonlinearities of backlash and dead zone. Applying the systematic design of fractional order PD (FOPD) controller for ultra-low speed position tracking with a significant nonlinear friction effect, the experimental tracking performance using the designed FOPD controller is much better than that using the optimized integer order PI controller. This advantage of the designed FOPD is explained by the describing function analysis. Furthermore, an optimized fractional order conditional integrator (OFOCI) is proposed. By tuning the fractional order and the other tuning parameter following the analytical optimal design specifications, this proposed OFOCI can achieve an optimized performance not achievable by integer order conditional integrators.

In order to further validate and demonstrate some of the presented fractional order controller design schemes in this work, two real-world applications of fractional order control are included: an unmanned aerial vehicle (UAV) flight control system and an industrial hard-disk-drive (HDD) servo system. These are really exciting real-world applications that clearly show the advantages of using fractional calculus for motion controls.

This book is organized as follows. Part I contains only Chapter 1, introducing fundamentals of fractional order systems and controls followed by research motivations and book contributions. Part II is dedicated to the fractional order velocity controls, which includes Chapters 2–5. Part III focuses on the fractional order position controls, including Chapters 6–10. The feasible regions of the specifications for integer and fractional order controller designs based on the stability analysis are studied in Part IV, which includes Chapters 11 and 12. Part V explains how to design a fractional order disturbance observer, a fractional order adaptive feed-forward controller, a fractional order adaptive controller, and a fractional order periodic adaptive learning controller to compensate for the external disturbances in motion control systems, shown in Chapters 13–16, respectively. Part VI is devoted to the fractional order controls on nonlinear control systems in Chapters 17–19. Applications of fractional order controls in UAV flight control system and the HDD servo system are presented in Part VII including Chapters 20 and 21.

It is our sincere hope that this book can well serve two purposes. For motion control researchers and engineers, this book offers some new schemes that can present further improved performance not achievable before. For researchers and students interested in fractional calculus, this book is a demonstration that fractional calculus is indeed useful in real-world applications, not just a pure math game. Given the pervasive and ubiquitous nature of fractional calculus, we do believe that, as demonstrated in this book, even for simple motion control problems, there are ample opportunities to apply fractional calculus-based control methods. For more complex engineering and non-engineering systems, the opportunities and beneficial consequences of applying fractional calculus are limited only by our imagination.

Ying LuoYangQuan ChenCalifornia, USA

Acknowledgments

This book provides a comprehensive summary of our research efforts during the past few years in fractional order control theory and its applications in motion systems. This book contains material from papers and articles that have been previously published as well as the Ph.D. dissertation of the first author. We are grateful and would like to acknowledge the copyright permissions from the following publishers who have released our works.

Acknowledgement is given to the Institute of Electrical and Electronics Engineers (IEEE) to reproduce material from the following papers:

© 2009 IEEE. Reprinted, with permission, from YangQuan Chen, I. Petras, and Dingyu Xue, “Fractional order control: A tutorial,” in Proceedings of American Control Conference, 10–12 June 2009, St. Louis, MO, pages 1397–1411 (material found in Chapter 1). DOI: 10.1109/ACC.2009.5160719.

© 2002 IEEE. Reprinted, with permission, from Dingyu Xue, and YangQuan Chen, “A comparative introduction of four fractional order controllers,” in Proceedings of the 4th World Congress on Intelligent Control and Automation, 2002, pages 3228–3235 (material found in Chapter 1). DOI: 10.1109/WCICA.2002.1020131.

© 2009 IEEE. Reprinted, with permission, from Chunyang Wang, Ying Luo, and YangQuan Chen, “Fractional order proportional integral (FOPI) and [proportional integral] (FO[PI]) controller designs for first order plus time delay (FOPTD) systems,” in Proceedings of the 21th IEEE Conference on Chinese Control and Decision, Guilin, China, June 17–19, 2009, pages 329–334 (material found in Chapter 2). DOI: 10.1109/CCDC.2009.5195105.

© 2005 IEEE. Reprinted, with permission, from YangQuan Chen and K. L. Moore, “Relay feedback tuning of robust PID controllers with iso-damping property,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, volume 35, issue 1, 2005, pages 23–31 (material found in Chapter 4). DOI: 10.1109/TSMCB.2004.837950.

© 2009 IEEE. Reprinted, with permission, from ChunYang Wang, YongShun Jin, and YangQuan Chen, “Auto-tuning of FOPI and FO[PI] controllers with iso-damping property,” in Proceedings of the 48th IEEE Conference on Decision and Control, 2009 Held Jointly with the 2009 28th Chinese Control Conference, 15–18 Dec. 2009, pages 7309–7314 (material found in Chapter 5). DOI: 10.1109/CDC.2009.5400057.

© 2010 IEEE. Reprinted, with permission, from HongSheng Li, Ying Luo and YangQuan Chen, “A fractional order proportional and derivative (FOPD) motion controller: Tuning rule and experiments,” IEEE Transactions on Control Systems Technology, vol. 18, no. 2, March 2010, pages 516–520 (material found in Chapter 6). DOI: 11.1109/TCST.2009.2019120.

© 2009 IEEE. Reprinted, with permission, from Ying Luo and YangQuan Chen, “Fractional-order [proportional derivative] controller for robust motion control: Tuning procedure and validation,” in Proceedings of the 2009 American Control Conference, St. Louis, Missouri, June 10–12 2009, pages 1412–1417 (material found in Chapter 7). DOI: 10.1109/ACC.2009.5160284.

© 2011 IEEE. Reprinted, with permission, from Yongshun Jin, YangQuan Chen, and Dingyu Xue, “Time-constant robust analysis of a fractional order [proportional derivative] controller,” IET Control Theory and Applications, volume 5, issue 1, January 2011, pages 164–172 (material found in Chapter 8). DOI: 10.1049/iet-cta.2009.0543.

© 2011 IEEE. Reprinted, with permission, from Ying Luo and YangQuan Chen, “Synthesis of robust PID controllers design with complete information on pre-specifications for the FOPTD systems,” in Proceedings of 2011 American Control Conference, San Francisco, CA, June 29–July 1, 2011 (material found in Chapter 11).

© 2011 IEEE. Reprinted, with permission, from Ying Luo and YangQuan Chen, “Stabilizing and robust FOPI controller synthesis for first order plus time delay systems,” in Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, FL, USA, December 12–15, 2011 (material found in Chapter 12).

© 2011 IEEE. Reprinted, with permission, from Ying Luo, YangQuan Chen and YouGuo Pi, “Fractional order adaptive feedforward cancelation,” in Proceedings of 2011 American Control Conference, San Francisco, CA, June 29–July 1, 2011 (material found in Chapter 14).

© 2011 IEEE. Reprinted, with permission, from Ying Luo, YangQuan Chen, Hyo-sung Ahn, and Youguo Pi, “Fractional order periodic adaptive learning compensation for the state-dependent periodic disturbance,” IEEE Transactions on Control Systems Technology, volume 20, issue 2, 2012, pages 465–472 (material found in Chapter 16). DOI: 10.1109/TCST.2011.2117426.

© 2006 IEEE. Reprinted, with permission, from Dingyu Xue, Chunna Zhao, and YangQuan Chen, “Fractional order PID control of a DC-motor with elastic shaft: A case study,” in Proceedings of American Control Conference, 14–16 June 2006, Minneapolis, MN (material found in Chapter 17). DOI: 10.1109/ACC.2006.1657207.

© 2010 IEEE. Reprinted, with permission, from Ying Luo, Haiyang Chao, Long Di, and YangQuan Chen, “Fractional order [proportional integral] roll channel flight control for small fixed-wing UAV,” in Proceedings of the 8th World Congress on Intelligent Control and Automation, Jinan, China, July 2010 (material found in Chapter 20).

Acknowledgement is given to the Elsevier B.V. to reproduce material from the following papers:

© 2010 Elsevier B.V. Reprinted, with permission, from Ying Luo, Chunyang Wang, YangQuan Chen and YouGuo Pi, “Tuning fractional order proportional integral controllers for fractional order systems,” Journal of Process Control, volume 20, issue 7, August 2010, pages 823–831 (material found in Chapter 3). DOI: 10.1016/j.jprocont.2010.04.011.

© 2011 Elsevier B.V. Reprinted, with permission, from Ying Luo, YangQuan Chen, and Youguo Pi, “Experimental study of fractional order proportional derivative controller synthesis for fractional order systems,” Mechatronics, volume 21, 2011, pages 204–214 (material found in Chapter 9). DOI: 10.1016/j.mechatronics. 2010.10.004.

© 2009 Elsevier B.V. Reprinted, with permission, from Ying Luo and YangQuan Chen, “Fractional-order [proportional derivative] controller for a class of fractional order systems,” Automatica, volume 45, issue 10, 2009, pages 2446–2450 (material found in Chapter 10). DOI: 10.1016/j.automatica.2009.06.022.

© 2010 Elsevier B.V. Reprinted, with permission, from Ying Luo, YangQuan Chen, Hyo-Sung Ahn and YouGuo Pi, “Fractional order robust control for cogging effect compensation in PMSM position servo systems: Stability analysis and experiments,” Control Engineering Practice, volume 18, issue 9, September 2010, pages 1022–1036 (material found in Chapter 15). DOI: 10.1016/j.conengprac.2010.05.005.

© 2011 Elsevier B.V. Reprinted, with permission, from Ying Luo, YangQuan Chen, and Youguo Pi, “Fractional order ultra low-speed position servo: Improved performance via describing function analysis,” ISA Transactions, volume 50, 2011, pages 53–60 (material found in Chapter 18). DOI: 10.1016/j.isatra.2010.09.003.

© 2011 Elsevier B.V. Reprinted, with permission, from Ying Luo, YangQuan Chen, Youguo Pi, Concepción A. Monje, and Blas M. Vinagre, “Optimized fractional order conditional integrator,” Journal of Process Control, volume 21, issue 6, July 2011, pages 960–966 (material found in Chapter 19). DOI: 10.1016/j.jprocont.2011.02.002.

Acknowledgement is given to the American Society of Mechanical Engineers (ASME) to reproduce material from the following paper:

© 2003 ASME. Reprinted, with permission, from YangQuan Chen, Blas M. Vinagre, and Igor Podlubny, “On fractional order disturbance observer,” in Proceedings of 2003 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Chicago, Illinois, USA, September 2–6, 2003 (material found in Chapter 14).

The research described in this book would not have been possible without the inspiration and help from the work of individuals in the research community, and we would like to acknowledge them. We would like to express our thanks to Dr. YouGuo Pi for his efforts in some chapters of this book, and all his great support and help to the first author of this book. Thanks go to Dr. DingYu Xue for his support on the robust analysis and discussion on the nonlinearities effect of fractional order PID controls (Chapters 8 and 17). Our thanks are directed to Dr. Haiyang Chao, Long Di, and Jinlu Han for their joint efforts on fractional order flight control on unmanned aerial vehicles (Chapter 20), to Dr. Yongshun Jin and Dr. Chunyang Wang for their joint work on fractional order controllers' design and tuning (Chapters 2, 5, and 8), and to Dr. HuiFang Dou for her help on linear motor modeling and control. We would like to thank Dr. Tao Zhang, Dr. C. I. Kang, and BongJin Lee for their help and guidance on fractional order control in the industrial hard-disk-drive servo system (Chapter 21), and Dr. Hyo-Sung Ahn for his efforts in our joint research on iterative and repetitive learning controls (Chapters 15 and 16). Our thanks go to Dr. Concepción A. Monje and Dr. Blas M. Vinagre for their work and guidance on the fractional order conditional integrator (Chapter 19).

Ying Luo would like to express his sincere thanks to his parents, XianShu Luo and Gui’E Xiong, for their constant and great support. He would also like to thank former and current CSOIS members: Dr. Yan Li, Yiding Han, Austin Jensen, Calvin Coopmans, Shayok Mukhopadhyay and Dr. Hu Sheng for their support during their studies in CSOIS at Utah State University.

YangQuan Chen would like to thank his wife, Dr. Huifang Dou, and his sons, Duyun, David and Daniel, for their patience, understanding and complete support throughout this work. He is thankful to Utah State University for the support and academic freedom he received where the main work of this book was performed while the final proof was completed during his move to University of California, Merced.

We wish to express our appreciation to five anonymous book proposal reviewers whose comments improved our presentation. In particular, we are thankful to Prof. Tomizuka for preparing an insightful Foreword for this book. Last but not least, we thank Sophia Travis (John Wiley & Sons – Chichester) and Paul Petralia (John Wiley & Sons – Hoboken) for their excellent professional support during the whole cycle of this book project.

Acronyms

AFCadaptive feed-forward cancellationCCIClegg conditional integratorCNCcomputerized numerical controlCRBcomplex root boundaryDCdirect currentDFdescribing functionDOBdisturbance observerESFerror sensitivity functionFOfractional orderFO-AFCfractional order adaptive feed-forward cancellationFOCfractional order controlFOCIfractional order conditional integratorFODOBfractional order disturbance observerFOIMPfractional order internal model principleFOLPFfractional order low-pass filterFOPIfractional order proportional integralFOPIDfractional order proportional integral derivativeFOPTDfirst order plus time delayFOPDfractional order proportional derivativeFORCfractional order robust controlFOSfractional order systemFOVSfractional order velocity systemsFO[PD]fractional order [proportional derivative]FO[PI]fractional order [proportional integral]FO-PALCfractional order periodic adaptive learning compensationHDDhard disk driveHILhardware in the loopICIintelligent conditional integratorIMPinternal model principleIMUinertial measurement unitsIOinteger orderIOAFCinteger order adaptive feed-forward cancellationIOCIinteger order conditional integratorIOPIDinteger order proportional integral derivativeIOPIinteger order proportional integralIORCinteger order robust controlIOSinteger order systemIO-PALCinteger order periodic adaptive learning compensationIRBinfinity root boundaryIRIDimpulse response invariant discretizationISEintegral of squared errorITAEintegral time absolute errorLTIlinear time invariantMICImodified intelligent conditional integratorMIMOmultiple input and multiple outputMZNPImodified Ziegler-Nichols proportional integralOFOCIoptimized fractional order conditional integratorPIDproportional integral derivativePMSMpermanent magnetic synchronous motorsRRBreal root boundaryRTWrealtime workshopSDPDState-dependent periodic disturbanceSISOsingle input and single outputTIDtilted integral derivativeUAVunmanned aerial vehicleVCMvoice coil motorZNPIDZiegler-Nichols proportional integral derivativew.r.twith respect to

Part I

Fundamentals of Fractional Order Controls