Fractional-order Modeling and Control of Dynamic Systems (eBook)

Aleksei Tepljakov (Autor)

eBook Download: PDF

2017 | 1st ed. 2017
XIX, 173 Seiten
Springer International Publishing (Verlag)
978-3-319-52950-9 (ISBN)

Infos

This book reports on an outstanding research devoted to modeling and control of dynamic systems using fractional-order calculus. It describes the development of model-based control design methods for systems described by fractional dynamic models. More than 300 years had passed since Newton and Leibniz developed a set of mathematical tools we now know as calculus. Ever since then the idea of non-integer derivatives and integrals, universally referred to as fractional calculus, has been of interest to many researchers. However, due to various issues, the usage of fractional-order models in real-life applications was limited. Advances in modern computer science made it possible to apply efficient numerical methods to the computation of fractional derivatives and integrals. This book describes novel methods developed by the author for fractional modeling and control, together with their successful application in real-world process control scenarios.

 

Inhalt

Supervisor’s Foreword 7
Parts of this thesis have been published in the following journal articles: 8
Acknowledgements 9
About the Author 10
Contents 11
Abbreviations 14
1 Introduction 15
1.1 State of the Art 16
1.2 Motivation and Problem Statement 18
1.3 Author's Contributions 19
1.4 Thesis Outline 20
References 22
2 Preliminaries 25
2.1 Mathematical Basis 25
2.2 Fractional-Order Models 27
2.2.1 Process Models 28
2.2.2 Stability Analysis 28
2.2.3 Time Domain Analysis 29
2.2.4 Frequency Domain Analysis 30
2.3 Approximation of Fractional-Order Operators 31
2.4 Fractional-Order Controllers 31
2.5 Optimization Methods 34
2.5.1 Newton-Raphson Method 34
2.5.2 Nonlinear Least-Squares Estimation Methods 34
2.5.3 Nelder-Mead Method 35
2.5.4 Optimization Problems with Bounds and Constraints 37
References 39
3 Identification of Fractional-Order Models 41
3.1 System Identification Fundamentals 41
3.2 Open-Loop Identification in the Time Domain 43
3.2.1 Parametric Identification 45
3.2.2 Residual Analysis 46
3.3 Closed-Loop Identification in the Time Domain 50
3.4 Frequency Domain Identification in Automatic Tuning Applications for Process Control 51
3.5 Conclusions 58
References 59
4 Fractional-Order PID Controller Design 61
4.1 Optimization Based Controller Design 61
4.2 Gain and Order Scheduling 66
4.3 Stabilization of Unstable Plants 68
4.4 Retuning FOPID Control for Existing PID Control Loops 70
4.5 Control Loop Analysis and Controller Design in the Frequency Domain ƒ 74
4.5.1 Computation of Control System Characteristics 74
4.5.2 FOPID Controller Design 81
4.6 Conclusions 87
References 88
5 Implementation of Fractional-Order Models and Controllers 91
5.1 An Update to Carlson's Approximation Method for Analog Implementations 91
5.2 Efficient Analog Implementation of Fractional-Order Models and Controllers 99
5.2.1 Approximation Methods 99
5.2.2 Unified Approach to Fractance Network Generation 102
5.3 Digital Implementation of Fractional-Order Controllers 104
5.3.1 Discrete-Time Oustaloup Filter Approximation for Embedded Applications 104
5.3.2 FOPID Controller Implementation 107
5.3.3 FO Lead-Lag Compensator Implementation 108
5.3.4 Controller Reset Logic 109
5.4 Experimental Platform for Real-Time Closed-Loop Simulations of Control Systems 109
5.5 Development of a Hardware FOPID Controller Prototype 111
5.5.1 Atmel AVR Microcontroller Family Based Implementation 111
5.5.2 STMicroelectronics STM32F407 Microcontroller Family Based Implementation 115
5.6 Conclusions 117
References 118
6 FOMCON: Fractional-Order Modeling and Control Toolbox 120
6.1 Overview of the Toolbox 120
6.2 Identification Module 123
6.3 Control Module 129
6.4 Implementation Module 132
6.5 Conclusions 139
References 141
7 Applications of Fractional-Order Control 143
7.1 Fluid Level Control in a Multi Tank System 143
7.1.1 Coupled Tanks System 144
7.1.2 Multi-tank System 150
7.2 Retuning Control of a Magnetic Levitation System 155
7.2.1 Identification of the Nonlinear Model of the MLS 158
7.2.2 FOPID Controller Design for the MLS 160
7.2.3 Experimental Results 161
7.3 Control of Ion-Polymer Metal Composite Actuator 163
7.3.1 Identification of the Actuator Model 165
7.3.2 FOPID Control 166
7.3.3 FOINVM Based Control 168
7.3.4 Hardware Implementation of the Controller 168
7.4 Conclusions 175
7.4.1 Multi Tank System 175
7.4.2 Magnetic Levitation System 176
7.4.3 IPMC Actuator 176
References 178
8 Conclusions 180
References 184

Produkt-Details

• Erscheint lt. Verlag: 8.2.2017
• Reihe/Serie: Springer Theses
• Reihe/Serie: Springer Theses
• Zusatzinfo: XIX, 173 p. 79 illus., 52 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management
• Schlagworte: Applications of Fractional-order Models • Complexity • FOMCON Toolbox for MATLAB • Fopid Controller • Fopid Tuning • Fotf Identification • Fractional Control • Fractional-order Calculus • Fractional-order Operators • Industrial Control Systems • Least-squares Parameter Estimation • Newton-Raphson Optimization • Quality Control, Reliability, Safety and Risk
• ISBN-10: 3-319-52950-1 / 3319529501
• ISBN-13: 978-3-319-52950-9 / 9783319529509