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EB

EB

ONLINE

Cham : Springer International Publishing, 2017

1 online zdroj

ISBN 978-3-319-52950-9 (e-kniha)

ISBN 9783319529493 (print)

Springer Theses, Recognizing Outstanding Ph.D. Research, ISSN 2190-5053

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. ..

* Complexity, Computational * Control engineering * Reliability * Industrial safety * Engineering. * Nonlinear Dynamics * Chaos Theory

001477452

1 Introduction 1 // 1.1 State of the Art 2 // 1.2 Motivation and Problem Statement 4 // 1.3 Author’s Contributions 5 // 1.4 Thesis Outline 6 // References 8 // 2 Preliminaries 11 // 2.1 Mathematical Basis 11 // 2.2 Fractional-Order Models 13 // 2.2.1 Process Models 14 // 2.2.2 Stability Analysis 14 // 2.2.3 Time Domain Analysis 15 // 2.2.4 Frequency Domain Analysis 16 // 2.3 Approximation of Fractional-Order Operators 17 // 2.4 Fractional-Order Controllers 17 // 2.5 Optimization Methods 20 // 2.5.1 Newton-Raphson Method 20 // 2.5.2 Nonlinear Least-Squares Estimation Methods 20 // 2.5.3 Nelder-Mead Method 21 // 2.5.4 Optimization Problems with Bounds and Constraints 23 // References 25 // 3 Identification of Fractional-Order Models 27 // 3.1 System Identification Fundamentals 27 // 3.2 Open-Loop Identification in the Time Domain 29 // 3.2.1 Parametric Identification 31 // 3.2.2 Residual Analysis 32 // 3.3 Closed-Loop Identification in the Time Domain 36 // 3.4 Frequency Domain Identification in Automatic Tuning // Applications for Process Control 37 // 3.5 Conclusions 44 // References 45 // 4 Fractional-Order PID Controller Design 47 // 4.1 Optimization Based Controller Design 47 // 4.2 Gain and Order Scheduling 52 // 4.3 Stabilization of Unstable Plants 54 // 4.4 Retuning FOPID Control for Existing PID Control Loops 56 // 4.5 Control Loop Analysis and Controller Design in the Frequency Domain for Automatic Tuning // Applications in Process Control 60 // 4.5.1 Computation of Control System Characteristics 60 // 4.5.2 FOPID Controller Design 67 // 4.6 Conclusions  5 // References 74 // 5 Implementation of Fractional-Order Models and Controllers 77 // 5.1 An Update to Carlson’s Approximation Method for Analog // Implementations 77 // 5.2 Efficient Analog Implementation of Fractional-Order Models and Controllers 85 // 5.2.1 Approximation Methods 85 //

5.2.2 Unified Approach to Fractance Network Generation 88 // 5.3 Digital Implementation of Fractional-Order Controllers 90 // 5.3.1 Discrete-Time Oustaloup Filter Approximation for // Embedded Applications 90 // 5.3.2 FOPID Controller Implementation 93 // 5.3.3 FO Lead-Lag Compensator Implementation 94 // 5.3.4 Controller Reset Logic 95 // 5.4 Experimental Platform for Real-Time Closed-Loop // Simulations of Control Systems 95 // 5.5 Development of a Hardware FOPID Controller Prototype 97 // 5.5.1 Atmel AYR Microcontroller Family Based // Implementation 97 // 5.5.2 STMicroelectronics STM32F407 Microcontroller // Family Based Implementation 101 // 5.6 Conclusions // References 104 // 6 FOMCON: Fractional-Order Modeling and Control Toolbox 107 // 6.1 Overview of the Toolbox 107 // 6.2 Identification Module HO // 6.3 Control Module ?6 // 6.4 Implementation Module 119 // 6.5 Conclusions 126 // References 128 // 7 Applications of Fractional-Order Control 131 // 7.1 Fluid Level Control in a Multi Tank System 131 // 7.1.1 Coupled Tanks System 132 // 7.1.2 Multi-tank System 138 // 7.2 Retuning Control of a Magnetic Levitation System 143 // 7.2.1 Identification of the Nonlinear Model of the MLS 146 // 7.2.2 FOPID Controller Design for the MLS 148 // 7.2.3 Experimental Results 149 // 7.3 Control of Ion-Polymer Metal Composite Actuator 151 // 7.3.1 Identification of the Actuator Model 153 // 7.3.2 FOPID Control 154 // 7.3.3 FOINVM Based Control 156 // 7.3.4 Hardware Implementation of the Controller 156 // 7.4 Conclusions 163 // 7.4.1 Multi Tank System 163 // 7.4.2 Magnetic Levitation System 164 // 7.4.3 IPMC Actuator 164 // References 166 // 8 Conclusions 169 // References 173