Operator-based nonlinear control systems design and applications

Control of nonlinear systems is a multidisciplinary field involving electrical engineering, computer science, and control engineering. Specifically, this book addresses uncertain nonlinearity. Beginning with how real plants are modeled as operator-based plants, the author develops a systematic methodology that enables readers to understand a quantitative stability result, a critical factor in any nonlinear control system's stability and performance.

Operator-Based Nonlinear Control Systems: Design and Applications focuses on the operator-theoretic approach, offering detailed examples on how to apply it to network controlled systems. In addition to current research results, the author explores future research directions and applications of the operator-theoretic approach. The book begins with an introduction that defines nonlinear systems. Next, it covers:

Robust right coprime factorization for nonlinear plants with uncertainties Robust stability of operator-based nonlinear control systems Tracking issues and fault detection issues in nonlinear control systems Operator-based nonlinear control systems with smart actuators Nonlinear feedback control for large-scale systems using a distributed control system device

Throughout the book, discussions of actual applications help readers understand how the operator-theoretic approach works in practice.

Operator-Based Nonlinear Control Systems is recommended for students and professionals in control theory engineering and applied mathematics. Working with this expertly written and organized book, they will learn how to obtain robust right coprime factorization for modeled plants. Moreover, they will discover state-of-the-technology research results on robust stability conditions as well as the latest system output tracking and fault detection issues that are challenging today's researchers.

Author Notes

Mingcong Deng, PhD. is Professor of Electrical and Electronic Engineering at Tokyo University of Agriculture and Technology. Dr. Deng has also held teaching or research positions at Kumamoto University, University of Exeter, NTT Communication Science Laboratories, and Okayama University.

1 Introduction	p. 1
1.1 Definition of Nonlinear Systems	p. 1
1.2 Nonlinear System Dynamics Analysis and Control	p. 1
1.3 Why Operator-Based Nonlinear Control System?	p. 2
1.4 Overview of the Book	p. 2
Acknowledgments	p. 3
2 Robust Right Coprime Factorization for Nonlinear Plants with Uncertainties	p. 5
2.1 Preliminaries	p. 5
2.1.1 Definition of Spaces	p. 5
2.1.2 Definition of Operators	p. 6
2.2 Operator Theory	p. 11
2.2.1 Right Coprime Factorization	p. 11
2.2.2 Robust Right Coprime Factorization	p. 12
2.2.3 Isomorphism-Based Robust Right Prime Factorization	p. 16
3 Robust Stability of Operator-Based Nonlinear Control Systems	p. 27
3.1 Concept of Operator-Based Robust Stability	p. 27
3.2 Design Methods of Nonlinear Systems with Uncertainties	p. 27
3.2.1 Robust Right Coprime Factorization Condition	p. 27
3.2.2 Tracking Control Design Scheme	p. 32
3.3 Operator-Based Robust Anti-Windup Nonlinear Feedback Control Systems Design	p. 41
3.3.1 Introduction	p. 41
3.3.2 Design Description	p. 42
3.3.3 Illustrative Examples	p. 47
3.3.4 Discussion	p. 55
3.4 Operator-Based Multi-Input-Multi-Output Nonlinear Feedback Control Systems Design	p. 55
3.4.1 Introduction	p. 55
3.4.2 Definitions and Notation	p. 56
3.4.3 Differentiable Operator-Based Nonlinear Robust Control for MTMO Nonlinear Systems Using Controller Factorization	p. 60
3.4.4 Nonlinear Robust Control for MTMO Nonlinear Systems by Considering Coupling Effects as Uncertainties of Plants	p. 70
3.4.5 Nonlinear Robust Control for MTMO Nonlinear Systems by Right Factorizing Coupling Operators	p. 75
3.4.6 Operator-Based Nonlinear Robust Control for MIMO Nonlinear Systems with Unknown Coupling Effects	p. 85
3.4.7 Summary	p. 106
3.5 Operator-Based Time-Varying Delayed Nonlinear Feedback Control Systems Design	p. 106
3.5.1 Networked Experimental System	p. 107
3.5.2 Networked Nonlinear Feedback Control Design	p. 110
3.5.3 Experimental Result	p. 112
3.5.4 Summary	p. 115
4 Tracking and Fault Detection Issues in Nonlinear Control Systems	p. 117
4.1 Operator-Based Tracking Compensator in Nonlinear Feedback Control Systems Design	p. 117
4.1.1 Introduction	p. 117
4.1.2 Tracking Controller Design Scheme Using Unimodular Operator	p. 118
4.1.3 Simulation	p. 121
4.1.4 Summary	p. 124
4.2 Robust Control for Nonlinear Systems with Unknown Perturbations using Simplified Robust Right Coprime Factorization	p. 125
4.2.1 Introduction	p. 125
4.2.2 Robust Design of Tracking Controller	p. 126
4.2.3 Illustrative Examples	p. 132
4.2.4 Summary	p. 140
4.3 Operator-Based Actuator Fault Detection Methods	p. 140
4.3.1 Introduction	p. 140
4.3.2 Actuator Fault Detetion Method in Nonlinear Systems	p. 141
4.3.3 Algorithm of Fault Detection System	p. 145
4.3.4 Experiments and Discussion	p. 147
4.3.5 Summary	p. 152
4.4 Operator-Based Input Command Fault Detection Method in Nonlinear Feedback Control Systems	p. 152
4.4.1 Introduction	p. 152
4.4.2 Modeling and Problem Setup	p. 154
4.4.3 Robust Input Command Fault Detection Method	p. 158
4.4.4 Simulation and Experimental Results	p. 161
4.4.5 Summary	p. 167
5 Operator-Based Nonlinear Control Systems with Smart Actuators	p. 169
5.1 Operator-Based Robust Nonlinear Feedback Control Systems Design for Nonsymmetric Backlash	p. 169
5.1.1 Introduction	p. 169
5.1.2 Problem Statement	p. 170
5.1.3 Nonsymmetric Backlash Control Design Scheme	p. 173
5.1.4 Simulation Results	p. 177
5.1.5 Summary	p. 182
5.2 Operator-Based Robust Nonlinear Feedback Control Systems Design for Symmetric and Nonsymmetric Hysteresis	p. 182
5.2.1 Introduction	p. 182
5.2.2 Problem Setup	p. 183
5.2.3 Nonsymmetric Prandtl-Ishlinskii Hysteresis Model	p. 185
5.2.4 Design of Robust Stable Control System	p. 190
5.2.5 Numerical Example	p. 192
5.2.6 Summary	p. 193
5.3 Operator-Based Nonlinear Feedback Systems Application for Smart Actuators	p. 194
5.3.1 Nonlinear Control of Piezoelectric Actuator	p. 194
5.3.2 Nonlinear Control of Shape Memory Alloy Actuator	p. 203
5.3.3 Nonlinear Control of IPMC	p. 216
5.3.4 Summary	p. 234
6 Application of Operator-Based Nonlinear Feedback Control to Large-Scale Systems using Distributed Control System Device	p. 235
6.1 Introduction	p. 235
6.2 Multitank Process Modeling	p. 237
6.3 Robust Right Coprime Factorization Design and Controller Realization	p. 242
6.4 Experimental Results	p. 248
6.5 Summary	p. 252
References	p. 253
Index	p. 261

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