Enables readers to master and apply the operator-theoretic approach 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.
1 Introduction 1 (4)
1.1 Definition of Nonlinear Systems 1 (1)
1.2 Nonlinear System Dynamics Analysis 1 (1)
and Control
1.3 Why Operator-Based Nonlinear Control 2 (1)
System?
1.4 Overview of the Book 2 (3)
Acknowledgments 3 (2)
2 Robust Right Coprime Factorization for 5 (22)
Nonlinear Plants with Uncertainties
2.1 Preliminaries 5 (6)
2.1.1 Definition of Spaces 5 (1)
2.1.2 Definition of Operators 6 (5)
2.2 Operator Theory 11 (16)
2.2.1 Right Coprime Factorization 11 (1)
2.2.2 Robust Right Coprime Factorization 12 (4)
2.2.3 Isomorphism-Based Robust Right 16 (11)
Prime Factorization
3 Robust Stability of Operator-Based 27 (90)
Nonlinear Control Systems
3.1 Concept of Operator-Based Robust 27 (1)
Stability
3.2 Design Methods of Nonlinear Systems 27 (14)
with Uncertainties
3.2.1 Robust Right Coprime 27 (5)
Factorization Condition
3.2.2 Tracking Control Design Scheme 32 (9)
3.3 Operator-Based Robust Anti-Windup 41 (14)
Nonlinear Feedback Control Systems Design
3.3.1 Introduction 41 (1)
3.3.2 Design Description 42 (5)
3.3.3 Illustrative Examples 47 (8)
3.3.4 Discussion 55 (1)
3.4 Operator-Based 55 (51)
Multi-Input-Multi-Output Nonlinear
Feedback Control Systems Design
3.4.1 Introduction 55 (1)
3.4.2 Definitions and Notation 56 (4)
3.4.3 Differentiable Operator-Based 60 (10)
Nonlinear Robust Control for MIMO
Nonlinear Systems Using Controller
Factorization
3.4.4 Nonlinear Robust Control for MIMO 70 (5)
Nonlinear Systems by Considering
Coupling Effects as Uncertainties of
Plants
3.4.5 Nonlinear Robust Control for MIMO 75 (10)
Nonlinear Systems by Right Factorizing
Coupling Operators
3.4.6 Operator-Based Nonlinear Robust 85 (21)
Control for MIMO Nonlinear Systems with
Unknown Coupling Effects
3.4.7 Summary 106(1)
3.5 Operator-Based Time-Varying Delayed 106(11)
Nonlinear Feedback Control Systems Design
3.5.1 Networked Experimental System 107(3)
3.5.2 Networked Nonlinear Feedback 110(2)
Control Design
3.5.3 Experimental Result 112(3)
3.5.4 Summary 115(2)
4 Tracking and Fault Detection Issues in 117(52)
Nonlinear Control Systems
4.1 Operator-Based Tracking Compensator 117(8)
in Nonlinear Feedback Control Systems
Design
4.1.1 Introduction 117(1)
4.1.2 Tracking Controller Design Scheme 118(3)
Using Unimodular Operator
4.1.3 Simulation 121(3)
4.1.4 Summary 124(1)
4.2 Robust Control for Nonlinear Systems 125(15)
with Unknown Perturbations using
Simplified Robust Right Coprime
Factorization
4.2.1 Introduction 125(1)
4.2.2 Robust Design of Tracking 126(6)
Controller
4.2.3 Illustrative Examples 132(8)
4.2.4 Summary 140(1)
4.3 Operator-Based Actuator Fault 140(12)
Detection Methods
4.3.1 Introduction 140(1)
4.3.2 Actuator Fault Detection Method 141(4)
in Nonlinear Systems
4.3.3 Algorithm of Fault Detection 145(2)
System
4.3.4 Experiments and Discussion 147(5)
4.3.5 Summary 152(1)
4.4 Operator-Based Input Command Fault 152(17)
Detection Method in Nonlinear Feedback
Control Systems
4.4.1 Introduction 152(2)
4.4.2 Modeling and Problem Setup 154(4)
4.4.3 Robust Input Command Fault 158(3)
Detection Method
4.4.4 Simulation and Experimental 161(6)
Results
4.4.5 Summary 167(2)
5 Operator-Based Nonlinear Control Systems 169(66)
with Smart Actuators
5.1 Operator-Based Robust Nonlinear 169(13)
Feedback Control Systems Design for
Nonsymmetric Backlash
5.1.1 Introduction 169(1)
5.1.2 Problem Statement 170(3)
5.1.3 Nonsymmetric Backlash Control 173(4)
Design Scheme
5.1.4 Simulation Results 177(5)
5.1.5 Summary 182(1)
5.2 Operator-Based Robust Nonlinear 182(12)
Feedback Control Systems Design for
Symmetric and Nonsymmetric Hysteresis
5.2.1 Introduction 182(1)
5.2.2 Problem Setup 183(2)
5.2.3 Nonsymmetric Prandtl-Ishlinskii 185(5)
Hysteresis Model
5.2.4 Design of Robust Stable Control 190(2)
System
5.2.5 Numerical Example 192(1)
5.2.6 Summary 193(1)
5.3 Operator-Based Nonlinear Feedback 194(41)
Systems Application for Smart Actuators
5.3.1 Nonlinear Control of 194(9)
Piezoelectric Actuator
5.3.2 Nonlinear Control of Shape Memory 203(13)
Alloy Actuator
5.3.3 Nonlinear Control of IPMC 216(18)
5.3.4 Summary 234(1)
6 Application of Operator-Based Nonlinear 235(18)
Feedback Control to Large-Scale Systems
using Distributed Control System Device
6.1 Introduction 235(2)
6.2 Multitank Process Modeling 237(5)
6.3 Robust Right Coprime Factorization 242(6)
Design and Controller Realization
6.4 Experimental Results 248(4)
6.5 Summary 252(1)
References 253(8)
Index 261
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