Robust control : theory and applications / Kang-Zhi Liu, Professor, Chiba University, Japan, Yu Yao, Professor, Harbin Institute of Technology, China.

Format:

Book

Author/Creator:

Liu, Kang-Zhi, author.

Language:

English

Subjects (All):

Robust control.

Control theory.

Physical Description:

1 online resource (485 pages) : illustrations (some color)

Edition:

1st ed.

Place of Publication:

Singapore : Wiley, 2016.

Summary:

Comprehensive and up to date coverage of robust control theory and its application * Presented in a well-planned and logical way * Written by a respected leading author, with extensive experience in robust control * Accompanying website provides solutions manual and other supplementary material

Contents:

Cover

Title Page

Copyright

Dedication

Contents

Preface

List of Abbreviations

Notations

Chapter 1 Introduction

1.1 Engineering Background of Robust Control

1.2 Methodologies of Robust Control

1.2.1 Small-Gain Approach

1.2.2 Positive Real Method

1.2.3 Lyapunov Method

1.2.4 Robust Regional Pole Placement

1.2.5 Gain Scheduling

1.3 A Brief History of Robust Control

Chapter 2 Basics of Linear Algebra and Function Analysis

2.1 Trace, Determinant, Matrix Inverse, and Block Matrix

2.2 Elementary Linear Transformation of Matrix and Its Matrix Description

2.3 Linear Vector Space

2.3.1 Linear Independence

2.3.2 Dimension and Basis

2.3.3 Coordinate Transformation

2.4 Norm and Inner Product of Vector

2.4.1 Vector Norm

2.4.2 Inner Product of Vector

2.5 Linear Subspace

2.5.1 Subspace

2.6 Matrix and Linear Mapping

2.6.1 Image and Kernel Space

2.6.2 Similarity Transformation of Matrix

2.6.3 Rank of Matrix

2.6.4 Linear Algebraic Equation

2.7 Eigenvalue and Eigenvector

2.8 Invariant Subspace

2.8.1 Mapping Restricted in Invariant Subspace

2.8.2 Invariant Subspace over Rn

2.8.3 Diagonalization of Hermitian/Symmetric Matrix

2.9 Pseudo-Inverse and Linear Matrix Equation

2.10 Quadratic Form and Positive Definite Matrix

2.10.1 Quadratic Form and Energy Function

2.10.2 Positive Definite and Positive Semidefinite Matrices

2.11 Norm and Inner Product of Matrix

2.11.1 Matrix Norm

2.11.2 Inner Product of Matrices

2.12 Singular Value and Singular Value Decomposition

2.13 Calculus of Vector and Matrix

2.13.1 Scalar Variable

2.13.2 Vector or Matrix Variable

2.14 Kronecker Product

2.15 Norm and Inner Product of Function

2.15.1 Signal Norm

2.15.2 Inner Product of Signals.

2.15.3 Norm and Inner Product of Signals in Frequency Domain

2.15.4 Computation of 2-Norm and Inner Product of Signals

2.15.5 System Norm

2.15.6 Inner Product of Systems

Exercises

Notes and References

Chapter 3 Basics of Convex Analysis and LMI

3.1 Convex Set and Convex Function

3.1.1 Affine Set, Convex Set, and Cone

3.1.2 Hyperplane, Half-Space, Ellipsoid, and Polytope

3.1.3 Separating Hyperplane and Dual Problem

3.1.4 Affine Function

3.1.5 Convex Function

3.2 Introduction to LMI

3.2.1 Control Problem and LMI

3.2.2 Typical LMI Problems

3.2.3 From BMI to LMI: Variable Elimination

3.2.4 From BMI to LMI: Variable Change

3.3 Interior Point Method*

3.3.1 Analytical Center of LMI

3.3.2 Interior Point Method Based on Central Path

Chapter 4 Fundamentals of Linear System

4.1 Structural Properties of Dynamic System

4.1.1 Description of Linear System

4.1.2 Dual System

4.1.3 Controllability and Observability

4.1.4 State Realization and Similarity Transformation

4.1.5 Pole

4.1.6 Zero

4.1.7 Relative Degree and Infinity Zero

4.1.8 Inverse System

4.1.9 System Connections

4.2 Stability

4.2.1 Bounded-Input Bounded-Output Stability

4.2.2 Internal Stability

4.2.3 Pole-Zero Cancellation

4.2.4 Stabilizability and Detectability

4.3 Lyapunov Equation

4.3.1 Controllability Gramian and Observability Gramian

4.3.2 Balanced Realization

4.4 Linear Fractional Transformation

Chapter 5 System Performance

5.1 Test Signal

5.1.1 Reference Input

5.1.2 Persistent Disturbance

5.1.3 Characteristic of Test Signal

5.2 Steady-State Response

5.2.1 Analysis on Closed-Loop Transfer Function

5.2.2 Reference Tracking

5.2.3 Disturbance Suppression

5.3 Transient Response.

5.3.1 Performance Criteria

5.3.2 Prototype Second-Order System

5.3.3 Impact of Additional Pole and Zero

5.3.4 Overshoot and Undershoot

5.3.5 Bandwidth and Fast Response

5.4 Comparison of Open-Loop and Closed-Loop Controls

5.4.1 Reference Tracking

5.4.2 Impact of Model Uncertainty

5.4.3 Disturbance Suppression

Chapter 6 Stabilization of Linear Systems

6.1 State Feedback

6.1.1 Canonical Forms

6.1.2 Pole Placement of Single-Input Systems

6.1.3 Pole Placement of Multiple-Input Systems*

6.1.4 Principle of Pole Selection

6.2 Observer

6.2.1 Full-Order Observer

6.2.2 Minimal Order Observer

6.3 Combined System and Separation Principle

6.3.1 Full-Order Observer Case

6.3.2 Minimal Order Observer Case

Chapter 7 Parametrization of Stabilizing Controllers

7.1 Generalized Feedback Control System

7.1.1 Concept

7.1.2 Application Examples

7.2 Parametrization of Controllers

7.2.1 Stable Plant Case

7.2.2 General Case

7.3 Youla Parametrization

7.4 Structure of Closed-Loop System

7.4.1 Affine Structure in Controller Parameter

7.4.2 Affine Structure in Free Parameter

7.5 2-Degree-of-Freedom System

7.5.1 Structure of 2-Degree-of-Freedom Systems

7.5.2 Implementation of 2-Degree-of-Freedom Control

Chapter 8 Relation between Time Domain and Frequency Domain Properties

8.1 Parseval's Theorem

8.1.1 Fourier Transform and Inverse Fourier Transform

8.1.2 Convolution

8.1.3 Parseval's Theorem

8.1.4 Proof of Parseval's Theorem

8.2 KYP Lemma

8.2.1 Application in Bounded Real Lemma

8.2.2 Application in Positive Real Lemma

8.2.3 Proof of KYP Lemma*

Chapter 9 Algebraic Riccati Equation.

9.1 Algorithm for Riccati Equation

9.2 Stabilizing Solution

9.3 Inner Function

Chapter 10 Performance Limitation of Feedback Control

10.1 Preliminaries

10.1.1 Poisson Integral Formula

10.1.2 All-Pass and Minimum-Phase Transfer Functions

10.2 Limitation on Achievable Closed-loop Transfer Function

10.2.1 Interpolation Condition

10.2.2 Analysis of Sensitivity Function

10.3 Integral Relation

10.3.1 Bode Integral Relation on Sensitivity

10.3.2 Bode Phase Formula

10.4 Limitation of Reference Tracking

10.4.1 1-Degree-of-Freedom System

10.4.2 2-Degree-of-Freedom System

Chapter 11 Model Uncertainty

11.1 Model Uncertainty: Examples

11.1.1 Principle of Robust Control

11.1.2 Category of Model Uncertainty

11.2 Plant Set with Dynamic Uncertainty

11.2.1 Concrete Descriptions

11.2.2 Modeling of Uncertainty Bound

11.3 Parametric System

11.3.1 Polytopic Set of Parameter Vectors

11.3.2 Matrix Polytope and Polytopic System

11.3.3 Norm-Bounded Parametric System

11.3.4 Separation of Parameter Uncertainties

11.4 Plant Set with Phase Information of Uncertainty

11.5 LPV Model and Nonlinear Systems

11.5.1 LPV Model

11.5.2 From Nonlinear System to LPV Model

11.6 Robust Stability and Robust Performance

Chapter 12 Robustness Analysis 1: Small-Gain Principle

12.1 Small-Gain Theorem

12.2 Robust Stability Criteria

12.3 Equivalence between H∞ Performance and Robust Stability

12.4 Analysis of Robust Performance

12.4.1 Sufficient Condition for Robust Performance

12.4.2 Introduction of Scaling

12.5 Stability Radius of Norm-Bounded Parametric Systems

Chapter 13 Robustness Analysis 2: Lyapunov Method.

13.1 Overview of Lyapunov Stability Theory

13.1.1 Asymptotic Stability Condition

13.1.2 Condition for State Convergence Rate

13.2 Quadratic Stability

13.2.1 Condition for Quadratic Stability

13.2.2 Quadratic Stability Conditions for Polytopic Systems

13.2.3 Quadratic Stability Condition for Norm-Bounded Parametric Systems

13.3 Lur'e System

13.3.1 Circle Criterion

13.3.2 Popov Criterion

13.4 Passive Systems

Chapter 14 Robustness Analysis 3: IQC Approach

14.1 Concept of IQC

14.2 IQC Theorem

14.3 Applications of IQC

14.4 Proof of IQC Theorem*

Chapter 15 H2 Control

15.1 H2 Norm of Transfer Function

15.1.1 Relation with Input and Output

15.1.2 Relation between Weighting Function and Dynamics of Disturbance/Noise

15.1.3 Computing Methods

15.1.4 Condition for ||G||2 &lt

γ

15.2 H2 Control Problem

15.3 Solution to Nonsingular H2 Control Problem

15.4 Proof of Nonsingular Solution

15.4.1 Preliminaries

15.4.2 Proof of Theorems 15.1 and 15.2

15.5 Singular H2 Control

15.6 Case Study: H2 Control of an RTP System

15.6.1 Model of RTP

15.6.2 Optimal Configuration of Lamps

15.6.3 Location of Sensors

15.6.4 H2 Control Design

15.6.5 Simulation Results

Chapter 16 H∞ Control

16.1 Control Problem and H∞ Norm

16.1.1 Input-Output Relation of Transfer Matrix's H∞ Norm

16.1.2 Disturbance Control and Weighting Function

16.2 H∞ Control Problem

16.3 LMI Solution 1: Variable Elimination

16.3.1 Proof of Theorem 16.1

16.3.2 Computation of Controller

16.4 LMI Solution 2: Variable Change

16.5 Design of Generalized Plant and Weighting Function

16.5.1 Principle for Selection of Generalized Plant

16.5.2 Selection of Weighting Function

16.6 Case Study.

16.7 Scaled H∞ Control.

Notes:

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed October 11, 2016).

ISBN:

1-118-75442-5

1-119-11307-5

1-118-75441-7

OCLC:

959150823