Robust Control System Design

Advanced State Space Techniques

Chia-Chi Tsui

• Publisher: CRC Press
• Year: 2022
• Print ISBN: 9781032195193
• eBook ISBN: 9781000562187
• Topic: Technik & Maschinenbau
• Subtopic: Elektrotechnik & Telekommunikation

This book presents a synthesized design principle versus the existing separation principle of modern control theory of over six decades since the start. Guided by this new principle, a generalized state feedback control can be designed based on the parameters of observer and for a great majority of plant systems, and the robust property of this control can be fully realized. The robust property of the existing state feedback control which is designed separate from the parameters of its realizing observer, cannot be realized for a great majority of plant systems.

By freely design and adjust the observer order, the corresponding generalized state feedback control can unify completely the existing state feedback control and static output feedback control, and can adjust effectively the tradeoff between performance and robustness. This generalized state feedback control can assign eigen-structure, and can improve performance and robustness far more effectively than the control designed using classical control theory.

Equally significant, the results of this book are very simple that can be comprehended and grasped very easily. These results are introduced and illustrated from the basic level, and use only the basic mathematical tools. Ample examples and exercise problems that can be solved by hand computation, are provided. This third edition made substantial improvement on this aspect. Modern control theoreticians only formulated the feedback control design problem in various ways, the point however is to really solve this problem.

1 System Mathematical Models

DOI: 10.1201/9781003259572-1

Unlike other engineering specialties whose subject of study is a specific engineering system such as an engine system or an airborne system, the control systems theory deals only with a general mathematical model of engineering systems. This chapter introduces two basic mathematical models and some basic system properties revealed by those models. There are four sections in this chapter.

Section 1.1 introduces the state space model and the transfer function model of linear time-invariant multi-input and multi-output systems and the derivation of the two models.

Section 1.2 describes the eigenstructure decomposition of the state space model, where the state matrix of the model is in Jordan form.

Section 1.3 introduces two basic system properties – controllability and observability. These two properties can be simply and clearly described based on the eigenstructure decomposition of the state space model. The corresponding canonical form of state space model realization of a transfer function model in a polynomial matrix fraction description form can also be simply and clearly derived.

Section 1.4 introduces two basic system parameters – system poles and zeros.

1.1 Two Kinds of Mathematical Models

This book deals with linear time-invariant systems, which have also been the main subject of the control systems theory. A linear time-invariant system can be represented by two kinds of mathematical models – the state space model and the transfer function model. The control theory that is based on the state space model is called the “state space control theory” or the “modern control theory”, and the control theory that is based on the transfer function model is called the “classical control theory”.

We will first introduce the state space model and its derivation.

A state space model is formed by a set of first-order linear differential equations with constant coefficients (1.1a) and a set of linear equations (1.1b).

$dx\left(t\right)/dt=Ax\left(t\right)+Bu\left(t\right)$ (1.1a)

$y\left(t\right)=Cx\left(t\right)+Du\left(t\right)$(1.1b)

where

• x(t) = [x₁(t), …, x_n(t)]′ is the system state vector (the symbol “′” stands for transpose),
• x_i(t), i = 1, …, n, represents the system state variables,
• u(t) = [u₁(t), …, u_p(t)]′ is the system input,
• y(t) = [y₁(t), …, y_m(t)]′ is the system output,

and t...

Table of contents

• Cover
• Half Title Page
• Title Page
• Copyright Page
• Table of Contents
• Preface
• Preface (Second Edition)
• Author
• 1. System Mathematical Models
• 2. Single-System Performance and Sensitivity
• 3. Feedback System Sensitivity
• 4. A New Feedback Control Design Principle/Approach
• 5. Solution of Matrix Equation TA-FT = LC
• 6. Observer Design for Robust Realization
• 7. Observer Design for Other Special Purposes
• 8. Control Design for Eigenvalue Assignment
• 9. Control Design for Eigenvector Assignment
• 10. Control Design for LQ Optimal Control
• Appendix A: Linear Algebra & Numerical Linear Algebra
• Appendix B: Design Projects and Problems
• References
• Index