Modern Control Systems: An Introduction An Introduction

by Tripathi, S.M.

• ISBN13: 9781934015216
• ISBN10: 1934015210
• Edition: CD
• Format: Paperback
• Copyright: 2008-05-12
• Publisher: Jones & Bartlett Learning

Summary

Designed for a short course on control systems or as a review for the professional engineer, this book provides a lucid introduction to modern control systems topics. The five chapters, "State-Variable Analysis of Continuous-Time Systems," "Analysis of Discrete-Time Systems," "Stability Analysis of Non-Linear Systems," "Optimal Control," and "Adaptive Control" have been written to emphasize concepts and provide the basic mathematical derivations. Complete coverage of standard topics, e.g., eigenvalues, eigenvectors, the z-transform, Lyapunov's Method, controllability, observability, etc. are discussed. Numerous examples and exercises have also been included in the book for self-study. A CD-ROM with MATLAB applications and third- party simulations provides practical design techniques and observations of real control systems.

Author Biography

S. M. Tripathi is an industry professional whose areas of interest include modern control systems, power electronics, and electric drives

Table of Contents

State-Variable Analysis of Continuous-Time Systems	p. 1
Introduction	p. 1
Definitions Concerning the State-Space Approach	p. 2
Block-Diagram Representation of a General Control System	p. 3
State Model of a General Control System	p. 3
State Model of a Linear Multi-Input-Multi-Output System	p. 6
State Model of a Linear Single-Input-Single-Output System	p. 9
Linearization of the State Equation of a General Time-Invariant Control System	p. 10
Homogeneous and Nonhomogeneous Linear Time-Invariant Systems	p. 12
Solution of State Equations for Linear Time-Invariant Systems	p. 13
Solution of State Equations for Linear Time-Varying Systems	p. 23
Transfer Matrix from the State Model	p. 28
Characteristic Equation, EigenValues, and EigenVectors	p. 32
State-Space Representation of Control Systems	p. 34
Similarity Transformation	p. 57
Concepts of Controllability and Observability	p. 75
Exercises	p. 93
References	p. 97
Analysis of Discrete-Time Systems	p. 99
Introduction	p. 99
Sampled-Data and Digital Control Systems	p. 99
The z-Transform	p. 110
The Inverse z-transform	p. 121
Solution of Difference-Equations using the z-transform	p. 126
The z-Transfer Function (Pulse Transfer Function)	p. 128
State-Space Representation of Discrete-Time Systems	p. 140
Solution of State-Equations for Linear Time-Invariant Discrete-Time Systems	p. 141
Exercises	p. 145
References	p. 147
Stability Analysis of nonlinear systems	p. 149
Introduction	p. 149
Autonomous System and Equilibrium State	p. 150
Stability Definitions	p. 150
Concept of Sign-Definiteness	p. 152
Quadratic Form of a Scalar Function	p. 154
Definiteness of a Matrix (Sylvestor's Theorem)	p. 154
Lyapunov's Stability Criterion: (Direct Method of Lyapunov)	p. 156
Lyapunov's Direct Method and Linear Time-Invariant System	p. 163
Constructing Lyapunov's Function for Nonlinear Systems(Krasovskii's Method)	p. 167
Popov's Criterion for Stability of Nonlinear Systems	p. 171
Exercises	p. 174
References	p. 176
Optimal Control	p. 177
Introduction	p. 177
Performance Indices	p. 178
Optimal Control Problems	p. 180
Minimization of Performance Index	p. 185
Principle of Optimality	p. 185
Solutions to Optimal Control Problems	p. 189
Exercises	p. 201
References	p. 202
Adaptive Control	p. 205
Introduction	p. 205
Essential Components of an Adaptive System	p. 206
Adaptive Schemes	p. 208
Abuses of Adaptive Control	p. 212
Applications	p. 213
Exercises	p. 213
References	p. 214
Selected Answers to the exercises	p. 215
Laplace and z-Transform Pairs	p. 219
About the CD-ROM	p. 221
Index	p. 223
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