CONTENTS

Prologue Preface

Chapter 1    INTRODUCTION TO AUTOMATIC CONTROL SYSTEMS

1.1.                           Introduction

1.2.            A brief historical review of automatic control systems

1.3.                           The basic structure of a control system

1.4.            Practical control examples

1.5.            References

Chapter 2    MATHEMATICAL BACKGROUND

2.1.            Introduction

2.2.            The basic control signals

2.3.            The Laplace transform

2.3.1.  The generalized linear integral transform

2.3.2.  Introduction to Laplace transform

2.3.3.  Properties and theorems of the Laplace transform

2.4.            The inverse Laplace transform

2.5.            Applications of the Laplace transform

2.6.            Matrix definitions and operations

2.6.1.  Matrix definitions

2.6.2.  Matrix operations

2.7.            Determinant of a matrix

2.8.            The inverse of a matrix

2.9.            Matrix eigenvalues and eigenvectors

2.10.        Similarity transformations

2.11.        The Cayley-Hamilton theorem

2.12.        Quadratic forms and Sylvester theorems

2.13.        Problems

2.14.        References

Chapter 3    MATHEMATICAL MODELS OF SYSTEMS

3.1.            Introduction

3.2.            General aspects of mathematical models

3.3.            Types of mathematical models

3.4.            Differential equations

3.5.            Transfer function

3.6.            Impulse response

3.7.            State equations

3.7.1.  General introduction

3.7.2.  Description of linear systems via state equations

3.7.3.  Transfer function and impulse response matrices

3.8.      Transition from one mathematical model to another

3.8.1.  From differential equation to transfer function for s.i.s.o.
systems

3.8.2.  From transfer function to differential equation for s.i.s.o.
systems

3.8.3.  From H(s) to H(t) and vice versa

3.8.4.  From state equations to transfer function matrix

3.8.5.  From transfer function matrix to state equations

3.9.            Equivalent state-space models

3.10.        Block diagrams

3.10.1.  Block diagram rules

3.10.2.  Simplification of block diagrams

3.11.        Signal-flow graphs
3.11.1. Definitions

3.12.        Mathematical models for control system components

3.12.1.  DC Motors

3.12.2.  AC Motors

3.12.3.  Tachometers

3.12.4.  Error detectors

3.12.5.  Gears

3.12.6.  Hydraulic actuator or servomotor

3.12.7.  Pneumatic amplifier

3.13.    Mathematical models for practical control systems

3.13.1.  Voltage control system

3.13.2.  Position (or servomechanism) control system

3.13.3.  Speed control system

3.13.4.  Liquid level control system

3.13.5.  Temperature control system

3.13.6.  Chemical composition control system

3.13.7.  Satellite orientation control system

3.14.        Problems

3.15.        References

Chapter 4    CLASSICAL TIME-DOMAIN ANALYSIS OF CONTROL SYSTEMS

4.1.            Introduction

4.2.            System time response

4.2.1.  Analytical expression of time response

4.2.2.  Characteristics of the graphical representation of time
response

4.3.      Time response of first and second order systems

4.3.1.  First order systems

4.3.2.  Second order systems

4.3.3.  Special issues for second order systems

4.4.            Model simplification

4.5.            Comparison between open-loop and closed-loop systems

4.5.1.  Effect on the output due to parameter variations in the
open-loop system

4.5.2.  Effect on the output due to parameter variations in the
feedback transfer function

4.6.      Sensitivity to parameter variations

4.6.1.  System sensitivity to parameter variations

4.6.2.  Pole sensitivity to parameter variations

4.7.      Steady-state errors

4.7.1.  Types of systems and error constants

4.7.2.  Steady-state errors with inputs of special forms

4.8.            Disturbance rejection

4.9.            Problems

4.10.        References

Chapter 5    STATE-SPACE ANALYSIS OF CONTROL SYSTEMS

5.1.            Introduction

5.2.            Solution of the homogenous equation

5.2.1.  Determination of the state transition matrix

5.2.2.  Properties of the state transition matrix

5.2.3.  Computation of the state transition matrix

5.3.            General solution of the state equations

5.4.            State vector transformations and special forms of state
equations

5.4.1.  The invariance of the characteristic polynomial and of the
transfer function matrix

5.4.2.  Special state-space forms: the phase canonical form

5.4.3.  Transition from an nth order differential equation to state
equations in phase canonical form

5.4.4.  Transition from the phase canonical form to the diagonal
form

5.5.            Block diagrams and signal flow graphs

5.6.            Controllability and observability

5.6.1.  State vector controllability

5.6.2.  Output vector observability

5.6.3.  State vector observability

5.6.4.  The invariance of controllability and observability

5.6.5.  Relation among controllability, observability and transfer
function matrix

5.7.            Kalman decomposition

5.8.            Problems

5.9.            References

Chapter 6    STABILITY

6.1.            Introduction

6.2.            Stability definitions

6.3.            Stability criteria

6.4.            Algebraic stability criteria

6.4.1.  Introductory remarks

6.4.2.  The Routh criterion

6.4.3.  The Hurwitz criterion

6.4.4.  The continued fraction expansion criterion

6.4.5.  Stability of practical control systems

6.5.      Stability in the sense of Lyapunov

6.5.1.  Introduction-definitions

6.5.2.  The first method of Lyapunov

6.5.3.  The second method of Lyapunov

6.5.4.  The special case of linear time-invariant systems

6.6.            Problems

6.7.            References

Chapter 7    THE ROOT LOCUS METHOD

7.1.            Introduction

7.2.            Introductory example

7.3.            Construction method of root locus

7.3.1.  Definition of root locus

7.3.2.  Theorems for constructing the root locus

7.3.3.  Additional information for constructing the root locus

7.3.4.  Root locus of practical control systems

7.4.            Applying the root locus method for determining the roots
of a polynomial

7.5.            Effects of addition of poles and zeros on the root locus

7.5.1.  Addition of poles and its effect on the root locus

7.5.2.  Addition of zeros and its effect on the root locus

7.6.            Problems

7.7.            References

Chapter 8    FREQUECY DOMAIN ANALYSIS

8.1.            Introduction

8.2.            Frequency response

8.3.            Correlation between frequency response and transient
response

8.3.1.  Characteristics of frequency response

8.3.2.  Correlation for first order systems

8.3.3.  Correlation for second order systems

8.3.4.  Correlation for higher order systems

8.4.      The Nyquist stability criterion

8.4.1.  Introduction

8.4.2.  Background material on complex function theory

for the formulation of the Nyquist criterion

8.4.3.  The Nyquist stability criterion

8.4.4.  Construction of Nyquist diagrams

8.4.5.  Gain and phase margins

8.4.6.  Comparison between algebraic criteria and the
Nyquist criterion

8.5.      Bode diagrams

8.5.1.  Introduction

8.5.2.  Bode diagrams for various types of transfer
function factors

8.5.3.  Transfer function Bode diagrams

8.5.4.  Gain and phase margins

8.5.5.  Bode's amplitude-phase theorem

8.6.      Nichols diagrams

8.6.1.  Constant amplitude loci

8.6.2.  Constant phase loci

8.6.3.  Constant amplitude and phase loci: Nichols charts

8.7.            Problems

8.8.            References

Chapter 9    CLASSICAL CONTROL DESIGN METHODS

9.1.            General aspects of the closed-loop control design problem

9.2.            General remarks on classical control design methods

9.3.            Closed-loop system specifications

9.4.            Controller circuits

9.4.1.   Phase-lead circuit

9.4.2.   Phase-lag circuit

9.4.3.   Phase lag-lead circuit

9.4.4.   Bridged T circuit

9.4.5.   Other circuits

9.5.            Design with proportional controllers

9.6.            Design with PID controllers

9.6.1.   Introduction to PID controllers

9.6.2.   PD controllers

9.6.3.   PI controllers

9.6.4.   PID controllers

9.6.5.   Design of PID controllers using the Ziegler-Nichols
methods

9.6.6.   Active circuit realization for PID controllers

9.7.            Design with phase-lead controllers

9.8.            Design with phase-lag controllers

9.9.            Design with phase lag-lead controllers

9.10.        Design with classical optimal control methods

9.10.1.   Free structure controllers

9.10.2.   Fixed structure controllers

9.11.        Problems

9.12.        References

Chapter 10 STATE-SPACE DESIGN METHODS

10.1.        Introduction

10.2.        Linear state and output feedback laws

10.3.        Pole placement

10.3.1.         Pole placement via state feedback

10.3.2.         Pole placement via output feedback

10.4.    Input-output decoupling

10.4.1.          Decoupling via state feedback

10.4.2.          Decoupling via output feedback

10.5.        Exact model matching

10.6.        State observers

10.6.1.         Introduction

10.6.2.         State vector reconstruction using a
Luenberger observer

10.6.3.         Reduced order observers

10.6.4.         Closed-loop system design using state observers

10.6.5. Observer examples

10.7.        Problems

10.8.        References

Chapter 11 OPTIMAL CONTROL

11.1.                    Introduction

11.2.        Mathematical background

11.2.1.  Maxima and minima using the calculus of variations

11.2.2.  The maximum principle

11.3.    Optimal linear regulator

11.3.1.  General remarks

11.3.2.          Solution of the optimal linear regulator problem

11.3.3.          The special case of linear time-invariant systems

11.4.        Optimal linear servomechanism or tracking problem

11.5.        Problems

11.6.        References

Chapter 12 DIGITAL CONTROL

12.1.    Introduction

12.1.1.  The basic structure of digital control systems

12.2.1.  Mathematical background

12.2.    Description and analysis of discrete-time systems

12.2.1.         Properties of discrete-time systems

12.2.2.         Description of linear time-invariant
discrete-time systems

12.2.3.         Analysis of linear time-invariant discrete-time
systems

12.3.    Description and analysis of sampled-data systems

12.3.1.          Introduction to D/A and A/D converters

12.3.2.          Hold circuits

12.3.3.         Conversion of G(s) to G(z)

12.3.4.         Conversion of differential state equations
to difference state equations

12.3.5.         Analysis of sampled-data systems

12.4.    Stability

12.4.1.         Definitions and basic theorems of stability

12.4.2.         Stability criteria

12.5.    Controllability and observability

12.5.1.         Controllability

12.5.2.         Observability

12.5.3.         Loss of controllability and observability
due to sampling

12.6.        Classical discrete-time controller design

12.7.        Discrete-time controllers derived from continuous-time
controllers

12.7.1.         Discrete-time controller design using
indirect techniques

12.7.2.         Specifications of the transient response of
continuous-time systems

12.8.        Controller design via the root-locus method

12.9.        Controller design based on the frequency response

12.9.1.         Introduction

12.9.2.         Bode diagrams

12.9.3.         Nyquist diagrams

12.10.  The PID controller

12.10.1. The proportional controller

12.10.2. The integral controller

12.10.3. The derivative controller

12.10.4. The three-term PID controller

12.10.5.          Design of PID controllers using the
Ziegler-Nichols methods

12.11.    Steady-state errors

12.12.    State-space design methods

12.13.    Optimal control

12.14.    Problems

12.15.    References

Chapter 13 SYSTEM IDENTIFICATION

13.1.        Introduction

13.2.        Off-line parameter estimation

13.2.1.         First-order systems

13.2.2.         Higher-order systems

13.3.        On-line parameter estimation

13.4.        Problems

13.5.        References

Chapter 14 ADAPTIVE CONTROL

14.1.                   Introduction

14.2.                   Adaptive control with the gradient method (MIT rule)

14.3.                   Model reference adaptive control-hyperstability design

14.3.1.  Introduction

14.3.2.          Definition of the model reference control problem

14.3.3.          Design in the case of known parameters

14.3.4.  Hyperstability design in the case of unknown parameters

14.4.     Self-tuning regulators

14.4.1.          Introduction

14.4.2.          Pole-placement self-tuning regulators

14.5.                   Problems

14.6.                   References

Chapter 15 ROBUST CONTROL

15.1.                   Introduction

15.2.       Model uncertainty and its representation

15.2.1.  Origins of model uncertainty

15.2.2.          Representation of uncertainty

15.3.    Robust stability in the H_m - context

15.3.1. Robust stability with a multiplicative uncertainty

15.3.2. Robust stability with an inverse multiplicative
uncertainty

15.4.    Robust performance in the H_m - context

15.4.1.         Nominal performance

15.4.2.         Robust performance

15.4.3. Some remarks on nominal performance, robust
stability and robust performance

15.5.    Kharitonov's theorem and related results

15.5.1.  Kharitonov's theorem for robust stability

15.5.2.          The sixteen plant theorem

15.6.       Problems

15.7.       References

Chapter 16 FUZZY CONTROL

16.1.       Introduction to intelligent control

16.2.                   General remarks on fuzzy controllers

16.3.                   Fuzzy sets

16.4.       Fuzzy controllers

16.5.       Elements of a fuzzy controller

16.6.       Fuzzification

16.7.       The rule base

16.8.       The inference engine

16.9.       Defuzzification

16.10.   Performance assessment

16.11.   Application example: kiln control