1 Introduction

1.1 Problem Definition

1.2 Overview of Design Approach

1.3 Computer-Aided Design

1.4 Suggestions for Further Reading

1.5 Summary

1.6 Problems

2 Review of Continuous Control

2.1 Dynamic Response

2.1.1 Differential Equations

2.1.2 Laplace Transforms and Transfer Functions

2.1.3 Output Time Histories

2.1.4 The Final Value Theorem

2.1.5 Block Diagrams

2.1.6 Response versus Pole Locations

2.1.7 Time-Domain Specifications

2.2 Basic Properties of Feedback

2.2.1 Stability

2.2.2 Steady-State Errors

2.2.3 PID Control

2.3 Root Locus

2.3.1 Problem Definition

2.3.2 Root Locus Drawing Rules

2.3.3 Computer-Aided Loci

2.4 Frequency Response Design

2.4.1 Specifications

2.4.2 Bode Plot Techniques

2.4.3 Steady-State Errors

2.4.4 Stability Margins

2.4.5 Bode’s Gain-Phase Relationship

2.4.6 Design

2.5 Compensation

2.6 State-Space Design

2.6.1 Control Law

2.6.2 Estimator Design

2.6.3 Compensation：Combined Control and Estimation

2.6.4 Reference Input

2.6.5 Integral Control

2.7 Summary

2.8 Problems

3 Introductory Digital Control

3.1 Digitization

3.2 Effect of Sampling

3.3 PID Control

3.4 Summary

3.5 Problems

4 Discrete Systems Analysis

4.1 Linear Difference Equations

4.2 The Discrete Transfer Function

4.2.1 The z-Transform

4.2.2 The Transfer Function

4.2.3 Block Diagrams and State-Variable Descriptions

4.2.4 Relation of Transfer Function to Pulse Response

4.2.5 External Stability

4.3 Discrete Models of Sampled-Data Systems

4.3.1 Using the z-Transform

4.3.2 Continuous Time Delay

4.3.3 State-Space Form

4.3.4 State-Space Models for Systems with Delay

4.3.5 Numerical Considerations in Computing Φ and Γ

4.3.6 Nonlinear Models

4.4 Signal Analysis and Dynamic Response

4.4.1 The Unit Pulse

4.4.2 The Unit Step

4.4.3 Exponential

4.4.4 General Sinusoid

4.4.5 Correspondence with Continuous Signals

4.4.6 Step Response

4.5 Frequency Response

4.5.1 The Discrete Fourier Transform （DFT）

4.6 Properties of the z-Transform

4.6.1 Essential Properties

4.6.2 Convergence of z-Transform

4.6.3 Another Derivation of the Transfer Function

4.7 Summary

4.8 Problems

5 Sampled-Data Systems

5.1 Analysis of the Sample and Hold

5.2 Spectrum of a Sampled Signal

5.3 Data Extrapolation

5.4 Block-Diagram Analysis of Sampled-Data Systems

5.5 Calculating the System Output Between Samples：The Ripple

5.6 Summary

5.7 Problems

5.8 Appendix

6 Discrete Equivalents

6.1 Design of Discrete Equivalents via Numerical Integration

6.2 Zero-Pole Matching Equivalents

6.3 Hold Equivalents

6.3.1 Zero-Order Hold Equivalent

6.3.2 A Non-Causal First-Order-Hold Equivalent：The Triangle-Hold Equivalent

6.4 Summary

6.5 Problems

7 Design Using Transform Techniques

7.1 System Specifications

7.2 Design by Emulation

7.2.1 Discrete Equivalent Controllers

7.2.2 Evaluation of the Design

7.3 Direct Design by Root Locus in the z-Plane

7.3.1 z-Plane Specifications

7.3.2 The Discrete Root Locus

7.4 Frequency Response Methods

7.4.1 Nyquist Stability Criterion

7.4.2 Design Specifications in the Frequency Domain

7.4.3 Low Frequency Gains and Error Coefficients

7.4.4 Compensator Design

7.5 Direct Design Method of Ragazzini

7.6 Summary

7.7 Problems

8 Design Using State-Space Methods

8.1 Control Law Design

8.1.1 Pole Placement

8.1.2 Controllability

8.1.3 Pole Placement Using CACSD

8.2 Estimator Design

8.2.1 Prediction Estimators

8.2.2 Observability

8.2.3 Pole Placement Using CACSD

8.2.4 Current Estimators

8.2.5 Reduced-Order Estimators

8.3 Regulator Design：Combined Control Law and Estimator

8.3.1 The Separation Principle

8.3.2 Guidelines for Pole Placement

8.4 Introduction of the Reference Input

8.4.1 Reference Inputs for Full-State Feedback

8.4.2 Reference Inputs with Estimators：The State-Command Structure

8.4.3 Output Error Command

8.4.4 A Comparison of the Estimator Structure and Classical Methods

8.5 Integral Control and Disturbance Estimation

8.5.1 Integral Control by State Augmentation

8.5.2 Disturbance Estimation

8.6 Effect of Delays

8.6.1 Sensor Delays

8.6.2 Actuator Delays

8.7 Controllability and Observability

8.8 Summary

8.9 Problems

9 Multivariable and Optimal Control

9.1 Decoupling

9.2 Time-Varying Optimal Control

9.3 LQR Steady-State Optimal Control

9.3.1 Reciprocal Root Properties

9.3.2 Symmetric Root Locus

9.3.3 Eigenvector Decomposition

9.3.4 Cost Equivalents

9.3.5 Emulation by Equivalent Cost

9.4 Optimal Estimation

9.4.1 Least-Squares Estimation

9.4.2 The Kalman Filter

9.4.3 Steady-State Optimal Estimation

9.4.4 Noise Matrices and Discrete Equivalents

9.5 Multivariable Control Design

9.5.1 Selection of Weighting Matrices Q1 and Q2

9.5.2 Pincer Procedure

9.5.3 Paper-Machine Design Example

9.5.4 Magnetic-Tape-Drive Design Example

9.6 Summary

9.7 Problems

10 Quantization Effects

10.1 Analysis of Round-Off Error

10.2 Effects of Parameter Round-Off

10.3 Limit Cycles and Dither

10.4 Summary

10.5 Problems

11 Sample Rate Selection

11.1 The Sampling Theorem’s Limit

11.2 Time Response and Smoothness

11.3 Errors Due to Random Plant Disturbances

11.4 Sensitivity to Parameter Variations

11.5 Measurement Noise and Antialiasing Filters

11.6 Multirate Sampling

11.7 Summary

11.8 Problems

12 System Identification

12.1 Defining the Model Set for Linear Systems

12.2 Identification of Nonparametric Models

12.3 Models and Criteria for Parametric Identification

12.3.1 Parameter Selection

12.3.2 Error Definition

12.4 Deterministic Estimation

12.4.1 Least Squares

12.4.2 Recursive Least Squares

12.5 Stochastic Least Squares

12.6 Maximum Likelihood

12.7 Numerical Search for the Maximum-Likelihood Estimate

12.8 Subspace Identification Methods

12.9 Summary

12.10 Problems

13 Nonlinear Control

13.1 Analysis Techniques

13.1.1 Simulation

13.1.2 Linearization

13.1.3 Describing Functions

13.1.4 Equivalent Gains

13.1.5 Circle Criterion

13.1.6 Lyapunov’s Second Method

13.2 Nonlinear Control Structures：Design

13.2.1 Large Signal Linearization：Inverse Nonlinearities

13.2.2 Time-Optimal Servomechanisms

13.2.3 Extended PTOS for Flexible Structures

13.2.4 Introduction to Adaptive Control

13.3 Design with Nonlinear Cost Functions

13.3.1 Random Neighborhood Search

13.4 Summary

13.5 Problems

14 Design of a Disk Drive Servo：A Case Study

14.1 Overview of Disk Drives

14.1.1 High Performance Disk Drive Servo Profile

14.1.2 The Disk-Drive Servo

14.2 Components and Models

14.2.1 Voice Coil Motors

14.2.2 Shorted Turn

14.2.3 Power Amplifier Saturation

14.2.4 Actuator and HDA Dynamics

14.2.5 Position Measurement Sensor

14.2.6 Runout

14.3 Design Specifications

14.3.1 Plant Parameters for Case Study Design

14.3.2 Goals and Objectives

14.4 Disk Servo Design

14.4.1 Design of the Linear Response

14.4.2 Design by Random Numerical Search

14.4.3 Time-Domain Response of XPTOS Structure

14.4.4 Implementation Considerations

14.5 Summary

14.6 Problems

Appendix A Examples

A.1 Single-Axis Satellite Attitude Control

A.2 A Servomechanism for Antenna Azimuth Control

A.3 Temperature Control of Fluid in a Tank

A.4 Control Through a Flexible Structure

A.5 Control of a Pressurized Flow Box

Appendix B Tables

B.1 Properties of z-Transforms

B.2 Table of z-Transforms

Appendix C A Few Results from Matrix Analysis

C.1 Determinants and the Matrix Inverse

C.2 Eigenvalues and Eigenvectors

C.3 Similarity Transformations

C.4 The Cayley-Hamilton Theorem

Appendix D Summary of Facts from the Theory of Probability and Stochastic Processes

D.1 Random Variables

D.2 Expectation

D.3 More Than One Random Variable

D.4 Stochastic Processes

Appendix E MATLAB Functions

Appendix F Differences Between MATLAB v5 and v4

F.1 System Specification

F.2 Continuous to Discrete Conversion

F.3 Optimal Estimation

References

Index