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1 Introduction 1

1.1 Problem definition 1

1.2 Example systems for study 4

1.3 Overview of design approach 5

1.4 Summary 7

Suggestions for further reading 7

Problems and exercises 9

2 Linear Discrete Dynamic Systems Analysis: The z-Transform 11

2.1 Introduction 11

2.2 Linear difference equations 11

2.3 The discrete transfer function 14

2.4 Signal analysis and dynamic response 26

2.5 Properties of the z-transform 36

2.6 Regions of convergence and the inverse integral 41

2.7 Implementation of difference equations in real time 44

2.8 Summary 48

Appendix to Chapter 2 48

Problems and exercises 50

3 Discrete Equivalents to Continuous Transfer Functions:The Digital Filter 53

3.1 Introduction 53

3.2 Design of digital filters by numerical integration 54

3.3 Pole-zero mapping 61

3.4 Hold equivalence 62

3.5 Butterworth and ITAE equivalents 66

3.6 Summary 73

Problems and exercises 73

4 Sampled Data Systems 77

4.1 Introduction 77

4.2 Sampling as impulse modulation 77

4.3 Sampled spectra and aliasing 79

4.4 Data extrapolation and impostors 82

4.5 Block diagram analysis of sampled data systems 85

4.6 Summary 92

Problems and exercises 92

5Design of Digital Control Systems Using Transform Techniques 95

5.1 Introduction 95

5.2 z-plane specifications of control system design 96

5.3 Design by discrete equivalent 105

5.4 Root locus in the z-plane 108

5.5 Frequency response methods: The w’-transform 113

5.6 Direct design method of Ragazzini 119

5.7 A second example: Temperature control via mixing 124

5.8 Summary 126

Problems and exercises 127

6 Design of Digital Control Systems Using State-Space Methods 131

6.1 Introduction 131

6.2 System representation 131

6.3 Control-law design 139

6.4 Estimator design 145

6.5 Regulator design 150

6.6 Servodesign: Introduction of the reference input by feedforward control 155

6.7 Controllability and observability 164

6.8 Summary 171

Appendix A to Chapter 6 171

Appendix B to Chapter 6 178

Problems and exercises 181

7 Quantization Effects 185

7.1 Introduction 185

7.2 Deterministic analysis of roundoff variables 185

7.3 Stochastic analysis of roundoff variables 190

7.4 Effects of roundoff of parameters 195

7.5 Limit cycles and dither 198

7.6 Summary 201

Appendix to Chapter 7 201

Problems and exercises 203

8 System Identification 207

8.1 Introduction and problem definition 207

8.2 Least squares 216

8.3 Recursive least squares 220

8.4 Stochastic least squares 224

8.5 Maximum likelihood 234

8.6 Numerical search for the maximum likelihood estimate 240

8.7 Summary 244

Problems and exercises 244

9 Multivariable and Optimal Control 247

9.1 Introduction 247

9.2 Decoupling 247

9.3 Optimal control 251

9.4 Optimal estimation 259

9.5 Example of multivariable control 265

9.6 Summary 270

Appendix to Chapter 9 270

Problems and exercises 271

10 Sample Rate Selection 275

10.1 Introduction 275

10.2 Tracking effectiveness in terms of bandwidth, time response, and roughness 275

10.3 Disturbance rejection 278

10.4 Sensitivity to parameter variations 280

10.5 Effect of prefilter design 283

10.6 Summary 285

Problems and exercises 288

Appendix A: Examples 291

A.1 Single-axis satellite attitude control 291

A.2 A servomechanism for antenna azimuth control 293

A.3 Tank fluid temperature control 296

A.4 Control through a flexible structure 298

A.5 Control of a pressurized flow box for a paper machine 300

Appendix B: Tables 303

B.1 Properties of z-transforms 303

B.2 Table of z-transforms 304

B.3 w-plane transfer functions 306

Appendix C: Matrix Analysis 307

C.1 Determinants and the matrix inverse 307

C.2 Eigenvalues and eigenvectors 309

C.3 Similarity transformations 310

C.4 The Cayley-Hamilton theorem 313

Appendix D: Summary of facts from the Theory ofProbability and Stochastic Processes 315

D.1 Random variables 315

D.2 Expectation 317

D.3 More than one random variable 319

D.4 Stochastic processes 321

References 327

Index 331