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Ⅰ MODELING AND ANALYSIS OF DISCRETE-TIME SYSTEMS 3

1 INTRODUCTION TO DIGITAL CONTROL 3

1.1 Basic system concepts and classification 4

1.2 Feedback systems and digital control 9

1.3 Sampling and reconstruction of signals 12

1.4 Computer interfacing 16

1.5 Discrete-time system response 21

1.6 Convolution of sequences 24

1.7 Linear difference equations 26

1.8 Solved Problems 30

1.9 Summary and references 35

Problems 35

2 TRANSFORM ANALYSIS 39

2.1 Introduction to z-transforms 39

2.2 Basic z-transform properties 45

2.3 Inverse transform techniques 51

2.4 Pulse transfer functions 59

2.5 Block diagrams and signal-flow graphs 64

2.6 Response from z-domain functions 71

2.7 A stability test for linear discrete-time systems 77

2.8 Solved problems 80

2.9 Summary and references 88

Problems 89

3 STATE-VARIABLE ANALYSIS FOR DISCRETE-TIME SYSTEMS 95

3.1 Introduction to discrete-time state variables 96

3.2 State variables for continuous-time systems 99

3.3 General solution for the continuous-time state model 101

3.4 Discrete-time state models for sampled-data systems 103

3.5 System response by recursion 107

3.6 State models from difference equations 109

3.7 Equivalent state models and multivariable systems 116

3.8 Discrete-time system stability 122

3.9 Solved problems 127

3.10 Summary and references 137

Problems 138

4 SYSTEM SIMULATION TECHNIQUES 145

4.1 Machine calculation of the transition matrices 146

4.2 Digital filter techniques 150

4.3 Homogenous equivalent systems 166

4.4 Discrete-time system simulation 168

4.5 Simulation of digital control systems 170

4.6 Solved problems 176

4.7 Summary and references 183

Problems 184

5 DIGITAL IMPLEMENTATION 191

5.1 Digital quantization 191

5.2 Sensitivity analysis 194

5.3 Response of discrete-time systems to white noise 196

5.4 Comparison of program realizations 199

5.5 Microprocessor implementation 202

5.6 Solved problems 206

5.7 Summary and references 211

Problems 212

Ⅱ DESIGN TECHNIQUES FOR DISCRETE-TIME SYSTEMS 219

6 DESIGN IN THE Z-DOMAIN 219

6.1 Second-order systemdesign 219

6.2 Dominant second-order systems 225

6.3 Design for steady-state error response 227

6.4 Parameter design by the root-locus method 231

6.5 Parameter sensitivity 243

6.6 A second-order tracking filter 245

6.7 Solved problems 248

6.8 Summary and references 257

Problems 258

7 CONTROLLABILITY AND STATE-VARIABLE FEEDBACK 263

7.1 State controllability 263

7.2 Minimum-norm solutions 267

7.3 Open-loop regulation 270

7.4 Design for deadbeat response 273

7.5 Transformation to controllable form 277

7.6 State-variable feedback design 280

7.7 Solved problems 285

7.8 Summary and references 298

Problems 299

8 OBSERVABILITY AND STATE ESTIMATOR DESIGN 307

8.1 State observability 307

8.2 Transformation to observable form 310

8.3 State estimator design 313

8.4 The separation principle 323

8.5 Output feedback controller design 325

8.6 Duality 328

8.7 Solved problems 330

8.8 Summary and references 341

Problems 342

9 INTRODUCTION TO OPTIMAL CONTROL 347

9.1 Quadratic cost functionals 347

9.2 Optimal regulation 349

9.3 Solution by dynamic programming 351

9.4 Root-square locus 356

9.5 Set-point control 359

9.6 Optimal stochastic control 363

9.7 Solved problems 371

9.8 Summary and references 382

Problems 383

APPENDICES 393

A Laplace Transforms 393

B Matrix Algebra 405

C Discrete-Time Random Signals 414

D Basic Language Programs 421

ANSWERS TO SELECTED PROBLEMS 447

INDEX 455