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1．Computer Control 1

1．1 Introduction 1

1．2 Computer Technology 2

1．3 Computer-Control Theory 11

1．4 Inherently Sampled Systems 22

1．5 How Theory Developed 25

1．6 Notes and References 28

2．Discrete-Time Systems 30

2．1 Introduction 30

2．2 Sampling Continuous-Time Signals 31

2．3 Sampling a Continuous-Time State-Space System 32

2．4 Discrete-Time Systems 42

2．5 Changing Coordinates in State-Space Models 44

2．6 Input-Output Models 46

2．7 The z-Transform 53

2．8 Poles and Zeros 61

2．9 Selection of Sampling Rate 66

2．10 Problems 68

2．11 Notes and References 75

3．Analysis of Discrete-Time Systems 77

3．1 Introduction 77

3．2 Stability 77

3．3 Sensitivity and Robustness 89

3．4 Controllability , Reachability , Observability ,and Detectability 93

3．5 Analysis of Simple Feedback Loops 103

3．6 Problems 114

3．7 Notes and References 118

4．Pole-Placement Design: A State-Space Approach 120

4．1 Introduction 120

4．2 Control-System Design 121

4．3 Regulation by State Feedback 124

4．4 Observers 135

4．5 Output Feedback 141

4．6 The Servo Problem 147

4．7 A Design Example 156

4．8 Conclusions 160

4．9 Problems 161

4．10 Notes and References 164

5．Pole-Placement Design: A Polynomial Approach 165

5．1 Introduction 165

5．2 A Simple Design Problem 166

5．3 The Diophantine Equation 170

5．4 More Realistic Assumptions 175

5．5 Sensitivity to Modeling Errors 183

5．6 A Design Procedure 186

5．7 Design of a Controller for the Double Integrator 195

5．8 Design of a Controller for the Harmonic Oscillator 203

5．9 Design of a Controller for a Flexible Robot Arm 208

5．10 Relations to Other Design Methods 213

5．11 Conclusions 220

5．12 Problems 220

5．13 Notes and References 223

6．1 Introduction 224

6．Design: An Overview 224

6．2 Operational Aspects 225

6．3 Principles of Structuring 229

6．4 A Top-Down Approach 230

6．5 A Bottom-Up Approach 233

6．6 Design of Simple Loops 237

6．7 Conclusions 240

6．8 Problems 241

6．9 Notes and References 241

7．Process-Oriented Models 242

7．1 Introduction 242

7．2 A Computer-Controlled System 243

7．3 Sampling and Reconstruction 244

7．4 Aliasing or Frequency Folding 249

7．5 Designing Controllers with Predictive First-Order Hold 256

7．6 The Modulation Model 262

7．7 Frequency Response 268

7．8 Pulse-Transfer-Function Formalism 278

7．9 Multirate Sampling 286

7．10 Problems 289

7．11 Notes and References 291

8．Approximating Continuous-Time Controllers 293

8．1 Introduction 293

8．2 Approximations Based on Transfer Functions 293

8．3 Approximations Based on State Models 301

8．4 Frequency-Response Design Methods 305

8．5 Digital PID-Controllers 306

8．6 Conclusions 320

8．7 Problems 320

8．8 Notes and References 323

9．Implementation of Digital Controllers 324

9．1 Introduction 324

9．2 An Overview 325

9．3 Prefiltering and Computational Delay 328

9．4 Nonlinear Actuators 331

9．5 Operational Aspects 336

9．6 Numerics 340

9．7 Realization of Digital Controllers 349

9．8 Programming 360

9．9 Conclusions 363

9．10 Problems 364

9．11 Notes and References 368

10．Disturbance Models 370

10．1 Introduction 370

10．2 Reduction of Effects of Disturbances 371

10．3 Piecewise Deterministic Disturbances 373

10．4 Stochastic Models of Disturbances 376

10．5 Continuous-Time Stochastic Processes 397

10．6 Sampling a Stochastic Differential Equation 402

10．7 Conclusions 403

10．8 Problems 404

10．9 Notes and References 407

11．1 Introduction 408

11．Optimal Design Methods: A State-Space Approach 408

11．2 Linear Quadratic Control 413

11．3 Prediction and Filtering Theory 429

11．4 Linear Quadratic Gaussian Control 436

11．5 Practical Aspects 440

11．6 Conclusions 441

11．7 Problems 441

11．8 Notes and References 446

12．Optimal Design Methods: A Polynomial Approach 447

12．1 Introduction 447

12．2 Problem Formulation 448

12．3 Optimal Prediction 453

12．4 Minimum-Variance Control 460

12．5 Linear Quadratic Gaussian（LQG）Control 470

12．6 Practical Aspects 487

12．7 Conclusions 495

12．8 Problems 496

12．9 Notes and References 504

13．Identification 505

13．1 Introduction 505

13．2 Mathematical Model Building 506

13．3 System Identification 506

13．4 The Principle of Least Squares 509

13．5 Recursive Computations 514

13．6 Examples 521

13．8 Problems 526

13．7 Summary 526

13．9 Notes and References 527

A．Examples 528

B．Matrices 533

B．1 Matrix Functions 533

B．2 Matrix-Inversion Lemma 536

B．3 Notes and References 536

Bibliography 537

Index 549