动态系统的数字控制 英文本PDF电子书下载

1 Introduction 1

1.1 Problem Definition 1

1.2 Overview of Design Approach 5

1.3 Computer-Aided Design 7

1.4 Suggestions for Further Reading 7

1.5 Summary 8

1.6 Problems 8

2 Review of Continuous Control 11

2.1 Dynamic Response 11

2.1.1 Differential Equations 12

2.1.2 Laplace Transforms and Transfer Functions 12

2.1.3 Output Time Histories 14

2.1.4 The Final Value Theorem 15

2.1.5 Block Diagrams 15

2.1.6 Response versus Pole Locations 16

2.1.7 Time-Domain Specifications 20

2.2 Basic Properties of Feedback 22

2.2.1 Stability 22

2.2.2 Steady-State Errors 23

2.2.3 PID Control 24

2.3 Root Locus 24

2.3.1 Problem Definition 25

2.3.2 Root Locus Drawing Rules 26

2.3.3 Computer-Aided Loci 28

2.4 Frequency Response Design 31

2.4.1 Specifications 32

2.4.2 Bode Plot Techniques 34

2.4.3 Steady-State Errors 35

2.4.4 Stability Margins 36

2.4.5 Bode’s Gain-Phase Relationship 37

2.4.6 Design 38

2.5 Compensation 39

2.6 State-Space Design 41

2.6.1 Control Law 42

2.6.2 Estimator Design 46

2.6.3 Compensation：Combined Control and Estimation 48

2.6.4 Reference Input 48

2.6.5 Integral Control 49

2.7 Summary 50

2.8 Problems 52

3 Introductory Digital Control 57

3.1 Digitization 58

3.2 Effect of Sampling 63

3.3 PID Control 66

3.4 Summary 68

3.5 Problems 69

4 Discrete Systems Analysis 73

4.1 Linear Difference Equations 73

4.2 The Discrete Transfer Function 78

4.2.1 The z-Transform 79

4.2.2 The Transfer Function 80

4.2.3 Block Diagrams and State-Variable Descriptions 82

4.2.4 Relation of Transfer Function to Pulse Response 90

4.2.5 External Stability 93

4.3 Discrete Models of Sampled-Data Systems 96

4.3.1 Using the z-Transform 96

4.3.2 Continuous Time Delay 99

4.3.3 State-Space Form 101

4.3.4 State-Space Models for Systems with Delay 110

4.3.5 Numerical Considerations in Computing Φ and Γ 114

4.3.6 Nonlinear Models 117

4.4 Signal Analysis and Dynamic Response 119

4.4.1 The Unit Pulse 120

4.4.2 The Unit Step 120

4.4.3 Exponential 121

4.4.4 General Sinusoid 122

4.4.5 Correspondence with Continuous Signals 125

4.4.6 Step Response 128

4.5 Frequency Response 131

4.5.1 The Discrete Fourier Transform （DFT） 134

4.6 Properties of the z-Transform 137

4.6.1 Essential Properties 137

4.6.2 Convergence of z-Transform 142

4.6.3 Another Derivation of the Transfer Function 146

4.7 Summary 148

4.8 Problems 149

5 Sampled-Data Systems 155

5.1 Analysis of the Sample and Hold 156

5.2 Spectrum of a Sampled Signal 160

5.3 Data Extrapolation 164

5.4 Block-Diagram Analysis of Sampled-Data Systems 170

5.5 Calculating the System Output Between Samples：The Ripple 180

5.6 Summary 182

5.7 Problems 183

5.8 Appendix 186

6 Discrete Equivalents 187

6.1 Design of Discrete Equivalents via Numerical Integration 189

6.2 Zero-Pole Matching Equivalents 200

6.3 Hold Equivalents 202

6.3.1 Zero-Order Hold Equivalent 203

6.3.2 A Non-Causal First-Order-Hold Equivalent：The Triangle-Hold Equivalent 204

6.4 Summary 208

6.5 Problems 209

7 Design Using Transform Techniques 211

7.1 System Specifications 212

7.2 Design by Emulation 214

7.2.1 Discrete Equivalent Controllers 215

7.2.2 Evaluation of the Design 218

7.3 Direct Design by Root Locus in the z-Plane 222

7.3.1 z-Plane Specifications 222

7.3.2 The Discrete Root Locus 227

7.4 Frequency Response Methods 234

7.4.1 Nyquist Stability Criterion 238

7.4.2 Design Specifications in the Frequency Domain 243

7.4.3 Low Frequency Gains and Error Coefficients 259

7.4.4 Compensator Design 260

7.5 Direct Design Method of Ragazzini 264

7.6 Summary 269

7.7 Problems 270

8 Design Using State-Space Methods 279

8.1 Control Law Design 280

8.1.1 Pole Placement 282

8.1.2 Controllability 285

8.1.3 Pole Placement Using CACSD 286

8.2 Estimator Design 289

8.2.1 Prediction Estimators 290

8.2.2 Observability 293

8.2.3 Pole Placement Using CACSD 294

8.2.4 Current Estimators 295

8.2.5 Reduced-Order Estimators 299

8.3 Regulator Design：Combined Control Law and Estimator 302

8.3.1 The Separation Principle 302

8.3.2 Guidelines for Pole Placement 308

8.4 Introduction of the Reference Input 310

8.4.1 Reference Inputs for Full-State Feedback 310

8.4.2 Reference Inputs with Estimators：The State-Command Structure 314

8.4.3 Output Error Command 317

8.4.4 A Comparison of the Estimator Structure and Classical Methods 319

8.5 Integral Control and Disturbance Estimation 322

8.5.1 Integral Control by State Augmentation 323

8.5.2 Disturbance Estimation 328

8.6 Effect of Delays 337

8.6.1 Sensor Delays 338

8.6.2 Actuator Delays 341

8.7 Controllability and Observability 345

8.8 Summary 351

8.9 Problems 352

9 Multivariable and Optimal Control 359

9.1 Decoupling 360

9.2 Time-Varying Optimal Control 364

9.3 LQR Steady-State Optimal Control 371

9.3.1 Reciprocal Root Properties 372

9.3.2 Symmetric Root Locus 373

9.3.3 Eigenvector Decomposition 374

9.3.4 Cost Equivalents 379

9.3.5 Emulation by Equivalent Cost 380

9.4 Optimal Estimation 382

9.4.1 Least-Squares Estimation 383

9.4.2 The Kalman Filter 389

9.4.3 Steady-State Optimal Estimation 394

9.4.4 Noise Matrices and Discrete Equivalents 396

9.5 Multivariable Control Design 400

9.5.1 Selection of Weighting Matrices Q1 and Q2 400

9.5.2 Pincer Procedure 401

9.5.3 Paper-Machine Design Example 403

9.5.4 Magnetic-Tape-Drive Design Example 407

9.6 Summary 419

9.7 Problems 420

10 Quantization Effects 425

10.1 Analysis of Round-Off Error 426

10.2 Effects of Parameter Round-Off 437

10.3 Limit Cycles and Dither 440

10.4 Summary 445

10.5 Problems 445

11 Sample Rate Selection 449

11.1 The Sampling Theorem’s Limit 450

11.2 Time Response and Smoothness 451

11.3 Errors Due to Random Plant Disturbances 454

11.4 Sensitivity to Parameter Variations 461

11.5 Measurement Noise and Antialiasing Filters 465

11.6 Multirate Sampling 469

11.7 Summary 474

11.8 Problems 476

12 System Identification 479

12.1 Defining the Model Set for Linear Systems 481

12.2 Identification of Nonparametric Models 484

12.3 Models and Criteria for Parametric Identification 495

12.3.1 Parameter Selection 496

12.3.2 Error Definition 498

12.4 Deterministic Estimation 502

12.4.1 Least Squares 503

12.4.2 Recursive Least Squares 506

12.5 Stochastic Least Squares 510

12.6 Maximum Likelihood 521

12.7 Numerical Search for the Maximum-Likelihood Estimate 526

12.8 Subspace Identification Methods 535

12.9 Summary 538

12.10 Problems 539

13 Nonlinear Control 543

13.1 Analysis Techniques 544

13.1.1 Simulation 545

13.1.2 Linearization 550

13.1.3 Describing Functions 559

13.1.4 Equivalent Gains 573

13.1.5 Circle Criterion 577

13.1.6 Lyapunov’s Second Method 579

13.2 Nonlinear Control Structures：Design 582

13.2.1 Large Signal Linearization：Inverse Nonlinearities 582

13.2.2 Time-Optimal Servomechanisms 599

13.2.3 Extended PTOS for Flexible Structures 611

13.2.4 Introduction to Adaptive Control 615

13.3 Design with Nonlinear Cost Functions 635

13.3.1 Random Neighborhood Search 635

13.4 Summary 642

13.5 Problems 643

14 Design of a Disk Drive Servo：A Case Study 649

14.1 Overview of Disk Drives 650

14.1.1 High Performance Disk Drive Servo Profile 652

14.1.2 The Disk-Drive Servo 654

14.2 Components and Models 655

14.2.1 Voice Coil Motors 655

14.2.2 Shorted Turn 658

14.2.3 Power Amplifier Saturation 659

14.2.4 Actuator and HDA Dynamics 660

14.2.5 Position Measurement Sensor 663

14.2.6 Runout 664

14.3 Design Specifications 666

14.3.1 Plant Parameters for Case Study Design 667

14.3.2 Goals and Objectives 669

14.4 Disk Servo Design 670

14.4.1 Design of the Linear Response 671

14.4.2 Design by Random Numerical Search 674

14.4.3 Time-Domain Response of XPTOS Structure 678

14.4.4 Implementation Considerations 683

14.5 Summary 686

14.6 Problems 687

Appendix A Examples 689

A.1 Single-Axis Satellite Attitude Control 689

A.2 A Servomechanism for Antenna Azimuth Control 691

A.3 Temperature Control of Fluid in a Tank 694

A.4 Control Through a Flexible Structure 697

A.5 Control of a Pressurized Flow Box 699

Appendix B Tables 701

B.1 Properties of z-Transforms 701

B.2 Table of z-Transforms 702

Appendix C A Few Results from Matrix Analysis 705

C.1 Determinants and the Matrix Inverse 705

C.2 Eigenvalues and Eigenvectors 707

C.3 Similarity Transformations 709

C.4 The Cayley-Hamilton Theorem 711

Appendix D Summary of Facts from the Theory of Probability and Stochastic Processes 713

D.1 Random Variables 713

D.2 Expectation 715

D.3 More Than One Random Variable 717

D.4 Stochastic Processes 719

Appendix E MATLAB Functions 725

Appendix F Differences Between MATLAB v5 and v4 727

F.1 System Specification 727

F.2 Continuous to Discrete Conversion 729

F.3 Optimal Estimation 730

References 731

Index 737