线性控制系统分析与设计 第4版 英文PDF电子书下载

1 Introduction 1

1.1 Introduction 1

1.2 Introduction to Control Systems 1

1.3 Definitions 6

1.4 Historical Background 8

1.5 Digital Control Development 12

1.6 Mathematical Background 13

1.7 General Nature of the Engineering Control Problem 15

1.8 Computer Literacy 16

1.9 Outline of Text 16

2 Writing System Equations 19

2.1 Introduction 19

2.2 Electric Circuits and Components 21

2.3 Basic Linear Matrix Algebra 25

2.4 State Concepts 28

2.5 Transfer Function and Block Diagram 34

2.6 Mechanical Translation Systems 35

2.7 Analogous Circuits 41

2.8 Mechanical Rotational Systems 41

2.9 Thermal Systems 46

2.10 Hydraulic Linear Actuator 48

2.11 Liquid-Level System 53

2.12 Rotating Power Amplifiers 54

2.13 DC Servomotor 56

2.14 AC Servomotor 57

2.15 Lagrange's Equation 59

2.16 Summary 63

3 Solution of Differential Equations 64

3.1 Introduction 64

3.2 Standard Inputs to Control Systems 65

3.3 Steady-State Response:Sinusoidal Input 66

3.4 Steady-State Response:Polynomial Input 67

3.5 Transient Response:Classical Method 70

3.6 Definition of Time Constant 73

3.7 Example:Second-Order Svstem—Mechanical 74

3.8 Example:Second-Order System—Electrical 76

3.9 Second-Order Transients 77

3.10 Time-Response Specifications 80

3.11 CAD Accuracy Checks(CADAC) 82

3.12 State-Variable Equations 82

3.13 Characteristic Values 84

3.14 Evaluating the State Transition Matrix 85

3.15 Complete Solution of the State Equation 88

3.16 Summary 89

4 Laplace Transform 91

4.1 Introduction 91

4.2 Definition of the Laplace Transform 92

4.3 Derivation of Laplace Transforms of Simple Functions 92

4.4 Laplace Transform Theorems 94

4.5 CAD Accuracy Checks:CADAC 97

4.6 Application of the Laplace Transform to Differential Equations 97

4.7 Inverse Transformation 98

4.8 Heaviside Partial-Fraction Expansion Theorems 99

4.9 MATLAB Partial-Fraction Example 106

4.10 Partial-Fraction Shortcuts 107

4.11 Graphical Interpretation of Partial-Fraction Coefficients 109

4.12 Frequency Response from the Pole-Zero Diagram 113

4.13 Location of Poles and Stability 116

4.14 Laplace Transform of the Impulse Function 117

4.15 Second-Order System with Impulse Excitation 119

4.16 Additional Matrix Operations and Properties 120

4.17 Solution of State Equation 126

4.18 Evaluation of the Transfer-Function Matrix 128

4.19 Summary 129

5 System Representation 131

5.1 Introduction 131

5.2 Block Diagrams 131

5.3 Determination of the Overall Transfer Function 136

5.4 Standard Block Diagram Terminology 138

5.5 Position Control System 140

5.6 Simulation Diagrams 144

5.7 Signal Flow Graphs 149

5.8 State Transition Signal Flow Graph 154

5.9 Parallel State Diagrams from Transfer Functions 158

5.10 Diagonalizing the A Matrix 160

5.11 Use of State Transformation for the State Equation Solution 168

5.12 Transforming a Matrix with Complex Eigenvalues 169

5.13 Transforming an A Matrix into Companion Form 172

5.14 Summary 175

6.2 Routh's Stability Criterion 176

6 Control-System Characteristics 176

6.1 Introduction 176

6.3 Mathematical and Physical Forms 182

6.4 Feedback System Types 183

6.5 Analysis of System Types 185

6.6 Example:Type 2 System 190

6.7 Steady-State Error Coefficients 192

6.9 Use of Steady-State Error Coefficients 196

6.8 CAD Accuracy Checks:CADAC 196

6.10 Nonunity-Feedback System 198

6.11 Summary 199

7 Root Locus 200

7.1 Introduction 200

7.2 Plotting Roots of a Characteristic Equation 201

7.3 Qualitative Analysis of the Root Locus 204

7.4 Procedure Outline 207

7.5 Open-Loop Transfer Function 208

7.6 Poles of the Control Ratio C(s)/R(s) 209

7.7 Application of the Magnitude and Angle Conditions 211

7.8 Geometrical Properties(Construction Rules) 215

7.9 CAD Accuracy Checks(CADAC) 225

7.10 Examples 225

7.11 Example l:MATLAB Root Locus 231

7.12 Performance Characteristics 234

7.13 Transport Lag 238

7.14 Synthesis 240

7.15 Summary of Root-Locus Construction Rules for Negative Feedback 241

7.16 Summary 242

8 Frequency Response 244

8.1 Introduction 244

8.2 Correlation of the Sinusoidal and Time Responses 245

8.3 Frequency-Response Curves 246

8.4 Bode Plots(Logarithmic Plots) 247

8.5 General Frequency-Transfer-Function Relationships 249

8.6 Drawing the Bode Plots 250

8.7 Example of Drawing a Bode Plot 256

8.8 System Type and Gain as Related to Log Magnitude Curves 259

8.9 CAD Accuracy Check(CADAC) 262

8.10 Experimental Determination of Transfer Functions 262

8.11 Direct Polar Plots 263

8.12 Summary:Direct Polar Plots 269

8.13 Nyquist's Stability Criterion 270

8.14 Examples of Nyquist's Criterion Using Direct Polar Plot 278

8.15 Nyquist's Stability Criterion Applied to Systems Having Dead Time 281

8.16 Definitions of Phase Margin and Gain Margin and Their Relation to Stability 283

8.17 Stability Characteristics of the Log Magnitude and Phase Diagram 285

8.18 Stability from the Nichols Plot(Log Magnitude-Angle Diagram) 286

8.19 Summary 288

9 Closed-Loop Tracking Performance Based on the Frequency Response 290

9.1 Introduction 290

9.2 Direct Polar Plot 291

9.3 Determination of Mm and ωm for a Simple Second-Order System 292

9.4 Correlation of Sinusoidal and Time Responses 295

9.5 Constant M(ω)and α(ω)Contours of C(jω)/R(jω)on the Complex Plane(Direct Plot) 296

9.6 Constant 1/M and α Contours(Unity Feedback)in the Inverse Polar Plane 303

9.7 Gain Adjustment for a Desired Mm of a Unity-Feedback System:Direct Polar Plot 304

9.8 Constant M and α Curves on the Log Magnitude-Angle Diagram(Nichols Chart) 307

9.9 Generation of MATLAB(1992 Student Version)Bode and Nyquist Plots 309

9.10 Adjustment of Gain by Use of the Log Magnitude-Angle Diagram 312

9.11 Correlation of Pole-Zero Diagram with Frequency and Time Responses 312

9.12 Summary 317

10.1 Introduction to Design 319

10 Root-Locus Compensation:Design 319

10.2 Transient Response:Dominant Complex Poles 321

10.3 Additional Significant Poles 326

10.4 Root-Locus Design Considerations 329

10.5 Reshaping the Root Locus 331

10.6 CAD Accuracy Checks(CADAC) 331

10.7 Ideal Integral Cascade Compensation(PI Controller) 332

10.8 Cascade Lag Compensation Design Using Passive Elements 333

10.9 Ideal Derivative Cascade Compensation(PD Controller) 339

10.10 Lead Compensation Design Using Passive Elements 340

10.11 General Lead-Compensator Design 345

10.12 Lag-Lead Cascade Compensation Design 346

10.13 Comparison of Cascade Compensators 349

10.14 PID Controller 352

10.15 Introduction to Feedback Compensation 353

10.16 Feedback Compensation:Design Procedures 355

10.17 Simplified Rate Feedback Compensation:A Design Approach 355

10.18 Design of Rate Feedback 358

10.19 Design:Feedback of Second Derivative of Output 362

10.20 Results of Feedback Compensation Design 364

10.21 Rate Feedback:Plants with Dominant Complex Poles 364

10.22 Summary 365

11 Frequency-Response Compensation Design 367

11.1 Introduction to Feedback Compensation Design 367

11.2 Selection of a Cascade Compensator 369

11.3 Cascade Lag Compensator 372

11.4 Design Example:Cascade Lag Compensation 375

11.5 Lead Compensator 379

11.6 Design Example:Cascade Lead Compensation 381

11.7 Lag-Lead Compensator 385

11.8 Design Example:Cascade Lag-Lead Compensation 387

11.9 Feedback Compensation Design Using Log Plots 390

11.10 Design Example:Feedback Compensation(Log Plots) 392

11.11 Application Guidelines:Basic Minor-Loop Feedback Compensators 397

11.12 Summary 398

12.1 Introduction 401

12 Control-Ratio Modeling 401

12.2 Modeling a Desired Tracking Control Ratio 402

12.3 Guillemin-Truxal Design Procedure 406

12.4 Introduction to Disturbance Rejection 408

12.5 A Second-Order Disturbance-Rejection Model 409

12.6 Disturbance-Rejection Design Principles for SISO Systems 411

12.7 Disturbance-Rejection Design Example 415

12.8 Disturbance-Rejection Models 418

12.9 Summary 422

13 Design:Closed-Loop Pole-Zero Assignment(State-Variable Feedback) 423

13.1 Introduction 423

13.2 Controllability and Observability 424

13.3 State Feedback for SISO Systems 431

13.4 State-Feedback Design for SISO Systems Using the Control Canonical(Phase-Variables)Form 433

13.5 State-Variable Feedback(Physical Variables) 436

13.6 General Properties of State Feedback(Using Phase Variables) 439

13.7 State-Variable Feedback:Steady-State Error Analysis 442

13.8 Use of Steady-State Error Coefficients 444

13.9 State-Variable Feedback:All-Pole Plant 448

13.10 Plants with Complex Poles 451

13.11 Compensator Containing a Zero 451

13.12 State-Variable Feedback:Pole-Zero Plant 453

13.13 Summary 460

14 Parameter Sensitivity and State Space Trajectories 462

14.1 Introduction 462

14.2 Sensitivity 462

14.3 Sensitivity Analysis 466

14.4 Parameter Sensitivity Examples 472

14.5 Inaccessible States 473

14.6 State-Space Trajectories 477

14.7 Linearization(Jacobian Matrix) 488

14.8 Summary 492

15 Digital Control Systems 493

15.1 Introduction 493

15.2 Sampling 494

15.3 Ideal Sampling 496

15.4 z-Transform Theorems 500

15.5 Synthesis in the z Domain(Direct Method) 500

15.6 The Inverse z Transform 503

15.7 Zero-Order Hold 504

15.8 Limitations 506

15.9 Tustin Transformation 507

15.10 Tustin Transformation Properties 509

15.11 Pseudo-Continuous-Time(PCT)Control System(DIG Method) 512

15.12 Analysis of a Basic(Uncompensated)System 514

15.13 Design of Digital Control Systems 519

15.14 Direct(DIR)Design Technique 520

15.15 Lead Controller(Compensator):DIR Design Method 521

15.16 Lag and Lag-Lead Controllers:DIR Design Method 523

15.17 Digitization(DIG)Design Technique 523

15.18 Summary 526

16 Entire Eigenstructure Assignment for Multivariable Systems 527

16.1 Introduction 527

16.2 Effect of Eigenstructure on Time Response 528

16.3 Entire Eigenstructure Assignment 530

16.4 Examples of Entire Eigenstructure Assignment for Regulators 531

16.5 MATLAB Eigenvectors 537

16.6 Uncontrollable Systems 539

16.7 Tracking Systems 541

16.8 Tracking-System Design Example 543

16.9 MATLAB Example of Tracker Design in Sec.16.8 546

16.10 Summary 551

17.1 Introduction 554

17 Design of Tracking Systems Using Output Feedback 554

17.2 Output Feedback Tracking System 555

17.3 Block Diagonalization 557

17.4 Analysis of Closed-Loop System Performance 559

17.5 Design Procedure for Regular Plants 562

17.6 Regular System Design Example 563

17.7 Irregular Plant Characteristics 566

17.8 Irregular System Performance 568

17.9 Design of the Measurement Matrix M 569

17.10 Irregular System Design Example 571

17.11 Tracker Simulation 574

17.12 Summary 578

18 Quantitative Feedback Theory(QFT)Technique 580

18.1 Introduction 580

18.2 Frequency Responses with Parameter Variations 582

18.3 Introduction to the QFT Method(Single-Loop System) 584

18.4 Minimum-Phase System Performance Specifications 586

18.5 Multiple-Input Multiple-Output(MIMO)Uncertain Plants 590

18.6 Plant Templates of P(s),？P(jωi) 592

18.7 U-Contour 595

18.8 Tracking Bounds Lm BR(jω)on the NC 597

18.9 Disturbance Bounds BD(jωi):Case 1[d2(t)=Dou-1(t),d1(t)=0] 600

18.10 Disturbance Bounds BD(jωi):Case 2[d1(t)=Dou-1(t),d2(t)=0] 605

18.11 The Composite Boundary Bo(jωi) 607

18.12 Shaping of Lo(jω) 608

18.13 Guidelines for Shaping Lo(jω) 614

18.14 Design of the Prefilter F(s) 615

18.15 Basic Design Procedure for a MISO System 617

18.16 Design Example 1 618

18.17 Design Example 2 629

18.18 Template Generation for Unstable Plants 630

18.19 Summary 632

Appendixes 636

A Table of Laplace Transform Pairs 636

B.1 Introduction 640

B Interactive Computer-Aided Design Programs for Digital and Continuous Control-System Analysis and Synthesis 640

B.2 Overview of ICECAP-PC and TOTAL-PC 641

B.3 Overview of MATLAB 645

B.4 QFT CAD Packages 647

B.5 Computer-Aided Design Accuracy Checks(CADAC) 647

B.6 Other Computer-Aided Design Packages 649

Problems 651

Answers to Selected Problems 722

Index 739