自动控制系统 第8版PDF电子书下载

CHAPTER 1 Introduction 1

1-1 Introduction 1

1-1-1 Basic Components of a Control System 2

1-1-2 Examples of Control-System Applications 2

1-1-3 Open-Loop Control Systems（Nonfeed-back Systems） 6

1-1-4 Closed-loop Control Systems（Feedback Control Systems） 7

1-2 What is Feedback and What are its Effects? 8

1-2-1 Effect of Feedback on Overall Gain 8

1-2-2 Effect of Feedback on Stability 9

1-2-3 Effect of Feedback on External Disturbance or Noise 10

1-3 Types of Feedback Control Systems 11

1-3-1 Linear versus Nonlinear Control Systems 11

1-3-2 Time-Invariant versus Time-Varying Systems 12

1-4 Summary 15

CHAPTER 2 Mathematical Foundation 16

2-1 Introduction 16

2-2 Laplace Transform 17

2-2-1 Definition of the Laplace Transform 17

2-2-2 Inverse Laplace Transformation 18

2-2-3 Important Theorems of the Laplace Transform 19

2-3 Inverse Laplace Transform by Partial-Fraction Expansion 21

2-3-1 Partial-Fraction Expansion 22

2-4 Application of the Laplace Transform to the Solution of Linear Ordinary Differential Equations 25

2-5 Impulse Response and Transfer Functions of Linear Systems 27

2-5-1 Impulse Response 27

2-5-2 Transfer Function（Single-Input，Single-Output Systems） 27

2-5-3 Transfer Function（Multivariable Systems） 29

2-6 MATLAB Tools and Case Studies 30

2-6-1 Description and Use of Transfer Function Tool 30

2-7 Summary 41

CHAPTER 3 Block Diagrams and Signal-Flow Graphs 44

3-1 Block Diagrams 44

3-1-1 Block Diagrams of Control Systems 45

3-1-2 Block Diagrams and Transfer Functions of Multivariable Systems 46

3-2 Signal-Flow Graphs （SFGs） 48

3-2-1 Basic Elements of an SFG 49

3-2-2 Summary of the Basic Properties of SFG 50

3-2-3 Definitions of SFG Terms 51

3-2-4 SFG Algebra 53

3-2-5 SFG of a Feedback Control System 54

3-2-6 Gain Formula for SFG 54

3-2-7 Application of the Gain Formula between Output Nodes and Noninput Nodes 56

3-2-8 Application of the Gain Formula to Block Diagrams 57

3-3 State Diagram 58

3-3-1 From Differential Equations to State Diagram 59

3-3-2 From State Diagram to Transfer Function 61

3-3-3 From State Diagram to State and Output Equations 61

3-4 MATLAB Tools and Case Studies 63

3-5 Summary 65

CHAPTER 4 Modeling of Physical Systems 77

4-1 Introduction 77

4-2 Modeling of Electrical Networks 77

4-3 Modeling of Mechanical Systems Elements 80

4-3-1 Translational Motion 80

4-3-2 Rotational Motion 83

4-3-3 Conversion Between Translational and Rotational Motions 85

4-3-4 Gear Trains 86

4-3-5 Backlash and Dead Zone（Nonlinear Characteristics） 88

4-4 Equations of Mechanical Systems 89

4-5 Sensors and Encoders in Control Systems 94

4-5-1 Potentiometer 94

4-5-2 Tachometers 99

4-5-3 Incremental Encoder 100

4-6 DC Motors in Control Systems 103

4-6-1 Basic Operational Principles of DC Motors 104

4-6-2 Basic Classifications of PM DC Motors 104

4-6-3 Mathematical Modeling of PM DC Motors 107

4-7 Linearization of Nonlinear Systems 110

4-8 Systems with Transportation Lags（Time Delays） 114

4-8-1 Approximation of the Time-Delay Function by Rational Functions 115

4-9 A Sun-Seeker System 116

4-9-1 Coordinate System 117

4-9-2 Error Discriminator 117

4-9-3 Op-Amp 118

4-9-4 Servoamplifier 118

4-9-5 Tachometer 118

4-9-6 DC Motor 118

4-10 MATLAB Tools and Case Studies 120

4-11 Summary 120

CHAPTER 5 State Variable Analysis 138

5-1 Introduction 138

5-2 Vector-Matrix Representation of State Equations 138

5-3 State-Transition Matrix 140

5-3-1 Significance of the State-Transition Matrix 141

5-3-2 Properties of the State-Transition Matrix 142

5-4 State-Transition Equation 143

5-4-1 State-Transition Equation Determined from the State Diagram 145

5-5 Relationship between State Equations and High-Order Differential Equations 147

5-6 Relationship between State Equations and Transfer Functions 149

5-7 Characteristic Equations，Eigenvalues，and Eigenvectors 151

5-7-1 Eigenvalues 152

5-7-2 Eigenvectors 153

5-8 Similarity Transformation 155

5-8-1 Invariance Properties of the Similarity Transformations 156

5-8-2 Controllability Canonical Form（CCF） 156

5-8-3 Observability Canonical Form（OCF） 158

5-8-4 Diagonal Canonical Form（DCF） 159

5-8-5 Jordan Canonical Form （JCF） 160

5-9 Decompositions of Transfer Functions 161

5-9-1 Direct Decomposition 162

5-9-2 Cascade Decomposition 166

5-9-3 Parallel Decomposition 167

5-10 Controllability of Control Systems 169

5-10-1 General Concept of Controllability 170

5-10-2 Detinition of State Controllability 171

5-10-3 Alternate Tests on Controllability 171

5-11 Observability of Linear Systems 173

5-11-1 Definition of Observability 173

5-11-2 Alternate Tests on Observability 174

5-12 Relationship Among Controllability，Observability，and Transfer Functions 175

5-13 Invariant Theorems on Controllability and Observability 177

5-14 A Final Illustrative Example：Magnetic-Ball Suspension System 178

5-15 MATLAB Tools and Case Studies 181

5-15-1 Description and Use of the State-Space Analysis Tool 182

5-15-2 Description and Use of tfsym for State-Space Applications 189

5-15-3 Another Example 189

5-16 Summary 195

CHAPTER 6 Stability of Linear Control Systems 211

6-1 Introduction 211

6-2 Bounded-Input，Bounded-Output（BIBO）Stability—Continuous-Data Systems 212

6-2-1 Relationship between Characteristic Equation Roots and Stability 212

6-3 Zero-Input and Asymptotic Stability of Continuous-Data Systems 213

6-4 Methods of Determining Stability 215

6-5 Routh-Hurwitz Criterion 216

6-5-1 Routh’s Tabulation（1） 217

6-5-2 Special Cases When Routh’s Tabulation Terminates Prematurely 219

6-6 MATLAB Tools and Case Studies 222

6-7 Summary 226

CHAPTER 7 Time-Domain Analysis of Control Systems 233

7-1 Time Response of Continuous-Data Systems：Introduction 233

7-2 Typical Test Signals for the Time Response of Control Systems 234

7-3 The Unit-Step Response and Time-Domain Specifications 236

7-4 Steady-State Error 237

7-4-1 Steady-State Error of Linear Continuous-Data Control Systems 237

7-4-2 Steady-State Error Caused by Nonlinear System Elements 249

7-5 Time Response of a First-Order System 251

7-5-1 Speed Control of a DC Motor 251

7-6 Transient Response of a Prototype Second-Order System 253

7-6-1 Damping Ratio and Damping Factor 253

7-6-2 Natural Undamped Frequency 255

7-6-3 Maximum Overshoot 257

7-6-4 Delay Time and Rise Time 259

7-6-5 Settling Time 261

7-7 Time-Domain Analysis of a Position-Control System 265

7-7-1 Unit-Step Transient Response 268

7-7-2 The Steady-State Response 271

7-7-3 Time Response to a Unit-Ramp Input 271

7-7-4 Time Response of a Third-Order System 273

7-8 Effects of Adding Poles and Zeros to Transfer Functions 276

7-8-1 Addition of a Pole to the Forward-Path Transfer Function：Unity-Feedback Systems 276

7-8-2 Addition of a Pole to the Closed-Loop Transfer Function 277

7-8-3 Addition of a Zero to the Closed-Loop Transfer Function 279

7-8-4 Addition of a Zero to the Forward-Path Transfer Function：Unity-Feedback Systems 280

7-9 Dominant Poles of Transfer Functions 281

7-9-1 The Relative Damping Ratio 282

7-9-2 The Proper Way of Neglecting the Insignificant Poles with Consideration of the Steady-State Response 282

7-10 The Approximation of High-Order Systems by Low- Order System the Formal Approach 283

7-10-1 Approximation Criterion 284

7-11 MATLAB Tools and Case Studies 293

7-12 Summary 307

CHAPTER 8 Root-Locus Technique 318

8-1 Introduction 318

8-2 Basic Properties of the Root Loci（RL） 319

8-3 Properties of the Root Loci 323

8-3-1 K=0 and K=±∞ Points 323

8-3-2 Number of Branches on the Root Loci 324

8-3-3 Symmetry of the RL 324

8-3-4 Angles of Asymptotes of the RL：Behavior of the RL at ︳s|=∞ 324

8-3-5 Intersect of the Asymptotes（Centroid） 325

8-3-6 Root Loci on the Real Axis 325

8-3-7 Angles of Departure and Angles of Arrival of the RL 325

8-3-8 Intersection of the RL with the Imaginary Axis 326

8-3-9 Breakaway Points （Saddle Points）on the RL 326

8-3-10 The Root Sensitivity [17，18，19] 326

8-4 Design Aspects of the Root Loci 330

8-4-1 Effects of Adding Poles and Zeros to G（s）H（s） 330

8-5 Root Contours（RC）：Multiple-Parameter Variation 336

8-6 Root Locus with the MATLAB Toolbox 342

8-7 Summary 345

CHAPTER 9 Frequency-Domain Analysis 352

9-1 Introduction 352

9-1-1 Frequency Response of Closed-Loop Systems 353

9-1-2 Frequency-Domain Specifiications 355

9-2 M?W? and Bandwidth of the Prototype Second-Order System 356

9-2-1 Resonant Peak and Resonant Frequency 356

9-2-2 Bandwidth 358

9-3 Effects of Adding a Zero to the Forward-Path Transfer Function 360

9-4 Effects of Adding a Pole to the Forward-Path Transfer Function 364

9-5 Nyquist Stability Criterion：Fundamentals 365

9-5-1 Stability Problem 366

9-5-2 Definition of Encircled and Enclosed 366

9-5-3 Number of Encirclements and Enclosures 367

9-5-4 Principle of the Argument 368

9-5-5 Nyquist Path 372

9-5-6 Nyquist Criterion and the L（s）or the G（s）H（s）plot 373

9-6 Nyquist Criterion for Systems with Minimum-Phase Transfer Functions 374

9-6-1 Application of the Nyquist Criterion to Minimum-Phase Transfer Functions that Are Not Strictly Proper 375

9-7 Relation Between the Root Loci and the Nyquist Plot 376

9-8 Illustrative Examples： Nyquist Criterion for Minimum-Phase Transfer Functions 378

9-9 Effects of Addition of Poles and Zeros to L（s）on the Shape of the Nyquist Plot 382

9-10 Relative Stability： Gain Margin and Phase Margin 386

9-10-1 Gain Margin（GM） 388

9-10-2 Phase Margin（PM） 389

9-11 Stability Analysis with the Bode Plot 392

9-11-1 Bode Plots of Systems with Pure Time Delays 394

9-12 Relative Stability Related to the Slope of the Magnitude Curve of the Bode Plot 396

9-12-1 Conditionally Stable System 396

9-13 Stability Analysis with the Magnitude-Phase Plot 399

9-14 Constant-M Loci in the Magnitude-Phase Plane：The Nichols Chart 400

9-15 Nichols Chart Applied to Nonunity-Feedback Systems 406

9-16 Sensitivity Studies in the Frequency Domain 407

9-17 MATLAB Tools and Case Studies 409

9-18 Summary 421

CHAPTER 10 Design of Control Systems 433

10-1 Introduction 433

10-1-1 Design Specifications 433

10-1-2 Controller Configurations 435

10-1-3 Fundamental Principles of Design 437

10-2 Design with the PD Controller 438

10-2-1 Time-Domain Interpretation of PD Control 440

10-2-2 Frequency-Domain Interpretation of PD Control 442

10-2-3 Summary of Effects of PD Control 442

10-3 Design with the PI Controller 454

10-3-1 Time-Domain Interpretation and Design of PI Control 456

10-3-2 Frequency-Domain Interpretation and Design of PI Control 456

10-4 Design with the PID Controller 468

10-5 Design with Phase-Lead Controller 471

10-5-1 Time-Domain Interpretation and Design of Phase-Lead Control 473

10-5-2 Frequency-Domain Interpretation and Design of Phase-Lead Control 474

10-5-3 Effects of Phase-Lead Compensation 489

10-5-4 Limitations of Single-Stage Phase-Lead Control 489

10-5-5 Multistage Phase-Lead Controller 489

10-5-6 Sensitivity Considerations 493

10-6 Design with Phase-Lag Controller 494

10-6-1 Time-Domain Interpretation and Design of Phase-Lag Control 494

10-6-2 Frequency-Domain Interpretation and Design of Phase-Lag Control 496

10-6-3 Effects and Limitations of Phase-Lag Control 506

10-7 Design with Lead-Lag Controller 507

10-8 Pole-Zero Cancellation Design：Notch Filter 508

10-8-1 Second-Order Active Filter 511

10-8-2 Frequency-Domain Interpretation and Design 512

10-9 Forward and Feedforward Controllers 520

10-10 Design of Robust Control Systems 521

10-11 Minor-Loop Feedback Control 530

10-11-1 Rate-Feedback or Tachometer-Feedback Control 531

10-11-2 Minor-Loop Feedback Control with Active Filter 532

10-12 State-Feedback Control 534

10-13 Pole-Placement Design through State Feedback 535

10-14 State Feedback with Integral Control 540

10-15 MATLAB Tools and Case Studies 545

10-16 Summary 558

CHAPTER 11 The Virtual Lab 578

11-1 Introduction 578

11-2 Important Aspects in the Response of a DC Motor 579

11-2-1 Speed Response and the Effects of Inductance and Disturbance-Open Loop Response 579

11-2-2 Speed Control of DC Motors： Closed-Loop Response 581

11-2-3 Position Control 582

11-3 Description of the Virtual Experimental System 583

11-3-1 Motor 584

11-3-2 Position Sensor or Speed Sensor 584

11-3-3 Power Amplifier 584

11-3-4 Interface 584

11-4 Description of SIMLab and Virtual Lab Software 585

11-5 Simulation and Virtual Experiments 589

11-5-1 Open-Loop Speed 589

11-5-2 Open-Loop Sine Input 591

11-5-3 Speed Control 593

11-5-4 Position Control 596

11-6 Design Project 598

11-7 Summary 603

INDEX 606