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Ⅰ THE ELEMENTS1

Ⅰ THE ELEMENTS1

PREVIEW3

1 THE EXCITEMENT OF CONTROL ENGINEERING5

1．2 Motivation for Control Engineering5

1．1 Preview5

1 The Excitement of Control Engineering5

1．3 Historical Periods of Control Theory9

1．4 Types of Control-System Design10

1．5 System Integration11

1．6 Summary18

1．7 Further Reading19

2 Introduction to the Principles of Feedback21

2 INTRODUCTION TO THE PRINCIPLES OF FEEDBACK21

2．1 Preview21

2．2 The Principal Goal of Control21

2．3 A Motivating Industrial Example22

2．4 Definition of the Problem27

2．5 Prototype Solution to the Control Problem via Inversion29

2．6 High-Gain Feedback and Inversion32

2．7 From Open-to Closed-Loop Architectures34

2．9 Measurements36

2．8 Trade-offs Involved in Choosing the Feedback Gain36

2．10 Summary38

2．11 Further Reading39

3 MODELING41

3．1 Preview41

3．2 The Raison d être for Models41

3 Modeling41

3．3 Model Complexity42

3．4 Building Models44

3．5 Model Structures45

3．6 State Space Models45

3．7 Solution of Continuous-Time State Space Models49

3．8 High-Order Differential and Difference-Equation Models50

3．9 Modeling Errors50

3．10 Linearization52

3．11 Case Studies57

3．12 Summary58

3．13 Further Reading60

3．14 Problems for the Reader61

4 Continuous-Time Signals and Systems65

4．2 Linear Continuous-Time Models65

4 CONTINUOUS-TIME SIGNALS AND SYSTEMS65

4．1 Preview65

4．3 Laplace Transforms66

4．4 Laplace Transform．Properties and Examples67

4．5 Transfer Functions70

4．6 Stability of Transfer Functions74

4．7 Impulse and Step Responses of Continuous-Time Linear Systems74

4．8 Poles，Zeros：and Time Responses76

4．9 Frequency Response85

4．10 Fourier Transform92

4．11 Models Frequently Encountered97

4．12 Modeling Errors for Linear Systems99

4．13 Bounds for Modeling Errors103

4．14 Summary104

4．15 Further Reading108

4．16 Problems for the Reader110

Ⅱ SISO CONTROL ESSENTIALS117

Ⅱ SISO CONTROL ESSENTIALS117

PREVIEW119

5 ANALYSIS OF SISO CONTROL LOOPS121

5．1 Preview121

5．2 Feedback Structures121

5 Analysis of SISO Control Loops121

5．3 Nominal Sensitivity Functions125

5．4 Closed-Loop Stability Based on the Characteristic Polynomial127

5．5 Stability and Polynomial Analysis128

5．6 Root Locus（RL）134

5．7 Nominal Stability using Frequency Response138

5．8 Relative Stability：Stability Margins and Sensitivity Peaks143

5．9 Robustness145

5．10 Summary150

5．11 Further Reading152

5．12 Problems for the Reader154

6 Classical PID Control159

6 CLASSICAL PID CONTROL159

6．1 Preview159

6．2 PID Structure159

6．3 Empirical Tuning162

6．4 Ziegler-Nichols（Z-N）Oscillation Method162

6．5 Reaction Curve Based Methods166

6．6 Lead-Lag Compensators170

6．7 Distillation Column171

6．8 Summary174

6．9 Further Reading175

6．10 Problems for the Reader176

7 SYNTHESIS OF SISO CONTROLLERS179

7．1 Preview179

7．2 Polynomial Approach179

7 Synthesis of SISO Controllers179

7．3 PI and PID Synthesis Revisited by using Pole Assignment187

7．4 Smith Predictor189

7．5 Summary191

7．6 Further Reading192

7．7 Problems for the Reader193

Ⅲ SISO CONTROL DESIGN197

Ⅲ SISO CONTROL DESIGN197

PREVIEW199

8 Fundamental Limitations in SISO Control201

8 FUNDAMENTAL LIMITATIONS IN SISO CONTROL201

8．1 Preview201

8．2 Sensors202

8．3 Actuators203

8．5 Model-Error Limitations206

8．4 Disturbances206

8．6 Structural Limitations207

8．7 An Industrial Application（Hold-Up Effect in Reversing Mill）222

8．8 Remedies225

8．9 Design Homogeneity，Revisited232

8．10 Summary232

8．11 Further Reading235

8．12 Problems for the Reader237

9 Frequency-Domain Design Limitations241

9 FREQUENCY-DOMAIN DESIGN LIMITATIONS241

9．1 Preview241

9．2 Bode s Integral Constraints on Sensitivity242

9．3 Integral Constraints on Complementary Sensitivity246

9．4 Poisson Integral Constraint on Sensitivity249

9．5 Poisson Integral Constraint on Complementary Sensitivity254

9．6 Example of Design Trade-offs256

9．7 Summary259

9．8 Further Reading260

9．9 Problems for the Reader263

10 Architectural Issues in SISO Control265

10 ARCHITECTURAL ISSUES IN SISO CONTROL265

10．2 Models for Deterministic Disturbances and References265

10．1 Preview265

10．3 Internal Model Principle for Disturbances267

10．4 Internal Model Principle for Reference Tracking271

10．5 Feedforward271

10．6 Industrial Applications of Feedforward Control279

10．7 Cascade Control281

10．8 Summary285

10．9 Further Reading288

10．10 Problems for the Reader289

11 Dealing with Constraints293

11 DEALING WITH CONSTRAINTS293

11．1 Preview293

11．2 Wind-Up294

11．3 Anti-Wind-up Scheme295

11．4 State Saturation301

11．5 Introduction to Model Predictive Control306

11．6 Summary306

11．7 Further Reading307

11．8 Problems for the Reader309

Ⅳ DIGITAL COMPUTER CONTROL315

Ⅳ DIGITAL COMPUTER CONTROL315

PREVIEW317

12 Models for Sampled-Data Systems319

12．1 Preview319

12 MODELS FOR SAMPLED-DATA SYSTEMS319

12．2 Sampling319

12．3 Signal Reconstruction321

12．4 Linear Discrete-Time Models322

12．5 The Shift Operator322

12．6 Z-Transform323

12．7 Discrete Transfer Functions324

12．8 Discrete Delta-Domain Models328

12．9 Discrete Delta-Transform331

12．10 Discrete Transfer Functions（Delta Form）335

12．12 Discrete System Stability336

12．11 Transfer Functions and Impulse Responses336

12．13 Discrete Models for Sampled Continuous Systems337

12．14 Using Continuous State Space Models340

12．15 Frequency Response of Sampled-Data Systems342

12．16 Summary345

12．17 Further Reading348

12．18 Problems for the Reader349

13 DIGITAL CONTROL353

13．1 Preview353

13．2 Discrete-Time Sensitivity Functions353

13 Digital Control353

13．3 Zeros of Sampled-Data Systems355

13．4 Is a Dedicated Digital Theory Really Necessary?357

13．5 Approximate Continuous Designs358

13．6 At-Sample Digital Design362

13．7 Internal Model Principle for Digital Control372

13．8 Fundamental Performance Limitations376

13．9 Summary380

13．10 Further Reading381

13．11 Problems for the Reader383

14 HYBRID CONTROL387

14．1 Preview387

14．2 Hybrid Analysis387

14．3 Models for Hybrid Control Systems387

14 Hybrid Control387

14．4 Analysis of Intersample Behavior391

14．5 Repetitive Control Revisited393

14．6 Poisson Summation Formula394

14．7 Summary396

14．8 Further Reading397

14．9 Problems for the Reader398

Ⅴ ADVANCED SISO CONTROL403

Ⅴ ADVANCED SISO CONTROL403

PREVIEW405

15 SISO Controller Parameterizations407

15 SISO CONTROLLER PARAMETERIZATIONS407

15．1 Preview407

15．2 Open-Loop Inversion Revisited407

15．3 Affine Parameterization：The Stable Case408

15．4 PID Synthesis by using the Affine Parameterization418

15．5 Affine Parameterization for Systems Having Time Delays427

15．6 Undesirable Closed-Loop Poles430

15．7 Affine Parameterization：The Unstable Open-Loop Case438

15．8 Discrete-Time Systems446

15．9 Summary447

15．10 Further reading451

15．11 Problems for the Reader453

16 Control Design based on Optimization457

16 CONTROL DESIGN BASED ON OPTIMIZATION457

16．1 Preview457

16．2 Optimal Q（Affine）Synthesis458

16．3 Robust Control Design with Confidence Bounds464

16．4 Cheap Control Fundamental Limitations478

16．5 Frequency-Domain Limitations Revisited480

16．6 Summary482

16．7 Further Reading483

16．8 Problems for the Reader486

17 Linear State Space Models491

17．1 Preview491

17．2 Linear Continuous-Time State Space Models491

17 LINEAR STATE SPACE MODELS491

17．3 Similarity Transformations492

17．4 Transfer Functions Revisited494

17．5 From Transfer Function to State Space Representation496

17．6 Controllability and Stabilizability498

17．7 Observability and Detectability508

17．8 Canonical Decomposition513

17．9 Pole-Zero Cancellation and System Properties516

17．10 Summary519

17．11 Further Reading521

17．12 Problems for the Reader523

18 Synthesis via State Space Methods527

18．1 Preview527

18．2 Pole Assignment by State Feedback527

18 SYNTHESIS VIA STATE SPACE METHODS527

18．3 Observers531

18．4 Combining State Feedback with an Observer537

18．5 Transfer-Function Interpretations539

18．6 Reinterpretation of the Affine Parameterization of all Stabilizing Controllers545

18．7 State Space Interpretation of Internal Model Principle546

18．8 Trade-Offs in State Feedback and Observers551

18．9 Dealing with Input Constraints in the Context of State-Estimate Feedback552

18．10 Summary553

18．11 Further Reading555

18．12 Problems for the Reader556

19 Introduction to Nonlinear Control559

19 INTRODUCTION TO NONLINEAR CONTROL559

19．1 Preview559

19．2 Linear Control of a Nonlinear Plant559

19．3 Switched Linear Controllers564

19．4 Control of Systems with Smooth Nonlinearities567

19．5 Static Input Nonlinearities567

19．6 Smooth Dynamic Nonlinearities for Stable and Stably Invertible Models568

19．7 Disturbance Issues in Nonlinear Control575

19．8 More General Plants with Smooth Nonlinearities580

19．9 Nonsmooth Nonlinearities583

19．10 Stability of Nonlinear Systems585

19．11 Generalized Feedback Linearization for nonstability-Invertible Plants595

19．12 Summary603

19．13 Further Reading604

19．14 Problems for the Reader607

Ⅵ MIMO CONTROL ESSENTIALS609

Ⅵ MIMO CONTROL ESSENTIALS609

PREVIEW611

20 ANALYSIS OF MIMO CONTROL LOOPS613

20．1 Preview613

20．2 Motivational Examples613

20 Analysis of MIMO Control Loops613

20．3 Models for Multivariable Systems615

20．4 The Basic MIMO Control Loop624

20．5 Closed-Loop Stability626

20．6 Steady-State Response for Step Inputs630

20．7 Frequency-Domain Analysis631

20．8 Robustness Issues641

20．9 Summary644

20．10 Further Reading646

20．11 Problems for the Reader648

21 Exploiting SISO Techniques in MIMO Control653

21．1 Preview653

21．2 Completely Decentralized Control653

21 EXPLOITING SISO TECHNIQUES IN MIMO CONTROL653

21．3 Pairing of Inputs and Outputs657

21．4 Robustness Issues in Decentralized Control660

21．5 Feedforward Action in Decentralized Control662

21．6 Converting MIMO Problems to SISO Problems664

21．7 Industrial Case Study（Strip Flatness Control）666

21．8 Summary670

21．9 Further Reading671

21．10 Problems for the Reader672

Ⅶ MIMO CONTROL DESIGN675

Ⅶ MIMO CONTROL DESIGN675

PREVIEW677

22 DESIGN VIA OPTIMAL CONTROL TECHNIQUES679

22．1 Preview679

22 Design via Optimal Control Techniques679

22．2 State-Estimate Feedback679

22．3 Dynamic Programming and Optimal Control682

22．4 The Linear Quadratic Regulator（LQR）685

22．5 Properties of the Linear Quadratic Optimal Regulator687

22．6 Model Matching Based on Linear Quadratic Optimal Regulators692

22．7 Discrete-Time Optimal Regulators695

22．8 Connections to Pole Assignment696

22．9 Observer Design698

22．10 Linear Optimal Filters699

22．11 State-Estimate Feedback713

22．12 Transfer-Function Interpretation713

22．13 Achieving Integral Action in LQR Synthesis716

22．14 Industrial Applications718

22．15 Summary730

22．16 Further Reading733

22．17 Problems for the Reader736

23 Model Predictive Control739

23．1 Preview739

23 MODEL PREDICTIVE CONTROL739

23．2 Anti-Wind-Up Revisited740

23．3 What is Model Predictive Control?744

23．4 Stability748

23．5 Linear Models with Quadratic Cost Function751

23．6 State Estimation and Disturbance Prediction756

23．7 Rudder Roll Stabilization of Ships758

23．8 Summary762

23．9 Further Reading763

23．10 Problems for the Reader766

24 Fundamental Limitations in MIMO Control771

24 FUNDAMENTAL LIMITATIONS IN MIMO CONTROL771

24．1 Preview771

24．2 Closed-Loop Transfer Function772

24．4 The Cost of the Internal Model Principle773

24．3 MIMO Internal Model Principle773

24．5 RHP Poles and Zeros774

24．6 Time-Domain Constraints775

24．7 Poisson Integral Constraints of MIMO Complementary Sensitivity780

24．8 Poisson Integral Constraints on MIMO Sensitivity782

24．9 Interpretation783

24．10 An Industrial Application：Sugar Mill785

24．11 Nonsquare Systems796

24．12 Discrete-Time Systems800

24．13 Summary800

24．14 Further Reading802

24．15 Problems for the Reader804

Ⅷ ADVANCED MIMO CONTROL807

Ⅷ ADVANCED MIMO CONTROL807

PREVIEW809

25．1 Preview811

25 MIMO CONTROLLER PARAMETERIZATIONS811

25．2 Affine Parameterization：Stable MIMO Plants811

25 MIMO Controller Parameterizations811

25．3 Achieved Sensitivities813

25．4 Dealing with Model Relative Degree813

25．5 Dealing with NMP Zeros824

25．6 Affine Parameterization：Unstable MIMO Plants841

25．7 State Space Implementation844

25．8 Summary847

25．9 Further Reading848

25．10 Problems for the Reader850

26 Decoupling851

26 DECOUPLING853

26．1 Preview853

26．2 Stable Systems854

26．3 Pre-and PostDiagonalization861

26．4 Unstable Systems863

26．5 Zeros of Decoupled and Partially Decoupled Systems873

26．6 Frequency-Domain Constraints for Dynamically Decoupled Systems876

26．7 The Cost of Decoupling878

26．8 Input Saturation882

26．9 MIMO Anti-Wind-Up Mechanism883

26．10 Summary891

26．11 Further Reading893

26．12 Problems for the Reader895