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Chapter 1 Introduction to Control Systems 1

1-1 Introduction 1

1-2 Examples of Control Systems 4

1-3 Closed-Loop Control Versus Open-Loop Control 7

1-4 Design and Compensation of Control Systems 9

1-5 Outline of the Book 10

Chapter 2 Mathematical Modeling of Control Systems 13

2-1 Introduction 13

2-2 Transfer Function and Impulse-Response Function 15

2-3 Automatic Control Systems 17

2-4 Modeling in State Space 29

2-5 State-Space Representation of Scalar Differential Equation Systems 35

2-6 Transformation of Mathematical Models with MATLAB 39

2-7 Linearization of Nonlinear Mathematical Models 43

Example Problems and Solutions 46

Problems 60

Chapter 3 Mathematical Modeling of Mechanical Systems and Electrical Systems 63

3-1 Introduction 63

3-2 Mathematical Modeling of Mechanical Systems 63

3-3 Mathematical Modeling of Electrical Systems 72

Example Problems and Solutions 86

Problems 97

Chapter 4 Mathematical Modeling of Fluid Systems and Thermal Systems 100

4-1 Introduction 100

4-2 Liquid-Level Systems 101

4-3 Pneumatic Systems 106

4-4 Hydraulic Systems 123

4-5 Thermal Systems 136

Example Problems and Solutions 140

Problems 152

Chapter 5 Transient and Steady-State Response Analyses 159

5-1 Introduction 159

5-2 First-Order Systems 161

5-3 Second-Order Systems 164

5-4 Higher-Order Systems 179

5-5 Transient-Response Analysis with MATLAB 183

5-6 Routh's Stability Cntenon 212

5-7 Effects of Integral and Derivative Control Actions on System Performance 218

5-8 Steady-State Errors in Unity-Feedback Control Systems 225

Example Problems and Solutions 231

Problems 263

Chapter 6 Control Systems Analysis and Design by the Root-Locus Method 269

6-1 Introduction 269

6-2 Root-Locus Plots 270

6-3 Plotting Root Loci with MATLAB 290

6-4 Root-Locus Plots of Positive Feedback Systems 303

6-5 Root-Locus Approach to Control-Systems Design 308

6-6 Lead Compensation 311

6-7 Lag Compensation 321

6-8 Lag-Lead Compensation 330

6-9 Parallel Compensation 342

Example Problems and Solutions 347

Problems 394

Chapter 7 Control Systems Analysis and Design by the Frequency-Response Method 398

7-1 Introduction 398

7-2 Bode Diagrams 403

7-3 Polar Plots 427

7-4 Log-Magnitude-versus-Phase Plots 443

7-5 Nyquist Stability Cntenon 445

7-6 Stability Analysis 454

7-7 Relative Stability Analysis 462

7-8 Closed-Loop Frequency Response of Unity-Feedback Systems 477

7-9 Experimental Determination of Transfer Functions 486

7-10 Control Systems Design by Frequency-Response Approach 491

7-11 Lead Compensation 493

7-12 Lag Compensation 502

7-13 Lag-Lead Compensation 511

Example Problems and Solutions 521

Problems 561

Chapter 8 PID Controllers and Modified PID Controllers 567

8-1 Introduction 567

8-2 Ziegler-Nichols Rules for Tuning PID Controllers 568

8-3 Design of PID Controllers with Frequency-Response Approach 577

8-4 Design of PID Controllers with Computational Optimization Approach 583

8-5 Modifications of PID Control Schemes 590

8-6 Two-Degrees-of-Freedom Control 592

8-7 Zero-Placement Approach to Improve Response Characteristics 595

Example Problems and Solutions 614

Problems 641

Chapter 9 Control Systems Analysis in State Space 648

9-1 Introduction 648

9-2 State-Space Representations of Transfer-Function Systems 649

9-3 Transformation of System Models with MATLAB 656

9-4 Solving the Time-Invariant State Equation 660

9-5 Some Useful Results in Vector-Matrix Analysis 668

9-6 Controllability 675

9-7 Observability 682

Example Problems and Solutions 688

Problems 720

Chapter 10 Control Systems Design in State Space 722

10-1 Introduction 722

10-2 Pole Placement 723

10-3 Solving Pole-Placement Problems with MATLAB 735

10-4 Design of Servo Systems 739

10-5 State Observers 751

10-6 Design of Regulator Systems with Observers 778

10-7 Design of Control Systems with Observers 786

10-8 Quadratic Optimal Regulator Systems 793

10-9 Robust Control Systems 806

Example Problems and Solutions 817

Problems 855

Appendix A Laplace Transform Tables 859

Appendix B Partial-Fraction Expansion 867

Appendix C Vector-Matrix Algebra 874

References 882

Index 886