Control Systems Engineering, eighth edition, offers students a comprehensive introduction to the design and analysis of feedback systems that support modern technology. It takes a practical approach, presenting clear and complete explanations. Real-world examples demonstrate the analysis and design process, while helpful skill-assessment exercises, numerous in-chapter examples, review questions, and problems reinforce key concepts. Multiple experiment formats demonstrate essential principles through hypothetical scenarios, simulations, and interactive virtual models, while Cyber Exploration Laboratory Experiments allow students to interface with actual hardware through National Instruments' myDAQ for real-world systems testing. This emphasis on practical applications has made it the most widely adopted text for core courses in mechanical, electrical, aerospace, biomedical, and chemical engineering.
This edition of the text maintains those aspects of the previous editions that have led to the book being so successful. In addition to introducing a new online chapter on Optimal Control Systems, this edition strengthens the coverage by including new sections on Servomechanism, Multivariable Systems, Tuning of PID Controllers, and All-Pass and Non-Minimum Phase Systems. Many of the end-of-chapter problems have been revised and new problems have been added.
Table of Contents
Preface v
1. Introduction 1
1.1 Introduction 1
1.2 System Configurations 4
1.3 Servomechanism 6
1.4 A History of Control Systems 7
1.5 Analysis and Design Objectives 11
1.6 The Design Process 16
1.7 Multivariable Systems 21
1.8 Computer-Aided Design 22
1.9 The Control Systems Engineer 24
Summary 25
Review Questions 26
Problems 26
Cyber Exploration Laboratory 34
Bibliography 34
2. Modeling in the Frequency Domain 37
2.1 Introduction 37
2.2 Laplace Transform Review 38
2.3 The Transfer Function 48
2.4 Electrical Network Transfer Functions 51
2.5 Translational Mechanical System Transfer Functions 65
2.6 Rotational Mechanical System Transfer Functions 73
2.7 Transfer Functions for Systems with Gears 77
2.8 Electromechanical System Transfer Functions 81
2.9 Electric Circuit Analogs 87
2.10 Nonlinearities 90
2.11 Linearization 91
Summary 99
Review Questions 99
Problems 100
Cyber Exploration Laboratory 114
Hardware Interface Laboratory 117
Bibliography 120
3. Modeling in the Time Domain 123
3.1 Introduction 123
3.2 Some Observations 124
3.3 The General State-Space Representation 129
3.4 Applying the State-Space Representation 131
3.5 Converting a Transfer Function to State Space 139
3.6 Converting from State Space to a Transfer Function 146
3.7 Linearization 148
Summary 156
Review Questions 157
Problems 157
Cyber Exploration Laboratory 169
Bibliography 171
4. Time Response Analysis 173
4.1 Introduction 174
4.2 Poles Zeros and System Response 174
4.3 First-Order Systems 177
4.4 Second-Order Systems: Introduction 180
4.5 The General Second-Order System 185
4.6 Underdamped Second-Order Systems 189
4.7 System Response with Additional Poles 198
4.8 System Response with Zeros 202
4.9 Effects of Nonlinearities upon Time Response 208
4.10 Laplace Transform Solution of State Equations 210
4.11 Time Domain Solution of State Equations 214
Summary 224
Review Questions 225
Problems 226
Cyber Exploration Laboratory 243
Hardware Interface Laboratory 246
Bibliography 252
5. Reduction of Multiple Subsystems 255
5.1 Introduction 255
5.2 Block Diagrams 256
5.3 Analysis and Design of Feedback Systems 265
5.4 Signal-Flow Graphs 268
5.5 Mason’s Rule 271
5.6 Signal-Flow Graphs of State Equations 274
5.7 Alternative Representations in State Space 276
5.8 Similarity Transformations 285
Summary 298
Review Questions 298
Problems 299
Cyber Exploration Laboratory 319
Bibliography 321
6. Stability 323
6.1 Introduction 323
6.2 Routh-Hurwitz Criterion 327
6.3 Routh-Hurwitz Criterion: Special Cases 329
6.4 Routh-Hurwitz Criterion: Additional Examples 335
6.5 Stability in State Space 342
Summary 347
Review Questions 347
Problems 348
Cyber Exploration Laboratory 361
Bibliography 362
7. Steady-state Errors 365
7.1 Introduction 365
7.2 Steady-State Error for Unity-Feedback Systems 369
7.3 Static Error Constants and System Type 375
7.4 Steady-State Error Specifications 378
7.5 Steady-State Error for Disturbances 381
7.6 Steady-State Error for Nonunity-Feedback Systems 383
7.7 Sensitivity 386
7.8 Steady-State Error for Systems in State Space 389
Summary 395
Review Questions 396
Problems 397
Cyber Exploration Laboratory 411
Bibliography 412
8. Root Locus Techniques 415
8.1 Introduction 415
8.2 Defining the Root Locus 420
8.3 Properties of the Root Locus 422
8.4 Sketching the Root Locus 424
8.5 Refining the Sketch 429
8.6 An Example 438
8.7 Transient Response Design via Gain Adjustment 441
8.8 Generalized Root Locus 445
8.9 Root Locus for Positive-Feedback Systems 447
8.10 Pole Sensitivity 449
Summary 456
Review Questions 457
Problems 457
Cyber Exploration Laboratory 479
Hardware Interface Laboratory 481
Bibliography 487
9. Design Via Root Locus 489
9.1 Introduction 489
9.2 Improving Steady-State Error via Cascade Compensation 493
9.3 Improving Transient Response via Cascade Compensation 502
9.4 Improving Steady-State Error and Transient Response 515
9.5 Feedback Compensation 528
9.6 Physical Realization of Compensation 536
9.7 Tuning of PID Controllers 541
Summary 560
Review Questions 561
Problems 561
Cyber Exploration Laboratory 578
Hardware Interface Laboratory 580
Bibliography 582
10. Frequency Response Techniques 585
10.1 Introduction 585
10.2 Asymptotic Approximations: Bode Plots 591
10.3 All-Pass and Nonminimum-Phase
Systems 610
10.4 Introduction to the Nyquist Criterion 615
10.5 Sketching the Nyquist Diagram 619
10.6 Stability via the Nyquist Diagram 625
10.7 Gain Margin and Phase Margin via the Nyquist Diagram 629
10.8 Stability Gain Margin and Phase Margin via Bode Plots 632
10.9 Relation Between Closed-Loop Transient and Closed-Loop Frequency Responses 635
10.10 Relation Between Closed- and Open-Loop Frequency Responses 638
10.11 Relation Between Closed-Loop Transient and Open-Loop Frequency Responses 644
10.12 Steady-State Error Characteristics from Frequency Response 648
10.13 Systems with Time Delay 652
10.14 Obtaining Transfer Functions Experimentally 657
Summary 662
Review Questions 664
Problems 665
Cyber Exploration Laboratory 676
Bibliography 678
11. Design Via Frequency Response 681
11.1 Introduction 681
11.2 Transient Response via Gain Adjustment 683
11.3 Lag Compensation 686
11.4 Lead Compensation 691
11.5 Lag-Lead Compensation 697
Summary 708
Review Questions 708
Problems 709
Cyber Exploration Laboratory 718
Bibliography 719
12. Design Via State Space 721
12.1 Introduction 721
12.2 Controller Design 723
12.3 Controllability 730
12.4 Alternative Approaches to Controller Design 733
12.5 Observer Design 739
12.6 Observability 746
12.7 Alternative Approaches to Observer Design 749
12.8 Steady-State Error Design via Integral Control 756
Summary 765
Review Questions 766
Problems 767
Cyber Exploration Laboratory 776
Bibliography 778
13. Digital Control Systems 779
13.1 Introduction 779
13.2 Modeling the Digital Computer 783
13.3 The z-Transform 786
13.4 Transfer Functions 791
13.5 Block Diagram Reduction 795
13.6 Stability 798
13.7 Steady-State Errors 805
13.8 Transient Response on the z-Plane 809
13.9 Gain Design on the z-Plane 811
13.10 Cascade Compensation via the s-Plane 815
13.11 Implementing the Digital Compensator 818
Summary 825
Review Questions 826
Problems 827
Cyber Exploration Laboratory 836
Bibliography 838
14. Optimal Control Systems 839
(Available Online)
14.1 Introduction 839
14.2 Performance Indices 841
14.3 Optimal Control Problem 846
14.4 Regulator Problem 849
14.5 State Regulator 851
14.6 Output Regulator 859
14.7 Tracking Problem 861
Summary 869
Review Questions 870
Problems 870
Cyber Exploration Laboratory 873
Bibliography 875
Appendix A1 List of Symbols A- 1
Appendix A2 Antenna Azimuth Position Control System A- 5
Appendix A3 Unmanned Free-Swimming Submersible Vehicle A- 7
Appendix A4 Key Equations A- 8
Glossary G-1
Answers to Selected Problems Ans-1
Index I- 1
Online Appendices
Appendix B MATLAB Tutorial
Appendix C Simulink Tutorial
Appendix D LabVIEW Tutorial
Appendix E MATLAB’s GUI Tools Tutorial
Appendix F MATLAB’s Symbolic Math Toolbox Tutorial
Appendix G Matrices Determinants and Systems of Equations
Appendix H Control System Computational Aids
Appendix I Derivation of a Schematic for a DC Motor
Appendix J Derivation of the Time Domain Solution of State Equations
Appendix K Solution of State Equations for t 0 ≠ 0
Appendix L Derivation of Similarity Transformations
Appendix M Root Locus Rules: Derivations
