1Introduction to Control Systems 1
1.1 Introduction 2
1.2 History of automatic control 4
1.3 Two examples of engineering creativity 7
1.4 Control engineering practice 8
1.5 Examples of modern control systems 10
1.6 Control engineering design 20
1.7 Design example 20
Exercises 22
Problems 23
Design problems 29
Terms and concepts 31
References 31
2Mathematical Models of Systems 35
2.1 Introduction 36
2.2 Differential equations of physical systems 36
2.3 Linear approximations of physical systems 42
2.4 The Laplace transform 45
2.5 The transfer function of linear systems 52
2.6 Block diagram models 64
2.7 Signal-flow graph models 69
2.8 Computer analysis of control systems 75
2.9 Design examples 79
2.10 Summary 84
Exercises 85
Problems 92
Design problems 110
Terms and concepts 112
References 112
3Feedback Control System Characteristics 115
3.1 Open- and closed-loop control systems 116
3.2 Sensitivity of control systems to parameter variations 117
3.3 Control of the transient response of control systems 121
3.4 Disturbance signals in a feedback control system 124
3.5 Steady-state error 129
3.6 The cost of feedback 132
3.7 Design example 134
3.8 Summary 137
Exercises 139
Problems 141
Design problems 152
Terms and concepts 154
References 155
4The Performance of Feedback Control Systems 157
4.1 Introduction 158
4.2 Time-domain performance specifications 159
4.3 The s-plane root location and the transient response 170
4.4 The steady-state error of feedback control systems 171
4.5 Performance indices 176
4.6 The simplilication of linear systems 185
4.7 Design example 188
4.8 Summary 191
Exercises 192
Problems 196
Design problems 204
Terms and concepts 205
References 205
5The Stability of Linear Feedback Systems 207
5.1 The concept of stability 208
5.2 The Routh-Hurwitz stability criterion 211
5.3 The relative stability of feedback control systems 218
5.4 The determination of root locations in the s-plane 220
5.5 Design example 223
5.6 Summary 225
Exercises 225
Problems 227
Design problems 231
Terms and concepts 233
References 233
6The Root Locus Method 235
6.1 Introduction 236
6.2 The root locus concept 236
6.3 The root locus procedure 241
6.4 An example of a control system analysis and design utilizing the root locus method 256
6.5 Parameter design by the root locus method 260
6.6 Sensitivity and the root locus 265
6.7 Design example 274
6.8 Summary 277
Exercises 277
Problems 282
Design problems 296
Terms and concepts 299
References 300
7Frequency Response Methods 301
7.1 Introduction 302
7.2 Frequency response plots 304
7.3 An example of drawing the Bode diagram 321
7.4 Frequency response measurements 325
7.5 Performance specifications in the frequency domain 327
7.6 Log magnitude and phase diagrams 330
7.7 Design example 332
7.8 Summary 335
Exercises 335
Problems 339
Design problems 349
Terms and concepts 351
References 352
8Stability in the Frequency Domain 353
8.1 Introduction 354
8.2 Mapping contours in the s-plane 355
8.3 The Nyquist criterion 360
8.4 Relative stability and the Nyquist criterion 371
8.5 The closed-loop frequency response 378
8.6 The stability of control systems with time delays 386
8.7 System bandwidth 388
8.8 Design example 392
8.9 Summary 403
Exercises 404
Problems 409
Design problems 424
Terms and concepts 427
References 428
9Time-Domain Analysis of Control Systems 429
9.1 Introduction 430
9.2 The state variables of a dynamic system 431
9.3 The state vector differential equation 434
9.4 Signal-flow graph state models 436
9.5 The stability of systems in the time domain 444
9.6 The time response and the transition matrix 450
9.7 A discrete-time evaluation of the time response 454
9.8 Design example 462
9.9 Summary 466
Exercises 466
Problems 470
Design problems 483
Terms and concepts 485
References 485
10The Design and Compensation of Feedback ControlSystems 487
10.1 Introduction 488
10.2 Approaches to compensation 490
10.3 Cascade compensation networks 492
10.4 System compensation on the Bode diagram using thephase-lead network 497
10.5 Compensation on the s-plane using the phase-leadnetwork 504
10.6 System compensation using integration networks 512
10.7 Compensation on the s-plane using a phase-lag network 515
10.8 Compensation on the Bode diagram using a phase-lagnetwork 520
10.9 Compensation on the Bode diagram using analytical andcomputer methods 526
10.10 The design of control systems in the time domain 527
10.11 State-variable feedback 539
10.12 Design example 542
10.13 Summary 546
Exercises 548
Problems 552
Design problems 567
Terms and concepts 570
References 571
11Robust Control Systems 573
11.1 Introduction 574
11.2 Digital computer control system applications 574
11.3 Automatic assembly and robots 576
11.4 Robust control systems 578
11.5 The design of robust control systems 583
11.6 Three-term controllers 590
11.7 The design of robust PID controlled systems 594
11.8 The future evolution of robotics and control systems 600
11.9 Summary 601
Exercises 603
Problems 604
Design problems 609
Terms and concepts 615
References 615
12Design Case Studies 617
12.1 Engineering design 618
12.2 Control system design 619
12.3 The design of an X-Y plotter 621
12.4 The design of a space telescope control system 624
12.5 The design of a robot control system 628
12.6 The design of a mobile robot control system 631
12.7 The design of an ROV control system 633
12.8 The design of a solar-powered racing car motor control system 637
12.9 Summary 640
Design problems 641
Terms and concepts 655
References 655
Appendix A 659
Laplace transform pairs 659
Appendix B 663
Symbols, units, and conversion factors 663
Appendix C 665
An introduction to matrix algebra 665
Appendix D 675
Decibel conversion 675
Appendix E 677
Complex numbers 677
Appendix F 683
The Control System Design Program 683
Answers to Selected Problems 703
Index and Glossary 709