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自动控制系统（第8版）
作者：（美国）库沃等著
出版社：高等教育出版社
出版时间：2003-12-01
ISBN：9787040137859
定价：¥48.50
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内容简介
本书是教育部高教司推荐的国外优秀信息科学与技术系列教学用书之一。本书共分11章，主要内容包括：绪论；数学基础；结构图和信号流图；物理系统建模；状态变量分析；线性系统的稳定性；控制系统的时域分析；根轨迹方法；频域分析；控制系统的设计；虚拟实验室等。本书从第1版到现在已有40多年的历史，第8版的不同是：为使原书的内容更加完整流畅，将原来版本中的一些内容作为附录放在光盘中；光盘同时提供了自动控制系统工具箱（ACSYS toolbox）和需要使用的MATLAB文件；另外光盘还提供了书中部分习题的答案。本书可供高等院校自动化专业本科生作为教材使用，也可供有关工程技术人员参考使用。
作者简介
暂缺《自动控制系统（第8版）》作者简介
目录
Preface v
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 tbols 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 Definition 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
CHAPTEF 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 = _+c, 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 theRLatls]= ~ 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 Specifications 355
9-2 Mr, mr, 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 Cri~terion 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 t0
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
CHAPTE 10
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
Complex Variable Theory CD-ROM
APPENDX B
Differential and Difference Equations CD-ROM
Elementary Matrix Theory and Algebra CD-ROM
APPENDlX D
Laplace Transform Table CD-ROM
Operational Amplifiers CD-ROM
APPENDIX
Properties and Construction of the Root
Loci CD-ROM
APPENDIX, G
Frequency-Domain Plots CD-ROM
APPENDIX H
General Nyquist Criterion CD-ROM
APPENDIX.
Discrete-Data Control Systems CD-ROM
APPENDIX J
z-Transform Table CD-ROM
APPENDIX K
ACSYS 2002: Description of the Software CD-ROM
ANSWERS TO SELECTED PROBLEm, S CD-ROM
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 tbols 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 Definition 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
CHAPTEF 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 = _+c, 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 theRLatls]= ~ 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 Specifications 355
9-2 Mr, mr, 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 Cri~terion 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 t0
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
CHAPTE 10
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
Complex Variable Theory CD-ROM
APPENDX B
Differential and Difference Equations CD-ROM
Elementary Matrix Theory and Algebra CD-ROM
APPENDlX D
Laplace Transform Table CD-ROM
Operational Amplifiers CD-ROM
APPENDIX
Properties and Construction of the Root
Loci CD-ROM
APPENDIX, G
Frequency-Domain Plots CD-ROM
APPENDIX H
General Nyquist Criterion CD-ROM
APPENDIX.
Discrete-Data Control Systems CD-ROM
APPENDIX J
z-Transform Table CD-ROM
APPENDIX K
ACSYS 2002: Description of the Software CD-ROM
ANSWERS TO SELECTED PROBLEm, S CD-ROM
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