Control Systems
Engineering
FIFTH EDITION
I.J. Nagrath
M. Gopal
Ansh
an
ANSHAN LTD
6 Newlands Road
Tunbridge Welis, Kent,
TN4 9AT, UK
CONTENTS
Preface to the Fifth Edition
Preface to the Third Edition
1.
INTRODUCTION
1.1
1.2
1.3
1.4
1.5
1.6
2.
3.
4.
91-129
Feedback and Non-feedback Systems 92
Reduction of Parameter Variations by Use of Feedback 93
Control Over System Dynamics by Use of Feedback 97
Control of the Effects of Disturbance Signals by Use of Feedback 100
Linearizing Effect of Feedback 102
Regenerative Feedback 103
Illustrative Examples 104
Problems 119
CONTROL SYSTEMS AND COMPONENTS
4.1
4.2
21-90
Introduction 22
Differential Equations of Physical Systems 24
Dynamics of Robotic Mechanisms 42
Transfer Functions 46
Block Diagram Algebra 54
Signal Flow Graphs 62
Illustrative Examples 72
Problems 83
FEEDBACK CHARACTERISTICS OF CONTROL SYSTEMS
3.1
3.2
3.3
3.4
3.5
3.6
3.7
1-20
The Control System 2
Servomechanisms 6
History and Development of Automatic Control 10
Digital Computer Control 14
Application of Control Theory in Non-engineering Fields 18
The Control Problem 19
MATHEMATICAL MODELS OF PHYSICAL SYSTEMS
2.1
2.2
2.3
2.4
2.5
2.6
2.7
v
vii
Introduction 132
Linear Approximation of Nonlinear Systems 133
131-192
CONTENTS
4.3
4.4
4.5
4.6
5.
Controller Components 134
Stepper Motors 154
Hydraulic Systems 163
Pneumatic Systems 177
Problems 185
TIME RESPONSE ANALYSIS, DESIGN SPECIFICATIONS
193-268
AND PERFORMANCE INDICES
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
6.
CONCEPTS OF STABILITY AND ALGEBRAIC CRITERIA
6.1
6.2
6.3
6.4
6.5
6.6
6.7
7.
Introduction 194
Standard Test Signals 195
Time Response of First-order Systems 197
Time Response of Second-order Systems 199
Steady-state Errors and Error Constants 210
Effect of Adding a Zero to a System 214
Design Specifications of Second-order Systems 215
Design Considerations for Higher-order Systems 221
Performance Indices 223
Illustrative Examples 227
Robotic Control Systems 237
State Variable Analysis—Laplace Transform Technique 245
The Approximation of Higher-order Systems by Lower-order 248
Problems 261
The Concept of Stability 270
Necessary Conditions for Stability 275
Hurwitz Stability Criterion 277
Routh Stability Criterion 278
Relative Stability Analysis 287
More on the Routh Stability Criterion 290
Stability of Systems Modelled in State Variable Form 291
Problems 293
T H E R O O T LOCUS TECHNIQUE
7.1
7.2
7.3
7.4
7.5
7.6
7.7
269-295
297-343
Introduction 298
The Root Locus Concepts 299
Construction Foot Loci 302
Root Contours 327
Systems with Transportation Lag 332
Sensitivity of the Roots of the Characteristic Equation 334
MATLAB: Tool for Design and Analysis of Control Systems—Appendix III 340
Problems 340
CONTENTS
8.
FREQUENCY RESPONSE ANALYSIS
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
9.
11.
425-511
The Design Problem 426
Preliminary Considerations of Classical Design 428
Realization of Basic Compensators 435
Cascade Compensation in Time Domain 440
Cascade Compensation in Frequency Domain 459
Tuning of PID Controllers 477
Feedback Compensation 483
Robust Control System Design 490
Problems 506
DIGITAL CONTROL SYSTEMS
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
377-423
Introduction 378
Mathematical Preliminaries 378
Nyquist Stability Criterion 381
Assessment of Relative Stability Using Nyquist Criterion 394
Closed-loop Frequency Response 409
Sensitivity Analysis in Frequency Domain 417
Problems 420
INTRODUCTION TO DESIGN
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
345-376
Introduction 346
Correlation between Time and Frequency Response 347
Polar Plots 352
Bode Plots 355
All-pass and Minimum-phase Systems 366
Experimental Determination of Transfer Functions 367
Log-magnitude versus Phase Plots 370
MATLAB: Tool for Design and Analysis of Control Systems—Appendix III 371
Problems 374
STABILITY IN FREQUENCY DOMAIN
9.1
9.2
9.3
9.4
9.5
9.6
10.
XI
Introduction 514
Spectrum Analysis of Sampling Process 517
Signal Reconstruction 519
Difference Equations 519
The 2-transform 521
The 2-transfer Function (Pulse Transfer Function) 531
The Inverse 2-transform and Response of Linear Discrete Systems 535
The 2-transform Analysis of Sampled-data Control Systems 538
The 2-and s-domain Relationship 548
513-568
CONTENTS
XII
11.10 Stability Analysis 549
11.11 Compensation Techniques 558
Problems 564
12. STATE VARIABLE ANALYSIS AND DESIGN
12.1
12.2
12.3
12.4
12.5
12.6
12.7
12.8
12.9
Introduction 570
Concepts of State, State Variables and State Model 571
State Models for Linear Continuous-Time Systems 578
State Variables and Linear Discrete-Time Systems 596
Diagonalization 599
Solution of State Equations 604
Concepts of Controllability and Observability 617
Pole Placement by State Feedback 625
Observer Systems 632
Problems 634
13. LIAPUNOV'S STABILITY ANALYSIS
13.1
13.2
13.3
13.4
663-712
Introduction 664
Parameter Optimization: Servomechanisms 665
Optimal Control Problems: Transfer Function Approach 673
Optimal Control Problems: State Variable Approach 684
The State Regulator Problem 688
The Infinite-time Regulator Problem 697
The Output Regulator and the Tracking Problems 702
Parameter Optimization: Regulators 704
Problems 707
15. NONLINEAR SYSTEMS
15.1
15.2
15.3
15.4
15.5
15.6
15.7
641-662
Introduction 642
Liapunov's Stability Criterion 646
The Direct Method of Liapunov and the Linear System 650
Methods of Constructing Liapunov Functions for Nonlinear Systems 652
Problems 660
14. OPTIMAL CONTROL SYSTEMS
14.1
14.2
14.3
14.4
14.5
14.6
14.7
14.8
569-640
Introduction 714
Common Physical Nonlinearities 719
The Phase-plane Method: Basic Concepts 723
Singular Points 725
Stability of Nonlinear System 731
Construction of Phase-trajectories 734
The Describing Function Method: Basic Concepts 742
713-764
CONTENTS
XIII
15.8 Derivation of Describing Functions 743
15.9 Stability Analysis by Describing Function Method 749
15.10 Jump Resonance 757
Problems 759
16.
ADVANCES IN CONTROL SYSTEMS
765-815
16.1 Introduction 766
16.2 Adaptive Control 767
16.3 Fuzzy Logic Control 783
16.4 Neural Networks 801
Problems 812
APPENDICES
Appendix-I
Fourier and Laplace Transforms and Partial Fractions 818
Appendix-II
Elements of Matrix Analysis 827
Appendix-Ill
MATLAB: Tool for Design and Analysis of Control Systems 836
Appendix-TV
Final Value Theorem 848
Appendix-V
Proof of a Transformation 849
Appendix-VI Answers to Problems 852
BIBLIOGRAPHY
869-886
INDEX
887-895