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HANDBOOK OF CONTROL SYSTEMS
ENGINEERING 2nd Edition
THE KLUWER INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE
HANDBOOK OF CONTROL SYSTEMS
ENGINEERING 2nd Edition
by
Louis C. Westphal University of Queensland, Australia
S P R I N G E R SCIENCE+BUSINESS M E D I A , L L C
Library of Congress Cataloging-in-Pubiication Data
Westphal, L . C. Handbook of control systems engineering / by Louis C. Westphal.—2 n d ed. p. cm.-(The Kluwer international series in engineering and computer science; SECS 635) I S B N 978-1-4613-5601-1 I S B N 978-1-4615-1533-3 (eBook) DOI 10.1007/978-1-4615-1533-3 1. Automatic control—Handbooks, manuals, etc. 2. Systems engineering—Handbooks,
manuals, etc. I. Title. II. Series
TJ213.W413 2001 629.8—dc21
2001044307
Copyright © 2001 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 2001 Softcover reprint of the hardcover 2nd edition 2001
A l l rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photo-copying, recording, or otherwise, without the prior written permission of the publisher. Springer Science+ Business Media, L L C .
Printed on acid-free paper.
The Publisher offers discounts on this book for course use and bulk purchases. For further information, send email to <lance.wobus@}vkap.com>
Contents
Preface ...................................................................................................... xxiii
1. Introduction and overview ...................................................................... 1 1.1 Why have feedback control systems? 2 1.2 Influences on development of the field 3 1.3 Types of control - regulation, tracking, trajectory design 6
1.3.1 Regulation 7 1.3.2 Tracking and servomechanism problems 8 1.3.3 Trajectory design/targeting problems 9 1.3.4 Systems 9
1.4 This book: elements of control systems engineering 10 1.4.1 Engineering 10 1.4.2 Process characteristics and modelling 12 1.4.3 Control theory and algorithms 13
1.5 Tools ofthe trade 16 1.6 This book - scope and goals 20 1.7 For more information 20
2. Elements of systems engineering of digital control ............................. 23 2.1 Synopsis 23
··2.2 Management-level considerations 24 2.3 Systems configuration engineering - the intermediate level 24
2.3.1 Closing the loops 24
VI Contents
2.3.2 Computer control configurations - central, distributed, and hierarchical control 29
2.3.3 The top-down alternative 32 2.4 Choosing system elements 32
2.4.1 Assumption: configuration known 33 2.4.2 Selection factors - technical, support, financial 33 2.4.3 Combining the factors - qualitative,
rankings, quantitative 35 2.5 Costing 39
2.5.1 Examples of costs 39 2.5.2 Internal rate of return 39
2.6 Summary comments 42 2.7 Further reading 42
3. Sensors and instrumentation ................................................................. 45 3.1 Synopsis 45 3.2 Sensors and instrumentation 47
3.2.1 Transduction principles 47 3.2.2 General properties 49
3.3 Commercial sensor packages 52 3.3.1 Sensor examples 52 3.3.2 Temperature sensors 53 3.3.3 Displacement measurement 56 3.3.4 Ranging devices 57 3.3.5 Time measurement 57 3.3.6 Pressure and force sensors 57 3.3.7 Level sensors 58 3.3.8 Flow measurement devices 59 3.3.9 Tachometry - speed measurement 61 3.3.10 Accelerometers 62 3.3.11 Attitude sensing - gyros 63 3.3.12 Light measurement 63 3.3.13 Others 64
3.4 Computer to system interfaces - ADCs and signal conditioners 64 3.4.1 Analog to digital converters (ADCs) 65 3.4.2 Associated components 65 3.4.3 Commercial signal conditioning systems 67
3.5 Intelligent instruments 67 3.6 Further reading 68
Contents Vll
4. Control elements, actuators, and displays •...•.....•..•...•.••.••••...•.••.•••.•.•.• 69 4.1 Synopsis 69 4.2 Actuators and transduction 70
4.2.1 Linear-acting devices 70 4.2.2 Rotating devices 71 4.2.3 Transduction via piezo-electricity 71 4.2.4 Heating 71 4.2.5 Light 71
4.3 Control elements and actuators 72 4.3.1 Amplifiers 72 4.3.2 Motors 73 4.3.3 Heater systems 77 4.3.4 Coupled transducers and control elements 77
4.4 Displays 78 4.5 Digital to analog converters and signal conditioners 81
4.5.1 Output Buffers 82 4.5.2 Signal Conditioning 82
4.6 Examples of costs 82 4.7 Further reading 83
5. Computer systems hardware ................................................................ 85 5.1 Synopsis 85 5.2 The generic processor element 87 5.3 Computer system 89
5.3.1 Components of the system -specialized for control 90
5.3.2 How the CPU maintains supervisory control 91 5.3.3 Device interfaces - the core ideas 92
5.4 Commercial systems 94 5.4.1 Microcontroller 94 5.4.2 Special purpose computation elements 95 5.4.3 Programmable logic controllers (PLCs) 95 5.4.4 Three-term (PID) process controllers 97 5.4.5 More general computer control systems 99 5.4.6 Alternative - inhouse design, construction,
and programming 99 5.5 Computer system requirements 99
5.5.1 Finite word length 100 5.5.2 Sampling 102 5.5.3 Rules of thumb 104
5.6 Examples 104 5.7 Summary and further reading 105
Vlll Contents
6. Computer software .............................................................................. 1 07 6.1 Synopsis 107 6.2 Basic problems - the multitasking environment 108
6.2.1 Dealing with the outside world: 110 109 6.2.2 Some special software considerations
with interrupts 110 6.3 Software programming 111
6.3.1 Program structure - procedures 111 6.3.2 Languages: levels of programming 114 6.3.3 Special purpose languages 118 6.3.4 Software considerations 119
6.4 Operating systems 121 6.4.1 Overview 122 6.4.2 Buying a RTOS 123
6.5 Verification and validation 124 6.6 Summary and further reading 127
7. Communications .................................................................................. 129 7.1 Synopsis 129 7.2 Sensor Wiring 130
7.2.1 Wiring, grounding, and shielding 131 7.2.2 Isolation 133 7.2.3 The fiber optic alternative 133
7.3 Communications Networks 133 7.3.1 Standard 110 arrangements 134
7.4 Communication between computers - networking of system elements 136
7.4.1 Topology 137 7.4.2 Technology 138 7.4.3 Communication protocols 139 7.4.4 What's happening - MAP/IEEE 802.4 and others 141
7.5 Network architecture - central vs. distributed control 144 7.6 Costing 145 7.7 Further Reading 145
8. Control laws without theory .........................•...........•.•...............•..•.•.•• 147 8.1 Synopsis 148 8.2 PLCs - The Semiconductor-implemented relay banks 148
8.2.1 The basic scheme 149 8.2.2 Programming in ladder logic 150 8.2.3 The programming of PLCs 151
Contents IX
8.3 Tuning of Controllers 152 8.3.1 Self-tuning controllers 152 8.3.2 Heuristics of PID controllers 154 8.3.3 Rule-of-thumb tuning ofPID controllers 161
8.4 Other Compensators 164 8.5 Further Reading 166
9. Sources of system models .................................................................... 169 9.1 Synopsis 170 9.2 Overview l70 9.3 A typical small plant: model development and use
for a DC motor l73 9.3.1 The model l74 9.3.2 Derivation ofthe model l74 9.3.3 Feedback control of the motor 177 9.3.4 System studies l79
9.4 Mathematical models for control systems 180 9.4.1 A generic response curve model 181 9.4.2 Modelling an exo-atmospheric rocket 182 9.4.3 Process control of a tank's contents 187 9.4.4 Dynamics of robot arms 192 9.4.5 Presses 195 9.4.6 Modelling of noise and disturbances 195 9.4.7 Sampling of data 197
9.5 Linearization 199 9.6 Model errors 202 9.7 Computer assistance 203 9.8 Commentary 203 9.9 Further reading 204
10. Continuous-time system representations ......................................... 207 10.1 Synopsis 207 10.2 Transfer functions 209
10.2.1 Single-input single-output (SISO) systems 209 10.2.2 Multi-input multi-output (MIMO)
- transfer functions 216 10.3 Frequency response 222 10.4 State variable representation 225
10.4.1 Obtaining state space descriptions - linear systems 225
10.4.2 Multi-input multi-output linear systems 233
x Contents
1004.3 Relationship to Laplace transfonns 238 100404 Changes of variable - similarity transfonns 239 10.4.5 Some state space descriptions
for nonlinear systems 241 10.4.6 Finding the system response to input
using state space and transition matrices 244 10.5 Noise and disturbances 248 10.6 Computer programs 252 10.7 Further infonnation 252
11. Sampled-data system representations .............................................. 253 11.1 Synopsis 253 11.2 Time response of difference equations 254 11.3 Transfer functions 259
11.3.1 Basics of use 260 11.3.2 Multivariable transfer functions 263
11.4 Frequency response 265 11.5 State-space representations 267
11.5.1 Introduction 267 11.5.2 Special forms 268 11.5.3 Combinations of state representations 272 11.504 Applications 276 11.5.5 Change of variable and similarity
transfonnations 277 11.5.6 The standard canonical forms 278 11.5.7 The z-transfonn of state equations 278 11.5.8 Transfer function to state-space conversions 279
11.6 Representing noise, disturbances, and errors 280 11.6.1 Modelling of noise and disturbances 280 11.6.2 Model errors 283
11.7 Computer programs 283 11.8 Further infonnation 283
12. Conversions of continuous-time to discrete-time models ............... 285 12.1 Synopsis 285 12.2 Conversions of continuous time control laws 287
12.2.1 Substitutions and their heuristics 289 12.2.2 Invariant transformations 291 12.2.3 Frequency response 292
12.3 Relation of discrete to continuous transfer functions for sampling of continuous time systems 295
Contents Xl
12.4 Discrete-time sampling of continuous systems in state space
12.5 Between-sample behavior 12.6 Computer support 12.7 Summary and further reading
299 302 303 303
13. System performance indicators ................. ~ ...................................... 305 13.1 Synopsis 305 13.2 Stability 306
13.2.1 Definitions 306 13.2.2 Relative stability 308
13.3 Classical response performance indicators 309 13.4 Modern performance indicators 312
13.4.1 Weighted error approaches 312 13.4.2 Modern control theory and optimal control 314
13.5 Other indicators of structure and performance 315 13.5.1 Controllability and observability 316 13.5.2 Sensitivity 317 13.5.3 Robustness 319 13.5.4 System type 321 13.5.5 Reachability 321 13.5.6 Detectability and stabilizability 321
13.6 Summary and further reading 322
14. BIBO stability and simple tests ......................................................... 325 14.1 Synopsis 326 14.2 BIBO stability tests for linear systems 326 14.3 Left half plane tests for continuous time systems 329 14.4 Discrete time systems 332
14.4.1 The Jury-Schur-Cohn test: Raible form 333 14.4.2 Jury test: Jury form 335 14.4.3 Refinements 336 14.4.4 Routh test of w-transformed equation 337
14.5 Relative stability 338 14.6 Design for stability 339 14.7 Computer assistance 342 14.8 Summary and further reading 342
15. Nyquist stability theory ..................................................................... 343 15.1 Synopsis 343
XlI Contents
15.2 The underlying basis - Cauchy's theorem 344 15.3 Application to determining stability of linear control
systems - Nyquist contours and curves. 346 15.4 The multivariable extension 350 15.5 Nonlinearities and limit cycles 354 15.6 Nyquist plots and closed loop response 357 15.7 Relative stability 359 15.8 Design using Nyquist plots 361 15.9 Nyquist and other plots 362 15.10 Computer aids 364 15.11 Further reading 364
16. Lyapunov stability testing ................................................................. 365 16.1 Synopsis 16.2 The basic ideas of Lyapunov's direct method 16.3 Design using Lyapunov's direct method 16.4 Continuous time systems 16.5 Lyapunov's first method 16.6 Converse theorems 16.7 Computer assistance 16.8 Comments and further reading
365 366 371 373 374 375 375 376
17. Steady state response: error constants and system type ................. 377 17.1 Synopsis 377 17.2 Discrete time problems 379 17.3 The continuous time case 384 17.4 Computer aids 386 17.5 Summary of properties 386 17.6 Further reading 387
18. Root locus methods for analysis and design .................................... 389 18.1 Synopsis 389 18.2 Sketching of root locus plots 390
18.2.1 Basics 390 18.2.2 Variations
18.3 Design in root locus 18.4 Computer aids 18.5 Summary and further reading
396 399 402 403
Contents Xlll
19. Desirable pole locations ..................................................................... 405 19.1 Synopsis 405 19.2 Placement of poles in the complex plane
for discrete time systems 406 19.3 Pole locations for continuous time systems 416 19.4 Design for desired poles 422
19.4.1 Design in root locus 422 19.4.2 Design for regions of the complex plane 423
19.5 Alternative pole specification - optimal poles 423 19.5.1 Prototype design 424 19.5.2 Optimal pole locations 427
19.6 Summary 428 19.7 Further Reading 429
20. Bode diagrams for frequency domain analysis and design ............ 431 20.1 Synopsis 431 20.2 The Bode plots 432
20.2.1 Continuous time systems and associated sketches 433
20.2.2 Application of Bode approximation methods to digital control systems 438
20.3 Applications of the Bode diagrams 446 20.3.1 Gain and phase margins 446 20.3.2 Design of compensators 449
20.4 Variations 456 20.4.1 Other frequency domain representations 456 20.4.2 Multidimensional transfer functions 458
20.5 Computer aided design 459 20.6 Summary and Further Reading 460
21. A special control law: deadbeat control ........................................... 461 21.1 Synopsis 461 21.2 Transfer function approaches to design 462 21.3 State-space approaches 465 21.4 Problems and fixes 470 21.5 Computer aids 21.6 Summary, evaluation, and further reading
471 471
22. Controllability .................................................................................... 473 22.1 Synopsis 473
XIV Contents
22.2 Definitions 474 22.3 Controllability tests for constant coefficient systems 475 22.4 Controllability and a controller 478 22.5 Other generalizations 483
22.5.1 Output controllability 483 22.5.2 Continuous-time system models 483 22.5.3 Controllability of linear combinations
of state variables 484 22.5.4 Time-varying systems 484 22.5.5 Minimum energy control from controllability 486 22.5.6 Controllability of nonlinear systems 486
22.6 Computer testing 487 22.7 Further reading 488
23. Controller design by pole placement •••.•.•.•.••.••••.••••••.•.•.•.•..••....•.•..... 489 23.1 Synopsis 489 23.2 The State-space approach 491
23.2.1 The simplest case 491 23.2.2 Single input systems of general form 494 23.2.3 Multiple input systems 497 23.2.4 Semi-arbitrary allocation 498 23.2.5 Systematic construction 498
23.3 Output feedback based upon state-space arguments 503 23.3.1 Scalar control with a canonical form 503 23.3.2 General systematic design of output feedback 506
23.4 The State-space approach to stabilization of non-controllable systems 509
23.5 Pole and zero placement with transfer functions 513 23.5.1 General approach 513 23.5.2 The open-loop control solution 516 23.5.3 Standard feedback control 516 23.5.4 More general solutions 517
23.6 Continuous time systems in state space 522 23.7 Placing poles in desirable regions 523 23.8 Computer aids 525 23.9 Summary 525 23.10 Further reading 526
24. Observability ...................................................................................... 527 24.1 Synopsis 527 24.2 Definitions 528
Contents xv
24.3 Tests for constant coefficient systems 24.3.1 Sampled data systems
529 529 532 534 536 538 538
24.3.2 Basic ideas in the time-varying case 24.3.3 The continuous time case
24.4 Other generalizations and comments 24.5 Computer aids 24.6 Further reading
25. Sta.te observers .................................................................................. 539 25.1 Synopsis 539 25.2 The basic Luenberger observer 540
25.2.1 The identity observer 540 25.2.2 General design equations for identity observers 543 25.2.3 Variation: The reduced order observer 548
25.3 A general formulation 551 25.4 Observers in continuous-time systems 555 25.5 Nonlinear observers 556 25.6 Computer aids 559 25.7 Summary 560 25.8 Further reading 560
26. Optimal control by multiplier-type methods ................................... S61 26.1 Synopsis 562 26.2 Performance criteria and approaches to optimization 565 26.3 Lagrange theory and the Pontryagin maximum principle 567
26.3.1 Parameter optimization and Lagrange multipliers567 26.3.2 Treatment of discrete time optimum control
as a problem in calculus 570 26.3.3 Special application of dynamic Lagrange
multipliers: linear quadratic (LQ) problems 573 26.4 A Pontryagin formulation 579
26.4.1 Basic approach 579 26.4.2 Application to linear quadratic tracking problem 581 26.4.3 Application to minimum time problems 584
26.5 Optimization of Continuous Time Systems 585 26.5.1 Basic Euler-Lagrange theory
for continuous systems 585 26.5.2 Application to linear quadratic (LQ) problem 589 26.5.3 Pontryagin's maximum principle
for continuous time models 591
XVI Contents
26.6.1 Implementation of switching lines 596 26.6.2 Choices of weighting matrices and solutions
of linear quadratic problems 598 26.6.3 Properties of linear quadratic regulator
(LQR) controllers 599 26.7 Computer aids 600 26.8 Summary 600 26.9 Further Reading 600
27. Other optimal control methods ......................................................... 601 27.1 Synopsis 601 27.2 Quadratic equation solution
-generalized predictive control 603 27.3 Minimum variance control 605
27.3.1 Basic result 605 27.3.2 Justification 607 27.3.3 Application 609
27.4 Optimum parameter setting 611 27.5 Minimum time problems using linear algebra 612 27.6 Dynamic programming for optimal control 617
27.6.1 Basic approach 618 27.6.2 Application to a special case: the LQ problem 620 27.6.3 Numerical dynamic programming 623
27.7 Numerical methods and approaches 624 27.7.1 Basics 625 27.7.2 Quasilinearization 628 27.7.3 Variation of extremals - the shooting method 630 27.7.4 Steepest descent in the calculus of variations. 630
27.8 Computer aids 632 27.9 Summary 632 27.10 Further reading 632
28. State estimation in noise .................................................................... 633 28.1 Overview 28.2 A linear unbiased minimum variance estimate
28.2.1 Linear combinations of estimates 28.2.2 Application to state estimation
28.3 Optimal observers for noise suppression 28.4 Continuous time Kalman filters 28.5 Filtering for nonlinear systems
28.5.1 Nonlinear filtering
634 635 635 637 641 646 648 648
Contents
28.5.2 Extended Kalman filter 28.6 Computer aids 28.7 Further reading and final comment
XVll
650 656 656
29. State feedback using state estimates ................................................. 657 29.1 Synopsis 657 29.2 Interaction with state estimators - separation 659 29.3 Combined use of observers and pole placement controllers 660 29.4 The Linear-Quadratic-Gaussian control problem 663 29.5 Computer aids 667 29.6 Summary and further reading 667
30. System identification .......................................................................... 669 30.1 Synopsis 670 30.2 Identification of transfer function parameters 671
30.2.1 Frequency response - a batch special input model-less approach 672
30.2.2 Step and impulse responses - batch or on-line special input methods 675
30.2.3 Auslander's method 676 30.2.3 Cauer form identification - on-line with
successive models and sequences of steps and impulses 678
30.3 Direct parameter estimation for postulated models 681 30.3.1 Least squares data fits for transfer function
models: batch form 681 30.3.2 Least squares data fits for transfer function
models: recursive form 684 30.3.3 Variations - weighted least squares 686 30.3.4 Kalman filtering for parameters
when state measured 687 30.3.5 An adaptive observer for on line parameter
estimation with state measurements 688 30.3.6 The general form for recursive parameter
estimation 690 30.3.7 Partitioned adaptive filters 692 30.3.8 Artificial intelligence methods 693
30.4 Computer aids 694 30.5 Further reading 694
XVlll Contents
31. Adaptive and self-tuning control ...................................................... 695 31.1 Synopsis 31.2 Definitions and concepts 31.3 Gain scheduling 31.4 Optimalizing controls 31.5 Self-tuning regulators 31.6 Model reference adaptive control (MRAC) 31.7 Stochastic optimal control theory 31.8 Computer assistance 31.9 Comments and further reading
696 697 699 700 702 705 710 713 713
32. Structures of multivariable controllers ............................................ 715 32.1 Summary 717 32.2 Cascade and feedforward structures 719 32.3 Transfer function approaches to multivariable systems I:
input -output pairing 722 32.3.1 The issue 722 32.3.2 Pairing selection using the relative gain array 725 32.3.3 Sequential loop closing 728 32.3.4 Decoupling compensators 728
32.4 Transfer function approaches II: diagonalization of transfer matrices 731
32.5 MIMO structures: state-space approaches 732 32.5.1 Loosely coupled systems 733 32.5.2 Systems with slow and fast modes 735 32.5.3 Model aggregation 738 32.5.4 Periodic coordination 742
32.6 Computer aids 743 32.7 Summary and further reading 743
33. Linearization methods for nonlinear systems .................................. 745 33.1 Synopsis 745 33.2 Linear methods for nonlinear systems 746
33.2.1 PI control for a class of nonlinear systems 746 33.2.2 Justification of controllers based upon
algebraic linearization 33.2.3 Krasovskii's stability result
33.3 Nonlinear controllers in linear systems 33.3.1 Method of harmonic balance 33.3.2 Methods based upon harmonic balance ideas 33.3.3 Aizerman's conjecture and Popov theory
750 758 759 759 762 775
Contents XIX
33.4 Feedback Linearization 778 33.4.1 Background 779 33.4.2 Input-state feedback linearization 782 33.4.3 Input-output feedback linearization 791 33.4.4 Existence of a suitable measurement function 796 33.4.5 Discrete time problems 801
33.5 Discussion 806 33.6 Further reading 806
34. Variable structures and sliding mode control ................................. 807 34.1 Synopsis 807 34.2 Introduction and motivation 808 34.3 The continuous-time case 813
34.3.1 Linear systems 814 34.3.2 Nonlinear systems 821 34.3.3 Obtaining the regular form 824 34.3.4 Designing the control surface 825 34.3.5 Controller design 825 34.3.6 Robustness of the control 827
34.4 Discrete-time variable structure systems 34.4.1 Special definitions 34.4.2 The linear system case 34.4.3 A nonlinear case
34.5 Variations 34.6 Comments and applications 34.7 Further reading
832 832 833 838 839 840 840
35. Intelligent control ............................................................................... 841 35.1 Synopsis 841 35.2 Artificial neural networks 844
35.2.1 Neurons and structures 844 35.2.2 Learning 849 35.2.3 Multi-inputs, multi-outputs, multi-layers
and back propagation 853 35.2.4 Applications of ANNs for control systems 858 35.2.5 Stability of adaptive ANN control of
discrete-time systems 862 35.2.6 Applications 865 35.2.7 Further reading 866
35.3 Genetic algorithms 867 35.4 Fuzzy Control 872
xx Contents
35.4.1 Fuzzy sets and fuzzy logic 873 35.4.2 Application to control 875 35.4.3 Variations 883 35.4.4 Stability 885 35.4.5 Learning, approximation, and adaptation 885 35.4.6 Some reported applications 889 35.4.7 Comments and further reading 890
35.5 Expert Systems 891 35.5.1 The notion of the artificial expert 891 35.5.2 Industrial expert systems 892 35.5.3 Comments and further reading 893
35.6 Adaptation and combinations of methods 893 35.7 Final remarks 894
36. Robust control .................................................................................... 895 36.1 Synopsis 895 36.2 A robust control problem 897 36.3 Basic notions and notations 902
36.3.1 Norms 902 36.3.2 Models of errors 905 36.3.3 Notations 907 36.3.4 Internal stability and sensitivity 909 36.3.5 Structures 910 36.3.6 Uncertainty and weighting 913 36.3.7 Gain parameterization 914
36.4 Transfer function approaches to robustness 916 36.4.1 Small gain theory 916 36.4.2 Robust stability 917 36.4.3 Robust performance 920 36.4.4 A design approach 925 36.4.5 Numerical robust control-
quantitative feedback theory 929 36.5 State space approaches 930
36.5.1 A special technique: loop transfer recovery (LTR) 930
36.5.2 Robust performance 934 36.5.3 The two-Riccati equation solution 935
36.6 Model reduction 938 36.7 Computer aids 944 36.8 Summary 945 36.9 Further reading 945
Contents XXI
37. Discrete event control systems .......................................................... 947 37.1 Overview 947 37.2 Desirable properties 948 37.3 A simple problem 948 37.4 The automatalformallanguage approach 952
37.4.1 Analysis 955 37.4.2 Making it work 957
37.5 Petri nets 959 37.5.1 Some theory 959 37.5.2 Variations 969
37.6 Other methods - time dependent performance 970 37.6.1 Queuing theory 970 37.6.2 The max-plus algebra 971 37.6.3 Simulation 975
37.7 Hybrid control - switching for continuous systems 977 37.8 Further reading 977
Appendix A. z-Transform ....................................................................... 979 Al Definition and important properties A2 The inverse z-transform A3 The 'equivalent' transform Zeq A4 Further reading
979 984 987 988
Appendix B. Review of matrices ............................................................. 993 B.l Definitions and notations 993 B.2 Rank 996 B.3 Matrix Inverses and decompositions 997 B.4 Similarity transformations 1001 B.5 Quadratic forms, positive definite matrices, etc. 1003 B.6 Projection matrices 1006 B.7 Matrix Identities 1007 B.8 The Cayley-Hamilton theorem 1008 B.9 Functions of matrices 1008 B.lO Minimization 1009 B.11 Ackermann's formula 1011 B.12 Special similarity transformations into the
standard canonical forms B.13 Metrics for matrices B.14 Notation for derivatives B .15 Further reading
1015 1023 1025 1026
XXll Contents
Appendix C. Description of random processes ................................... 1027 e.l Events, probabilities, and probability density functions 1027 e.2 Averages and moments: means and variances 1029 e.3 Random processes 1031 C.4 Spectra 1033 e.5 Effect of linear systems 1034 e.6 Gaussian processes 1035 e. 7 Time averages and ergodicity 1035 e.S Further reading 1036
References ................................................................................................ 1037
Index ......................................................................................................... 1055
Preface
This book is a revision and extension of my 1995 Sourcebook of Control Systems Engineering. Because of the extensions and other modifications, it has been retitled Handbook of Control Systems Engineering, which it is intended to be for its prime audience: advanced undergraduate students, beginning graduate students, and practising engineers needing an understandable review of the field or recent developments which may prove useful.
There are several differences between this edition and the first.
• Two new chapters on aspects of nonlinear systems have been incorporated. In the first of these, selected material for nonlinear systems is concentrated on four aspects: showing the value of certain linear controllers, arguing the suitability of algebraic linearization, reviewing the semi-classical methods of harmonic balance, and introducing the nonlinear change of variable technique known as feedback linearization. In the second chapter, the topic of variable structure control, often with sliding mode, is introduced.
• Another new chapter introduces discrete event systems, including several approaches to their analysis.
• The chapters on robust control and intelligent control have been extensively revised.
• Modest revisions and extensions have also been made to other chapters, often to incorporate extensions to nonlinear systems.
• Many references have been updated to more recent books, although old standards are still cited. Also, some of the advances in computer and communications technology are reflected.
XXIV Preface
The structure of the book is as in the first edition, and a more detailed guide to the chapters is outlined in Chapter 1. Briefly, the aim is to present the topics in a fairly modular manner with certain main groupings.
• The first several chapters are concerned with the hardware and software of the control task as well as systems engineering associated with the selection of appropriate components.
• The next chapters look at the sources and representations of the mathematical models used in the theory.
• A number of chapters then are concerned with standard classical or transform domain material as is usually presented in a first level university course, including stability theory, root locus diagrams, and Bode plots.
• The next group of chapters then concerns the standard modem or state space material usually met in a second level course. Included here are observers, pole placement, and optimal control
• Overlapping into usual graduate level courses are the next several chapters on more advanced optimal control, Kalman filtering, system identification, and standard adaptive control.
• The final chapters introduce more advanced, research level, subjects. Here are selected topics in nonlinear control, intelligent control, robust control, and discrete event systems.
The topics covered are intended to represent the mainstream of control systems teaching. Examples are presented to illustrate the computability of the theory presented. A number of topics that some readers might like to see included, such as distributed parameter systems and real applications, are not in this book, as it, like the Sourcebook before it, is not intended to be encyclopedic, but simply to provide a basic reference for its target audience.
Preface to the First Edition
LCW 2001
This book joins the multitude of Control Systems books now available, but is neither a textbook nor a monograph. Rather it may be described as a resource book or survey of the elements/essentials of feedback control systems. The material included is a result of my development, over a period of several years, of summaries written to supplement a number of standard textbooks for undergraduate and early post-graduate courses. Those notes,
Preface xxv
plus more work than I care right now to contemplate, are intended to be helpful both to students and to professional engineers.
Too often standard textbooks seem to overlook some of the engineering realities of (roughly) how much things cost or how big computer programs for simple algorithms are, of hardware for sensing and actuation, of special systems such as PLCs and PID controllers, of the engineering of real systems from coverage of SISO theories, and of the special characteristics of computers, their programming, and their potential interactions into systems. In particular, students with specializations other than control systems are not being exposed to the breadth of the considerations needed in control systems engineering, perhaps because it is assumed that they are always to be part of a multicourse sequence taken by specialists. The lectures given to introduce at least some of these aspects were more effective when supported by written material: hence, the need for my notes which preceded this book.
By design and because of its background, this book is different and unusual. A detailed outline may be found in Chapter 1, but here note that:
• the coverage of topics is exceptionally broad for a book which does not claim to be a handbook, although the theory is mostly restricted to linear time-invariant dynamic systems;
• the multiplicity of chapters almost constitutes modularization, a property which makes the book a useful elementary reference and which leads to some overlap of chapters and repetition of basics;
• the level of the book is mostly undergraduate and elementary, with references to more advanced and complete presentations added for those wishing to progress further - examples are very simple ones, intended to show how the theory translates into usable algorithms; and
• the modularization is mostly on the basis of usefulness, as I am unconvinced that so-called unifying theories are appropriate for non-specialists and students just beginning to learn about the subject.
Thus the book will be helpful to several classes of readers:
• students, especially undergraduates and early postgraduates - to supplement their textbooks and as a handy overview;
• engineers who are not control specialists - to summarize in one place the nature of the field so they can interact with specialists or, with this as a starting place, learn enough to help with a particular job; and
• control systems specialists - as a refresher concerning topics outside their speciality.
XXVI Preface
It is appropriate to acknowledge a number of influences here. Although students who made it clear that standard textbooks were not entirely satisfactory were the original motivation, the Electrical Engineering Department provided helpful support, and my industrial experience undoubtedly influenced my attitudes. Several colleagues, notably Drs. Gerry Ledwich, Gerry Shannon, and Pra Murthy, contributed by discussing the concepts and conveying their experiences in trying various aspects of teaching.
Lew 1992
