Introduction to control theory
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford ; New York ; Tokyo
Oxford University Press
1993
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| Ausgabe: | second edition |
| Schriftenreihe: | Oxford science publications
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| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Jacobs, Oliver L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to control theory |c O. L. R. Jacobs |
| 250 | |a second edition | ||
| 264 | 1 | |a Oxford ; New York ; Tokyo |b Oxford University Press |c 1993 | |
| 300 | |a xii, 390 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102/MAT 496f 2001 A 19200 |
|---|---|
| DE-BY-TUM_katkey | 647389 |
| DE-BY-TUM_media_number | 040010361312 |
| _version_ | 1816711708998107136 |
| adam_text | Contents
1 Introduction 1
1.1 Feedback control systems 1
1.2 Linear theory 3
1.3 Organization of this book 3
1.3.1 Part I Ordinary control theory 4
1.3.2 Part II Optimal control theory 4
1.3.3 Part III Stochastic control theory 5
PART I ORDINARY CONTROL THEORY
2 Ordinary linear systems 9
2.1 Dynamic systems 9
2.1.1 Principle of superposition 9
2.2 Dynamic equations 10
2.2.1 Solutions 12
2.3 Continuous time step responses 13
2.3.1 First order equations 14
2.3.2 Second order equations 15
2.3.3 Higher order equations 19
2.4 Discrete time step responses 19
2.4.1 First order systems 19
2.4.2 Second order systems 21
2.5 Continuous time exponentials and sine waves 22
2.5.1 Exponential forcing 22
2.5.2 Sinusoidal forcing and frequency response 22
2.6 Transformations and transfer functions 26
2.6.1 Laplace transform, for continuous time sys¬
tems 26
2.6.2 ^ transform, for difference equations 29
2.6.3 Transfer functions 31
2.6.4 Correspondence between difference equations
and ^ equations 32
2.7 Impulse response 34
2.7.1 Discrete time 35
viii Contents
2.7.2 Continuous time 36
2.8 Evaluating quadratic integrals 37
2.8.1 Continuous time Ic 38
2.8.2 Discrete time Id 39
2.9 Sampled data 40
2.9.1 Aliasing and choice of sampling frequency 41
2.9.2 Correspondence between the differential equa¬
tion governing y{t) and the difference equa¬
tion governing y (i) 43
2.9.3 Reconstructing continuous time y(t) 45
2.10 Minimum phase equations 46
2.11 Problems 47
3 Feedback control and integral action 55
3.1 Introduction 55
3.2 Feedback systems 57
3.3 Feedback control systems 58
3.3.1 Requirements for good control 59
3.3.2 Robustness 60
3.3.3 Response to exogenous variables 60
3.4 Integrators 61
3.5 Integrators and steady state performance 62
3.5.1 Target tracking with unity feedback 63
3.5.2 Disturbance rejection 64
3.5.3 Target tracking with non unity feedback 65
3.5.4 Discrete time systems 67
3.5.5 Conclusions about the effect of integrators
on steady state performance 68
3.6 Problems 69
4 Stability of feedback systems 74
4.1 Introduction 74
4.2 Stability of continuous time systems 77
4.3 Stability of discrete time systems 80
4.4 The Nyquist criterion 83
4.5 Relative stability 88
4.5.1 Phase margin 89
4.5.2 Gain margin 90
4.5.3 Closed loop frequency response 92
4.6 Problems 94
Contents ix
5 Root locus diagrams 98
5.1 Introduction 98
5.2 Angle and magnitude conditions 100
5.3 Rules for drawing root locus diagrams 103
5.4 Additional features of root locus diagrams 108
5.5 Discrete time systems 111
5.6 Problems 113
6 Transfer functions for controllers 118
6.1 Introduction 118
6.2 Phase advance and phase lag 119
6.3 Combining phase advance and phase lag 126
6.3.1 Three term, PID, controllers 128
6.4 Analytic design 129
6.4.1 Performance criteria 129
6.4.2 Two levels of design 134
6.4.3 Fixed configuration design 134
6.5 Problems 137
7 Non linear systems 140
7.1 Introduction 140
7.2 Describing functions 141
7.3 Phase plane 149
7.3.1 Relay control systens 154
7.3.2 Variable structure control 159
7.3.3 Some other non linearities 161
7.4 Problems 166
PART II OPTIMAL CONTROL THEORY
8 Linear state equations and their properties 173
8.1 State space and state variables 173
8.2 Dynamic properties of A, B 175
8.2.1 Transient behaviour 175
8.2.2 Controllability 176
8.3 Outputs 178
8.3.1 Observability 178
8.3.2 Transfer functions 179
8.4 State space realizations 180
8.4.1 Additional state variables 180
8.4.2 Linear transformations 182
8.4.3 Realizations for SISO systems 182
X Contents
8.5 Uncontrollability and unobservability 184
8.5.1 Lack of linear independence 185
8.5.2 Subsystems having identical dynamics 186
8.5.3 Pole zero cancellations 187
8.5.4 Stabilizability and detectability 188
8.6 Problems 188
9 Optimal LQP control 192
9.1 Introduction 192
9.2 LQP introduction to optimal control theory 193
9.2.1 Discrete time scalar problem 194
9.2.2 Continuous time scalar problem 197
9.3 General results about LQP optimal control 201
9.3.1 Continuous time LQP results 201
9.3.2 For discrete time systems 202
9.4 Regulation, target tracking, and disturbance rejec¬
tion 203
9.5 Steady state LQP optimal control 206
9.5.1 Example with uncontrollable exogenous vari¬
ables 211
9.6 Problems 212
10 Optimal, linear, feedback controllers 216
10.1 Introduction 216
10.1.1 Notation 217
10.2 Observers 218
10.2.1 The gain matrix Ko 220
10.3 Ideal LQP feedback control 222
10.3.1 Structure of the ideal controller transfer func¬
tion 223
10.3.2 Classical controllers 224
10.3.3 An example of an ideal LQP controller 225
10.3.4 Behaviour of the closed loop control system 228
10.4 General conclusions 229
10.4.1 Specifying the problem 230
10.4.2 Controller structure 230
10.4.3 Controller dynamics 231
10.5 Problems 231
11 Optimal control theory 236
11.1 Introduction 236
Contents xi
11.2 Scalar, time invariant problems 238
11.2.1 Discrete time 238
11.2.2 Continuous time 240
11.3 Problems having multiple states 241
11.3.1 The principle of optimality 243
11.4 LQP problems 244
11.5 Calculus of variations 246
11.5.1 The Pontriagin maximum principle 246
11.5.2 Problems with constrained controls 247
11.6 Features of dynamic programming 251
11.7 Problems 252
PART III STOCHASTIC CONTROL THEORY
12 Probability and random processes 259
12.1 Introduction 259
12.2 Probability 259
12.3 Probability distributions 263
12.4 Stochastic state space models 270
12.4.1 Discrete time, linear stochastic systems 272
12.4.2 Continuous time, stochastic systems 273
12.5 Stochastic variables 274
12.5.1 Discrete time 274
12.5.2 Continuous time 277
12.6 Random processes 280
12.7 Problems 286
13 Estimating uncertain states 293
13.1 Introduction 293
13.2 Bayes s rule 295
13.2.1 Scalar linear example 298
13.2.2 The need for prior information 300
13.3 Kalman filters 301
13.3.1 Introductory, first order example 301
13.3.2 Discrete time systems of any order 302
13.3.3 The covariance equations 305
13.3.4 Summary of the discrete time Kalman filter 308
13.3.5 Continuous time systems 309
13.4 Parameter estimation 309
13.4.1 The basic recursive algorithm 310
13.4.2 Preventing convergence of the Kalman gain
to zero 312
xii Contents
13.4.3 Real systems 314
13.5 Estimation for non linear sytems 314
13.5.1 Normal approximation 316
13.5.2 Predictor corrector 316
13.5.3 Extended Kalman filter 317
13.6 Problems 320
14 Optimal stochastic control 325
14.1 Introduction 325
14.2 Fixed configuration problems 328
14.2.1 A simple example 330
14.3 Discrete time problems with known current state 331
14.3.1 LQP problems 333
14.4 Discrete time, optimal, stochastic control 335
14.4.1 LQG problems 337
14.5 Continuous time LQG problems 340
14.5.1 A simple example 341
14.6 Problems 344
15 Information and feedback control 353
15.1 Introduction 353
15.2 Cost of uncertainty about controlled objects 355
15.2.1 Notation 355
15.2.2 Information variability and object variability 355
15.2.3 Discrete time LQG example 356
15.3 Interaction between controller functions 359
15.3.1 Structural properties of controlled objects 359
15.3.2 Intentional errors, caution and probing 362
15.4 Various controller designs 365
15.4.1 Classical transfer functions 365
15.4.2 Receding horizon controllers 366
15.4.3 Adaptive control 366
15.4.4 Extremal control 368
* 15.5 General, practical conclusions 369
Answers to problems 371
Bibliography 382
Index 385
|
| any_adam_object | 1 |
| author | Jacobs, Oliver L. |
| author_facet | Jacobs, Oliver L. |
| author_role | aut |
| author_sort | Jacobs, Oliver L. |
| author_variant | o l j ol olj |
| building | Verbundindex |
| bvnumber | BV010041757 |
| classification_rvk | SK 880 |
| classification_tum | MAT 496f |
| ctrlnum | (OCoLC)299549207 (DE-599)BVBBV010041757 |
| dewey-full | 629.8312 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 629 - Other branches of engineering |
| dewey-raw | 629.8312 |
| dewey-search | 629.8312 |
| dewey-sort | 3629.8312 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| edition | second edition |
| format | Book |
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| genre_facet | Einführung Matériel didactique |
| id | DE-604.BV010041757 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-25T17:14:19Z |
| institution | BVB |
| isbn | 0198562489 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006659567 |
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| owner | DE-91G DE-BY-TUM DE-83 |
| owner_facet | DE-91G DE-BY-TUM DE-83 |
| physical | xii, 390 Seiten |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Oxford University Press |
| record_format | marc |
| series2 | Oxford science publications |
| spellingShingle | Jacobs, Oliver L. Introduction to control theory Kontrolltheorie (DE-588)4032317-1 gnd Regelungstheorie (DE-588)4122327-5 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4122327-5 (DE-588)4151278-9 |
| title | Introduction to control theory |
| title_auth | Introduction to control theory |
| title_exact_search | Introduction to control theory |
| title_full | Introduction to control theory O. L. R. Jacobs |
| title_fullStr | Introduction to control theory O. L. R. Jacobs |
| title_full_unstemmed | Introduction to control theory O. L. R. Jacobs |
| title_short | Introduction to control theory |
| title_sort | introduction to control theory |
| topic | Kontrolltheorie (DE-588)4032317-1 gnd Regelungstheorie (DE-588)4122327-5 gnd |
| topic_facet | Kontrolltheorie Regelungstheorie Einführung Matériel didactique |
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