Modern control theories: nonlinear, optimal and adaptire systems
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Budapest
Akad. Kiadó
1972
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | EST: Korszerü szabályozáselmélet (engl.) |
| Beschreibung: | 1096 S. |
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| 245 | 1 | 0 | |a Modern control theories |b nonlinear, optimal and adaptire systems |c by Frigyes Czáki |
| 264 | 1 | |a Budapest |b Akad. Kiadó |c 1972 | |
| 300 | |a 1096 S. | ||
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Datensatz im Suchindex
| _version_ | 1804117396855717888 |
|---|---|
| adam_text | CONTENTS
Symbols 13
Preface 17
References 27
PAET 1
1. Introduction 31
1.1 Characteristic features of nonlinear systems 31
1.1.1 Importance of nonlinear systems 31
1.1.2 Fundamental equations 31
1.1.3 State and phase equations 33
1.1.4 Some special features of nonlinear systems 30
1.1.5 Classification of nonlinearities 38
1.1.6 Analysis of nonlinear systems 40
References 40
l ART 2
2. Methods of linearization 45
2.1 Linearization about an operating point; tangential approximation 46
2.1.1 Determination of the linearized coefficients by expansion 46
2.1.2 An alternate method of linearization 52
2.1.3 The most usual ways of algebraic linearization 54
2.1.4 Linearization of chai acteristic curves 54
2.1.5 Determination of linearized coefficients by least square approximation 57
2.1.6 The first test method of Lyapunov (SI
2.1.7 Summary 66
References 67
2.2 Harmonic linearization . (JS
2.2.1 Fundamental assumptions of the describing function method 6S
2.2.2 Fundamental relations (] )
2.2.3 Generalized describing functions 77
2.2.4 Describing functions of some simple nonlinearities 7S
2.2.5 Approximate determination of the describing function 86
2.2.6 An alternate approximate method for the determination of describing
functions 90
2.2.7 Stability test 93
2.2.S Examples for the uses of describing functions 103
2.2.9 The root locus of a nonlinear system 110
2.2.10 Drawbacks of the describing function method 114
2.2.11 Compensation in nonlinear systems 119
2.2.12 The harmonic balance method 120
6 CONTENTS
2.2.13 Harmonic linearization of state equations 121
2.2.1,4 Comparison of the three methods 123
2.2.15 Other describing functions 125
2.2.16 The inverse problem 128
References 132
2.3 Statistical linearization 136
2.3.1 Fundamental relations 136
2.3.2 Statistical linearization of nonlinear characteristics 140
2.3.3 Expressions of linearized gains 142
2.3.4 Examples of statistical linearization 147
2.3.5 A variant of linearized gain. calculation 156
2.3.6 Statistical linearization of some typical nonlinearities 157
2.3.7 Statistical systems analysis 162
References 169
2.4 Combined describing functions 171
2.4.1 Dual input describing functions 171
2.4.2 Incremental locus 174
2.4.3 Approximate dual input describing function 178
2.4.4 Combined harmonic and random linearization 183
2.4.5 A review of combined linearization formulae 185
2.4.6 Approximate combined linearization 187
References 189
PART 3
3. Transient processes 193
3.1 Graphical methods 194
. 3.1.1 First order linear system 194
3.1.2 Linear integrator 197
3.1.3 Single energy storage nonlinear system 198
3.1.4 Feedback control systems 199
3.1.5 Supplementary comments 201
3.1.6 The secant method 202
3.1.7 Supplementary comments to the secant method 205
3.1.8 The tangent method 209
References 211
3.2 Numerical methods 212
3.2.1 Taylor series expansion 212
3.2.2 The Euler method 215
3.2.3 The modified Euler method 216
3.2.4 The Adams method 217
3.2.5 The Milne method 219
3.2.6 The Runge Kutta method 220
3.2.7 Predictor corrector methods 222
3.2.8 Checking the numerical methods 226
3.2.9 Least square fitting 227
3.2.10 The use of 2 forms in the evaluation of transient processes 229
3.2.11 Naumov s grapho analytical method 232
References 235
CONTENTS 7
3.3 Analytical methods 237
3.3.1 Variation of parameters 238
3.3.2 Expansion according to a small parameter 241
3.3.3 A special case of expansion according to a small parameter 244
3.3.4 Finding of periodic solutions by the perturbation method 246
3.3.5 The method of reversion 249
3.3.6 The method of Lighthill. and Temple 250
3.3.7 The method of collocation 253
3.3.8 The Galerkin method 256
3.3.9 The Ritz Galerkin method 258
3.3.10 The Lie series method 261
3.3.11 The asymptotic series method 263
3.3.12 The Taylor Cauchy transformation 263
3.3.13 The method of recurrence relations 265
3.3.14 The method of complex convolution 268
3.3.15 The method of successive integrations 270
3.3.16 Method of Lalesco s nonlinear integral equations 271
References 275
3.4 Closed form solutions for transient processes 276
3.4.1 Directly integrable differential equations 277
3.4.2 Linear differential equations of the first order 278
3.4.3 Separable differential equations 279
3.4.4 Introduction of a homogeneous variable 279
3.4.5 Solution of equations derived from a total differential 280
3.4.6 Introduction of an integrating factor 281
3.4.7 Introduction of a new variable 281
3.4.8 Incomplete second order differential equations 282
3.4.9 The Bernoulli equation 283
3.4.10 The Riccati equation 283
3.4.11 The Euler Cauchy equation 284
3.4.12 Solution of variable coefficient linear differential equations 284
3.4.13 Elliptic functions 285
3.4.14 Hyperelliptic functions 289
References 290
PART i
4. The state plane and phase plane method 293
4.1 The state plane and phase plane method 294
4.1.1 Writing up the phase equations 296
4.1.2 Determination of the phase portrait by computation 301
4.1.3 Graphical methods for constructing phase trajectories 312
4.1.4 The evolute methods 322
4.1.5 Time calibration of phase trajectories 326
4.1.6 The Poineare analysis of singular points 333
4.1.7 Some comments on the Poincare method 348
4.1.8 Energy relationships and the phase portrait 351
4.1.9 Phase trajectory construction by energy considerations 353
g CONTEXTS
4.1.10 Limit cycle examination 356
References 362
4.2 Piecewise linear systems 304
4.2.1 Saturation or limitation 364
4.2.2 Dead band or threshold 367
4.2.3 Variable gain 308
4.2.4 Backlash or hysteresis 371
4.2.5 Adhesion and Coulomb friction 374
4.2.6 Variable damping 377
4.2.7 Examination of piecewise linear systems 380
References 380
4.3 On off control systems 382
4.3.1 The block diagram of on off control 3S4
4.3.2 Analytical determination of phase trajectories 385 ;
4.3.3 Examples of on off control 389
4.3.4 The method of characteristic curves 398
4.3.5 The method of point transformation 400
4.3.6 Limit cycle calculation in relay systems 409
4.3.7 Optimal relay control system 416
4.3.8 Minimum time systems 425
References 433
PART 3
5. Stability of nonlinear systems 439
5.1 Lyapunov s second or direct method 441
5.1.1 The fundamental ideas of stability 442
5.1.2 The notion of sign definiteness 445
5.1.3 Lyapunov functions 448
5.1.4 The Lyapunov theorems . 450
5.1.5 Examples for the application of the Lyapunov method to auto¬
nomous systems 456
5.1.6 Proof of the Lyapunov method 40(5
5.1.7 Application of the Lyapunov method to nonautonomous systems 470
5.1.8 Practical stability 472
5.1.9 Eventual stability 473
References 475
5.2 Determination of the Lyapunov functions 477
5.2.1 Determination of Lyapunov functions for autonomous linear systems 477
5.2.2 Determination of Lyapunov functions for autonomous nonlinear
systems 480
5.2.3 The Ivrasovskii method 483
5.2.4 The Ai/.erman method 489
5.2.5 The variable gradient method for generating Lyapunov functions 491
5.2.0 The Zubov method 494
5.2.7 Determination of Lyapunov functions for nonautonomous systems 498
References 500
5.3 Canonical forms and transformations 501
5.3.1 The basic equations of direct control 504
CONTENTS (,
5.3.2 The fundamental equations of indirect control 512
5.3.3 Closed formulae of canonical transformation for direct control 51S
5.3.4 Closed formulae of canonical transformation for indirect control 523
5.3.5 Methods for constructing the Lyapunov function. Introduction 52X
5.3.6 Construction of the Lyapunov function for indirect control 529
5.3.7 Construction of the Lyapunov function for direct control 537
5.3.8 Lur e s polynomial transformation 539
5.3.9 Special cases of Lur e s polynomial transformation 547
5.3.10 Simplified stability criteria 550
5.3.11 Pole shifting and zero shifting 551
References ¦ 500
5.4 Synthesis by the Lyapunov method 501
5.4.1 Synthesis on the basis of an integral criterion 501
;. 5.4.2 Synthesis of linear excited systems on the basis of the integral
criterion 503
5.4.3 Synthesis of closed loop control systems 505
5.4.4 Synthesis of an excited nonlinear system 506
5.4.5 The parameter identification method 5t 9
5.4.6 Synthesis of nonlinear adaptive control systems 571
5.4.7 Synthesis of asymptotically stable optimal nonlinear systems 573
5.4.8 Estimation of the damping rate of a transient process 579
References 5S0
5.5 Sampled data systems 5X7
5.5.1 Stability definitions 5X7
5.5.2 Stability theorems 5XX
5.5.3 The relation between the Routh Hurwitz criterion and the Lyapunov
method 593
5.5.4 The Krasovskii method for discrete data systems 59
5.5.5 Synthesis of discrete data systems 599
5.5.6 Estimating the transient process 000
References 001
5.6 Absolute stability 002
5.6.1 Definition of absolute stability 003
5.6.2 The Popov criterion and its proof tit . »
5.6.3 Geometric interpretation of Popov s criterion OOii
5.6.4 Extension of the Popov criterion 014
5.6.5 Application examples of Popov s criterion 017
5.6.6 Absolute stability of the control process in nonlinear systems ti2l
5.6.7 The stability degree of nonlinear systems 024
5.6.S The integral criterion for nonlinear .systems 02t
5.6.9 Relationship between the Popov and Lyapunov methods 02s
References 029
5.7 Absolute stability of nonlinear discrete data systems 031
5.7.1 Absolute stability in discrete data systems 031
5.7.2 Interpretation of the Popov criterion O3.~
5.7.3 Generalization of the stability criterion 030
5.7.4 The necessary and sufficient conditions of absolute stability 037
5.7.5 Estimation of the degree of stability (•,:{;
1 0 CONTENTS
5.7.6 Quadratic estimation 638
5.7.7 Relationship between the Popov criterion and the Lyapunov method
in discrete data control systems 639
References 641
5.8 Generalization of the frequency method 642
5.8.1 Absolute stability of systems including a nonlinearity of limited slope 642
5.8.2 Modified stability criteria in the frequency domain 646
5.8.3 Absolute stability of multivariable systems 650
5.8.4 Generalization for time variable nonlinearities 654
References 655
PART 6
8. Optimal systems 663
6.1 Application of the calculus of variations to the solution of optimal control .
problems 665
6.1.1 The principal theorems of the classical calculus of variations 665
6.1.2 Variants of the optimal control problems 682
6.1.3 Optimal control of time invariant systems 693
6.1.4 Linear optimization problems 696
References 707
6.2 Pontryagin s principle 709
6.2.1 Pontryagin s maximum principle 709
6.2.2 Some examples involving the maximum principle 727
6.2.3 The Pontryagin minimum principle 735
6.2.4 Optimal control of linear time invariant controlled plants 745
6.2.5 Some features of optimal systems 751
6.2.6 Synthesis of minimum time systems 763
6.2.7 Design of fuel optimal systems 820
6.2.8 Design of energy optimal control 830
6.2.9 Optimal control with a hypersphere type constraint 837
6.2.10 Optimal control of systems with transportation lags 846
References 855
6.3 Dynamic programming 867
6.3.1 Fundamentals 867
6.3.2 Connection between dynamic programming and the minimum
(maximum) principle 878
6.3.3 Connection between dynamic programming and the calculus of varia¬
tions 881
6.3.4 Connection between the Lyapunov functions and dynamic program¬
ming 884
References S88
6.4 Functional analysis in the solution of optimal control problems 891
6.4.1 Optimal control of single variable plants 891
6.4.2 Optimal control of multivariable controlled plants 895
6.4.3 Optimal control of time variable multivariable controlled plants 899
6.4.4 Complementary comments 900
6.4.5 Some numerical examples 901
References 904
CONTENTS 11
PART 7
7. Adaptive control systems 909
7.1 Variants of adaptive control systems 910
7.1.1 Passive adaptation 912
7.1.2 Input variable adaptation 912
7.1.3 Extremal or optimizing systems 914
7.1.4 System variable adaptation 914
7.1.5 System characteristic adaptation 915
7.1.6 Supplementary comments 910
References 917
7.2 Some examples of adaptive systems 918
7.2.1 High gain adaptive systems 918
7.2.2 Adaptive systems with a prescribed damping factor 919
7.2.3 Adaptive missile acceleration control 922
7.2.4 Input signal self adaptation of a tracking servo 924
7.2.5 Model reference adaptive systems 92(5
References 929
7.3 Optimizing methods 930
7.3.1 Fundamental concepts of optimizing systemB 931
7.3.2 Some types of optimizing systems 932
7.3.3 Analysis of quasi stationary processes 945
7.3.4 Methods of searching in complicated optimizing systems 950
References 954
7.4 The theoretical bases of adaptation, learning, and optimizing 956
7.4.1 The criteria of optimality 956
7.4.2 The adaptation process and its algorithm 957
7.4.3 Adaptation under constraints 958
7.4.4 Pattern recognition 959
7.4.5 Identification 962
7.4.6 Adaptive filters 963
7.4.7 Adaptive (dual) control 964
References 966
PART 8
8. Appendix 971
8.1 Some fundamental principles of matrix calculus and vector analysis 972
8.1.1 Some fundamental theorems of matrix algebra 972
8.1.2 Bilinear and quadratic forms 975
8.1.3 Norms 970
8.1.4 Fundamentals of vector analysis 981
8.1.5 Some rules of differentiation 985
References 988
8.2 State variables, state equations 989
8.2.1 Deduction of the transfer matrix of a controlled plant from the state
equations 990
8.2.2 Deduction of the state equations from the transfer function or
transfer matrix 991
8.2.3 State equations of feedback systems 996
] 2 CONTEXTS
8.2.4 Normal plants 997
8.2.5 Canonical form 998
8.2.6 Determination of the phase variable form 1002
References 1004
8.3 Solution of the state differential equations 1007
8.3.1 Solution of a time invariant linear homogeneous vector differential
equation 1007
8.3.2 Determination of the fundamental matrix 1009
8.3.3 Determination of the fundamental matrix in cases with multiple
eigenvalues 1014
8.3.4 Solution of the time invariant inhomogeneous state equations 1015
References 1010
8.4 Variable coefficient differential equations 1017
8.4.1 Solution of time variable homogeneous state equations 1017
8.4.2 Solution of the time variable inhomogeneous differential equation 1019
8.4.3 The adjoint system 1021
8.4.4 Determination of the transition matrix 1022
References 1026
8.5 Reachable states, controllability, observability 1027
8.5.1 Reachable states 1027
8.5.2 Definition of controllability and observability 1027
8.5.3 Controllability of linear time invariant systems 1028
8.5.4 Observability of linear time invariant systems 1031
8.5.5 Normal plants 1033
References 1034
8.6 State and phase equations of sampled data systems 1035
S.fi.l Determination of homogeneous phase equations 1035
8.6.2 Determination of the phase variable form from the pulsed data
transfer function 1038
8.6.3 General state equations of sampled data systems 1040
8.6.4 Solution of linear state equations 1043
8.6.5 2 transformation 1045
8.6.6 Determination of the transition matrix 1047
8.6.7 Determination of the transition matrix of a time variable plant 1048
8.6.8 Controllability and observability 1050
References 1052
8.7 Some connections with theoretical mechanics 1053
8.7.1 I in Iamontal concepts and connections 1053
8.7.2 The Lagrange equation 1056
References 1061
List of references 1063
Index 1087
|
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| indexdate | 2024-07-09T15:53:44Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001949295 |
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| physical | 1096 S. |
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| spelling | Csáki, Frigyes Verfasser aut Korszerú szabályozáselmélet Modern control theories nonlinear, optimal and adaptire systems by Frigyes Czáki Budapest Akad. Kiadó 1972 1096 S. txt rdacontent n rdamedia nc rdacarrier EST: Korszerü szabályozáselmélet (engl.) Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001949295&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Csáki, Frigyes Modern control theories nonlinear, optimal and adaptire systems Kontrolltheorie (DE-588)4032317-1 gnd |
| subject_GND | (DE-588)4032317-1 |
| title | Modern control theories nonlinear, optimal and adaptire systems |
| title_alt | Korszerú szabályozáselmélet |
| title_auth | Modern control theories nonlinear, optimal and adaptire systems |
| title_exact_search | Modern control theories nonlinear, optimal and adaptire systems |
| title_full | Modern control theories nonlinear, optimal and adaptire systems by Frigyes Czáki |
| title_fullStr | Modern control theories nonlinear, optimal and adaptire systems by Frigyes Czáki |
| title_full_unstemmed | Modern control theories nonlinear, optimal and adaptire systems by Frigyes Czáki |
| title_short | Modern control theories |
| title_sort | modern control theories nonlinear optimal and adaptire systems |
| title_sub | nonlinear, optimal and adaptire systems |
| topic | Kontrolltheorie (DE-588)4032317-1 gnd |
| topic_facet | Kontrolltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001949295&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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