Mathematical methods for the study of automatic control systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Oxford [u.a.]
Pergamon Press [u.a.]
1962
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Transl. from the Russian |
| Physical Description: | XI, 327 S. |
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| 245 | 1 | 0 | |a Mathematical methods for the study of automatic control systems |c by V. I. Zubov |
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| 300 | |a XI, 327 S. | ||
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Record in the Search Index
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| adam_text | CONTENTS
Preface to the English Edition
vii
Preface to the Russian Edition
Chapter I General Theorems on Stability of Motion 1
§ 1. Formulation of the problem of stability of motion — Basic
definitions 5
2. Two methods in the solution of the stability problem —
Lyapunov functions 14
3. Theorems on stability and instability 23
4. Investigation of the problem of stability of the homogeneous so¬
lutions relative to separately given coordinates 51
5. The concept of the region of asymptotic stability 56
Chapter II Investigation of Transient Processes in Linear Systems with
Variable Coefficients 70
§ 6. Necessary and sufficient conditions for stability and asymptotic
stability of a definite type 70
7. Influence of errors in calculating the coefficients o f the equation
on the behaviour of the solutions and the stability properties .. 88
8. The stability of the homogeneous solution of a linear system
with respect to given coordinates 96
9. Investigation of the stability of linear systems by construction
of exact solutions 101
10. Investigation of the behaviour of transient processes in a 1 inear
system in a finite time interval by the method of approximate
integration 108
11. New method of constructing the regions of stability in the space
of admissible parameters of the automatic control system . . 115
Chapter III Estimation of the Behaviour of Transient Processes in Non¬
linear Systems 123
§ 12. Method of estimates — Technical stability 123
13. Stability in a finite interval 131
14. Stability of nonlinear systems in the first approximation .. .. 138
15. System with lag 141
Chapter IV Construction of Solutions for Nonlinear Systems of Dif¬
ferential Equations in the Neighbourhood of a Regular Sing¬
ularity 145
§ 16. Auxiliarly theorems from the theory of equations with partial
derivatives 145
17. Representation of the solutions of systems of ordinary differ¬
ential equations in the neighbourhood of a singularity .. 151
Chapter V Estimation of the Influence of Constantly Acting Perturba¬
tions Upon Transient Processes in a Nonstationary System 158
§ 18. Influence of constantly acting perturbations 158
19. Constantly acting perturbations of a random nature 166
20. A method of finding estimates for the correlation functions
of a stochastic solution in terms of the correlation functions
of the given process 170
v
VI MATHEMATICS OF AUTOMATIC CONTROL SYSTEMS
Chapter VI Investigation of the Problem of Stability in Doubtful Cases 177
§21. Formulation of the problem — Basic definitions 177
22. Fundamental theorems on the proposed method of investi¬
gating doubtful cases 179
23. Investigation of the problem of stability of a system of equa¬
tions in the absence of linear terms in the expansion of their
right hand members 182
24. Stability in the first nonlinear approximation 194
Chapter VII Periodic and Almost Periodic Oscillations in Nonlinear
Systems 198
§ 25. Self oscillations 198
26. Periodic forced oscillations appearing under the action of ex¬
ternal force 213
27. Periodic and almost periodic oscillations in nonlinear auto
nomic systems 227
28. Methods of approximate construction of periodic behaviours.. 238
Chapter Vm Application of Electronic Computing Machines to the Analysis
and Synthesis of Automatic Control Systems 243
§ 29. General features of computing machines and devices .. .. 243
30. Synthesis and analysis of automatic control systems from sta¬
bility conditions 256
31. Automatic optimization of automatic control systems .. .. 269
Appendix I Methods of Approximating Families of Solutions of Differ¬
ential Equations 283
Appendix II The Theory of Linear Stationary Systems with a Lagging
Argument 290
Appendix III The Correlation Functions of Stochastic Solutions .. .. 308
Appendix IV Description of the Programme 315
Appendix V Self Oscillations and Convergence 317
Bibliography 320
Index 325
|
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| 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 | Wirtschaftswissenschaften Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
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| id | DE-604.BV002276436 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:43:13Z |
| institution | BVB |
| language | English Russian |
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| physical | XI, 327 S. |
| psigel | TUB-nvmb |
| publishDate | 1962 |
| publishDateSearch | 1962 |
| publishDateSort | 1962 |
| publisher | Pergamon Press [u.a.] |
| record_format | marc |
| spelling | Zubov, Vladimir I. Verfasser aut Matematičeskie metodi issledovanija sistem avtomatičeskogo regukirovanija Mathematical methods for the study of automatic control systems by V. I. Zubov Oxford [u.a.] Pergamon Press [u.a.] 1962 XI, 327 S. txt rdacontent n rdamedia nc rdacarrier Transl. from the Russian Servomécanismes Automatic control Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Regelungstechnik (DE-588)4076594-5 gnd rswk-swf Kontrolltheorie (DE-588)4032317-1 s Mathematik (DE-588)4037944-9 s DE-604 Regelungstechnik (DE-588)4076594-5 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001495482&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zubov, Vladimir I. Mathematical methods for the study of automatic control systems Servomécanismes Automatic control Kontrolltheorie (DE-588)4032317-1 gnd Mathematik (DE-588)4037944-9 gnd Regelungstechnik (DE-588)4076594-5 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4037944-9 (DE-588)4076594-5 |
| title | Mathematical methods for the study of automatic control systems |
| title_alt | Matematičeskie metodi issledovanija sistem avtomatičeskogo regukirovanija |
| title_auth | Mathematical methods for the study of automatic control systems |
| title_exact_search | Mathematical methods for the study of automatic control systems |
| title_full | Mathematical methods for the study of automatic control systems by V. I. Zubov |
| title_fullStr | Mathematical methods for the study of automatic control systems by V. I. Zubov |
| title_full_unstemmed | Mathematical methods for the study of automatic control systems by V. I. Zubov |
| title_short | Mathematical methods for the study of automatic control systems |
| title_sort | mathematical methods for the study of automatic control systems |
| topic | Servomécanismes Automatic control Kontrolltheorie (DE-588)4032317-1 gnd Mathematik (DE-588)4037944-9 gnd Regelungstechnik (DE-588)4076594-5 gnd |
| topic_facet | Servomécanismes Automatic control Kontrolltheorie Mathematik Regelungstechnik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001495482&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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