Introduction to mathematical control theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Pr.
1985
|
| Edition: | 2. ed. |
| Series: | Oxford applied mathematics and computing science series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 404 S. graph. Darst. |
| ISBN: | 0198596405 0198596391 |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to mathematical control theory |c S. Barnett and R. G. Cameron |
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Record in the Search Index
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| adam_text | Contents
1. INTRODUCTION TO CONTROL THEORY
1.1. General remarks and examples 1
1.2. Classical control and transform theory
1.2.1. Continuous time systems: Laplace transform 11
1.2.2. Discrete time systems: z transform 16
Additional problems 22
2. PRELIMINARY MATRIX THEORY
2.1. Definitions 26
2.2. Linear dependence and rank 30
2.3. Polynomials 34
2.4. Characteristic roots (eigenvalues) 35
2.5. Polynomial and rational matrices 42
2.6. Jordan canonical form 51
2.7. Functions of a matrix 54
2.8. Quadratic and Hermitian forms 58
2.9. Gaussian elimination 62
3. MATRIX SOLUTION OF LINEAR SYSTEMS
3.1. Solution of uncontrolled system: spectral form 65
3.2. Solution of uncontrolled system: exponential matrix 68
3.3. Solution of uncontrolled system: repeated roots 72
3.4. Solution of controlled system 74
3.5. Time varying systems 76
3.6. Discrete time systems 79
3.7. Relationships between state space and classical
forms 84
Additional problems 93
4. LINEAR CONTROL SYSTEMS
4.1. Controllability 97
4.2. Observability 111
4.3. tcontrollability and polynomials 119
4.4. Linear feedback 122
f May be omitted on a first reading.
x Contents
4.5. State observers 134
4.6. Realization of constant systems 137
4.7. Discrete time systems 153
4.8. t Realization of time varying systems 157
Additional problems 161
5. STABILITY
5.1. Definitions 169
5.2. Algebraic criteria for linear systems
5.2.1. Continuous time 177
5.2.2. Discrete time 186
5.2.3. Time varying 191
5.3. Nyquist criterion for linear systems 195
5.4. Liapunov theory 204
5.5. Application of Liapunov theory to linear systems 213
5.6. Construction of Liapunov functions
5.6.1. Variable gradient method 221
5.6.2. Zubov s method 224
5.7. Stability and control
5.7.1. Input output stability 226
5.7.2. Linear feedback 228
5.7.3. tNonlinear feedback 230
Additional problems 238
6. OPTIMAL CONTROL
6.1. Performance indices
6.1.1. Measures of performance 245
6.1.2. Evaluation of quadratic indices 248
6.2. Calculus of variations 252
6.3. Pontryagin s principle 263
6.4. Linear regulator 275
Additional problems 284
7. MULTIVARIABLE SYSTEMS:
THE FREQUENCY DOMAIN APPROACH
7.1. Poles and zeros of the internal model 291
7.2. Poles and zeros of the external model 305
7.2.1. Definition via the Smith McMillan form 306
7.2.2. Matrix fraction description 309
f May be omitted on a first reading.
Contents xi
I
7.3. Generalizations of the Nyquist diagram
j 7.3.1. Characteristic gain and characteristic
i frequency functions 318
| 7.3.2. Algebraic functions and the Riemann
surface 322
7.3.3. Poles and zeros: characteristic gain and
frequency loci 323
7.3.4. The inverse Nyquist array 332
7.4. Design of multivariable controllers
7.4.1. Preamble: the design problem and
objectives 340
7.4.2. The inverse Nyquist array method 343
7.4.3. The characteristic locus method 355
Additional problems 369
APPENDIX: The Kalman Bucy filter 374
REFERENCES 379
ANSWERS TO EXERCISES 383
ANSWERS TO ADDITIONAL PROBLEMS 392
INDEX 400
|
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| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| edition | 2. ed. |
| format | Book |
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| institution | BVB |
| isbn | 0198596405 0198596391 |
| language | English |
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| physical | XI, 404 S. graph. Darst. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
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| publisher | Clarendon Pr. |
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| series2 | Oxford applied mathematics and computing science series |
| spelling | Barnett, Stephen Verfasser aut Introduction to mathematical control theory S. Barnett and R. G. Cameron 2. ed. Oxford Clarendon Pr. 1985 XI, 404 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford applied mathematics and computing science series Kontrolltheorie Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Kontrolltheorie (DE-588)4032317-1 s DE-604 Cameron, R. G. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001281549&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Barnett, Stephen Cameron, R. G. Introduction to mathematical control theory Kontrolltheorie Kontrolltheorie (DE-588)4032317-1 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4151278-9 |
| title | Introduction to mathematical control theory |
| title_auth | Introduction to mathematical control theory |
| title_exact_search | Introduction to mathematical control theory |
| title_full | Introduction to mathematical control theory S. Barnett and R. G. Cameron |
| title_fullStr | Introduction to mathematical control theory S. Barnett and R. G. Cameron |
| title_full_unstemmed | Introduction to mathematical control theory S. Barnett and R. G. Cameron |
| title_short | Introduction to mathematical control theory |
| title_sort | introduction to mathematical control theory |
| topic | Kontrolltheorie Kontrolltheorie (DE-588)4032317-1 gnd |
| topic_facet | Kontrolltheorie Einführung |
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