Polynomial methods for control systems design:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Springer
1996
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | X, 255 S. graph. Darst. |
| ISBN: | 3540760776 |
Internformat
MARC
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| 245 | 1 | 0 | |a Polynomial methods for control systems design |c Michael J. Grimble ... (ed.) |
| 264 | 1 | |a London [u.a.] |b Springer |c 1996 | |
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Datensatz im Suchindex
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| adam_text | Titel: Polynomial methods for control systems design
Autor: Grimble, Michael J
Jahr: 1996
Contents Preface..................................... ix 1 A Tutorial on Hi Control Theory: The Continuous Time Case 1 1.1 Introduction.............................. 1 1.2 LQG control theory ......................... 2 1.2.1 Problem formulation..................... 2 1.2.2 Finite horizon solution.................... 3 1.2.3 Infinite horizon solution................... 7 1.3 Hi control theory........................... 8 1.3.1 Preliminaries......................... 8 1.3.2 State space solution..................... 10 1.3.3 Wiener- Hopf solution .................... 19 1.3.4 Diophantine equations solution............... 30 1.4 Comparison and examples...................... 39 1.4.1 The LQG as an Hi problem................. 40 1.4.2 Internal stability....................... 41 1.4.3 Solvability assumptions................... 42 1.4.4 Non-proper plants...................... 45 1.4.5 Design examples....................... 48 1.5 References............................... 55 2 Frequency Domain Solution of the Standard Hao Problem 57 2.1 Introduction.................... 57 2.1.1 Introduction ......................... 57 2.1.2 Problem formulation..................... 58 2.1.3 Polynomial matrix fraction representations........ 61 2.1.4 Outline............................ 62 2.2 Well-posedness and closed-loop stability.............. 62 2.2.1 Introduction ......................... 62 2.2.2 Well-posedness........................ 62 2.2.3 Closed-loop stability..................... 63 2.2.4 Redefinition of the standard problem............ 63 2.3 Lower bound............................. 65 2.3.1 Introduction ......................... 65
vi Contents 2.3.2 Lower bound......................... 65 2.3.3 Examples........................... 67 2.3.4 Polynomial formulas..................... 68 2.4 Sublevel solutions........................... 70 2.4.1 Introduction ......................... 70 2.4.2 The basic inequality..................... 70 2.4.3 Spectral factorization .................... 71 2.4.4 All sublevel solutions..................... 72 2.4.5 Polynomial formulas..................... 75 2.5 Canonical spectral factorizations.................. 76 2.5.1 Definition........................... 76 2.5.2 Polynomial formulation of the rational factorization ... 78 2.5.3 Zeros on the imaginary axis................. 80 2.6 Stability................................ 82 2.6.1 Introduction ......................... 82 2.6.2 All stabilizing sublevel compensators............ 82 2.6.3 Search procedure - Type A and Type B optimal solutions 83 2.7 Factorization algorithm ....................... 85 2.7.1 Introduction ......................... 85 2.7.2 State space algorithm.................... 85 2.7.3 Noncanonical factorizations................. 89 2.8 Optimal solutions........................... 90 2.8.1 Introduction ......................... 90 2.8.2 All optimal compensators.................. 90 2.8.3 Examples........................... 91 2.9 Conclusions.............................. 95 2.10 Appendix: Proofs for section 2.3.................. 95 2.11 Appendix: Proofs for section 2.4.................. 97 2.12 Appendix: Proof of theorem 2.7................... 100 2.13 Appendix: Proof of the equalizing property............ 104 2.14 References............................... 105 3 LQG Multivariable Regulation and Tracking Problems for General System Configurations 109 3.1 Introduction.............................. 109 3.2 Regulation problem.......................... 110 3.2.1 Problem solution....................... 114 3.2.2 Connection with the Wiener-Hopf
solution.........118 3.2.3 Innovations representations.................120 3.2.4 Relationships with other polynomial solutions.......125 3.3 Tracking, servo and accessible disturbance problems.......129 3.3.1 Problem formulation..................... 130 3.4 Conclusions.............................. 137 3.5 Appendix............................... 137 3.6 References............................... 141
Contents vii 4 A Game Theory Polynomial Solution to the #00 Control Problem 143 4.1 Abstract................................ 143 4.2 Introduction.............................. 143 4.3 Problem definition.......................... 145 4.4 The game problem.......................... 147 4.4.1 Main result.......................... 147 4.4.2 Summary of the simplified solution procedure.......155 4.4.3 Comments........................... 156 4.5 Relations to the J-factorization H^ problem........... 156 4.5.1 Introduction ......................... 156 4.5.2 The J-factorization solution................. 157 4.5.3 Connection with the game solution............. 158 4.6 Relations to the minimum entropy control problem........159 4.7 A design example: mixed sensitivity................ 160 4.7.1 Mixed sensitivity problem formulation........... 160 4.7.2 Numerical example...................... 161 4.8 Conclusions.............................. 162 4.9 Appendix............................... 164 4.10 References............................... 168 4.11 Acknowledgements.......................... 170 5 Hi Design of Nominal and Robust Discrete Time Filters 171 5.1 Abstract................................ 171 5.2 Introduction.............................. 171 5.2.1 Digital communications: a challenging application area . . 174 5.2.2 Remarks on the notation .................. 176 5.3 Wiener filter design based on polynomial equations........177 5.3.1 A general Hi filtering problem............... 177 5.3.2 A structured problem formulation ............. 178 5.3.3 Multisignal deconvolution.................. 180 5.3.4 Decision feedback equalizers................. 188 5.4 Design of robust filters in input-output form............. 195 5.4.1 Approaches to robust Hi estimation............ 196 5.4.2 The averaged Hi estimation problem............ 197 5.4.3 Parameterization of the extended design model......198 5.4.4 Obtaining error models
................... 200 5.4.5 Covariance matrices for the stochastic coefficients.....203 5.4.6 Design of the cautious Wiener filter ............204 5.5 Robust H 2 filter design ....................... 208 5.5.1 Series expansion....................... 209 5.5.2 The robust linear state estimator.............. 211 5.6 Parameter tracking.......................... 212 5.7 Acknowledgement........................... 214 5.8 References............................... 214
Contents 6 Polynomial Solution of ii 2 and #oo Optimal Control Problems with Application to Coordinate Measuring Machines.....223 6.1 Abstract................................223 6.2 Introduction..............................223 6.3 #2 control design...........................226 6.3.1 System model......................... 226 6.3.2 Assumptions......................... 227 6.3.3 The Hi cost function.....................227 6.3.4 Dynamic weightings.....................228 6.3.5 The Hi controller ...................... 229 6.3.6 Properties of the controller.................230 6.3.7 Design procedure....................... 231 6.4 Hoo Robust control problem..................... 231 6.4.1 Generalised Hi and Hoo controllers............. 232 6.5 System and disturbance modelling................. 233 6.5.1 System modelling....................... 234 6.5.2 Disturbance modelling....................234 6.5.3 Overall system model ....................235 6.6 Simulation and experimental studies................236 6.6.1 System definition.......................236 6.6.2 Simulation studies......................237 6.6.3 Experimental studies.....................244 6.6.4 Hoo control..........................246 6.7 Conclusions.............................. 247 6.8 Acknowledgements.......................... 250 6.9 References............................... 250 6.10 Appendix: two-DOF Hi optimal control problem.........251
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| spelling | Polynomial methods for control systems design Michael J. Grimble ... (ed.) London [u.a.] Springer 1996 X, 255 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturangaben Mathematik Automatic control Mathematics Polynomials System design Robuste Regelung (DE-588)4206985-3 gnd rswk-swf Robuste Kontrolle (DE-588)4232797-0 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Systemmodell (DE-588)4304916-3 gnd rswk-swf Polynommatrix (DE-588)4121492-4 gnd rswk-swf Optimalwertregelung (DE-588)4331044-8 gnd rswk-swf Robuste Kontrolle (DE-588)4232797-0 s Optimale Kontrolle (DE-588)4121428-6 s Systemmodell (DE-588)4304916-3 s Polynommatrix (DE-588)4121492-4 s DE-604 Robuste Regelung (DE-588)4206985-3 s Optimalwertregelung (DE-588)4331044-8 s Grimble, Michael J. Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007279166&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Polynomial methods for control systems design Mathematik Automatic control Mathematics Polynomials System design Robuste Regelung (DE-588)4206985-3 gnd Robuste Kontrolle (DE-588)4232797-0 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Systemmodell (DE-588)4304916-3 gnd Polynommatrix (DE-588)4121492-4 gnd Optimalwertregelung (DE-588)4331044-8 gnd |
| subject_GND | (DE-588)4206985-3 (DE-588)4232797-0 (DE-588)4121428-6 (DE-588)4304916-3 (DE-588)4121492-4 (DE-588)4331044-8 |
| title | Polynomial methods for control systems design |
| title_auth | Polynomial methods for control systems design |
| title_exact_search | Polynomial methods for control systems design |
| title_full | Polynomial methods for control systems design Michael J. Grimble ... (ed.) |
| title_fullStr | Polynomial methods for control systems design Michael J. Grimble ... (ed.) |
| title_full_unstemmed | Polynomial methods for control systems design Michael J. Grimble ... (ed.) |
| title_short | Polynomial methods for control systems design |
| title_sort | polynomial methods for control systems design |
| topic | Mathematik Automatic control Mathematics Polynomials System design Robuste Regelung (DE-588)4206985-3 gnd Robuste Kontrolle (DE-588)4232797-0 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Systemmodell (DE-588)4304916-3 gnd Polynommatrix (DE-588)4121492-4 gnd Optimalwertregelung (DE-588)4331044-8 gnd |
| topic_facet | Mathematik Automatic control Mathematics Polynomials System design Robuste Regelung Robuste Kontrolle Optimale Kontrolle Systemmodell Polynommatrix Optimalwertregelung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007279166&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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