Polynomial Methods for Control Systems Design
(Sprache: Englisch)
This monograph was motivated by a very successful workshop held before the 3rd IEEE Conference on Decision and Control held at the Buena Vista Hotel, lake Buena Vista, Florida, USA. The workshop was held to provide an overview of polynomial system methods...
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This monograph was motivated by a very successful workshop held before the 3rd IEEE Conference on Decision and Control held at the Buena Vista Hotel, lake Buena Vista, Florida, USA. The workshop was held to provide an overview of polynomial system methods in LQG (or H ) and Hoo optimal control and 2 estimation. The speakers at the workshop were chosen to reflect the important contributions polynomial techniques have made to systems theory and also to show the potential benefits which should arise in real applications. An introduction to H2 control theory for continuous-time systems is included in chapter 1. Three different approaches are considered covering state-space model descriptions, Wiener-Hopf transfer function methods and finally polyno mial equation based transfer function solutions. The differences and similarities between the techniques are explored and the different assumptions employed in the solutions are discussed. The standard control system description is intro duced in this chapter and the use of Hardy spaces for optimization. Both control and estimation problems are considered in the context of the standard system description. The tutorial chapter concludes with a number of fully worked ex amples.
The subject of this volume is the design of optimal and robust control systems using system models which are represented by polynomial matrices, the polynomial approach being close to the frequency domain design method that engineers use in practice. The subject matter ranges from fundamental systems theory to application problems The text introduces the polynomial systems approach to solving both control and filtering problems. The benefits of frequency domain analysis and design procedures are demonstrated and the power of polynomial modelling procedures in applications is reveal ed. Both H2 and H¿ design methods are considered involving both scalar and multivariable problem solutions. Both the editors and the contributors are well known in the field for their contributi on to polynomial systems theory, robust design methods and industrial applications.
Inhaltsverzeichnis zu „Polynomial Methods for Control Systems Design “
Preface ix.- 1 A Tutorial on H2 Control Theory: The Continuous Time Case.- 1.1 Introduction.- 1.2 LQG control theory.- 1.3 H2 control theory.- 1.4 Comparison and examples.- 1.5 References.- 2 Frequency Domain Solution of the Standard H? Problem.- 2.1 Introduction.- 2.2 Well-posedness and closed-loop stability.- 2.3 Lower bound.- 2.4 Sublevel solutions.- 2.5 Canonical spectral factorizations.- 2.6 Stability.- 2.7 Factorization algorithm.- 2.8 Optimal solutions.- 2.9 Conclusions.- 2.10 Appendix: Proofs for section 2.3.- 2.11 Appendix: Proofs for section 2.4.- 2.12 Appendix: Proof of theorem 2.7.- 2.13 Appendix: Proof of the equalizing property.- 2.14 References.- 3 LQG Multivariable Regulation and Tracking Problems for General System Configurations.- 3.1 Introduction.- 3.2 Regulation problem.- 3.3 Tracking, servo and accessible disturbance problems.- 3.4 Conclusions.- 3.5 Appendix.- 3.6 References.- 4 A Game Theory Polynomial Solution to the H? Control Problem.- 4.1 Abstract.- 4.2 Introduction.- 4.3 Problem definition.- 4.4 The game problem.- 4.5 Relations to the J-factorization H? problem.- 4.6 Relations to the minimum entropy control problem.- 4.7 A design example: mixed sensitivity.- 4.8 Conclusions.- 4.9 Appendix.- 4.10 References.- 4.11 Acknowledgements.- 5 H2 Design of Nominal and Robust Discrete Time Filters.- 5.1 Abstract.- 5.2 Introduction.- 5.3 Wiener filter design based on polynomial equations.- 5.4 Design of robust filters in input-output form.- 5.5 Robust H2 filter design.- 5.6 Parameter tracking.- 5.7 Acknowledgement.- 5.8 References.- 6 Polynomial Solution of H2 and H? Optimal Control Problems with Application to Coordinate Measuring Machines.- 6.1 Abstract.- 6.2 Introduction.- 6.3 H.2 control design.- 6.4 H? Robust control problem.- 6.5 Systemand disturbance modelling.- 6.6 Simulation and experimental studies.- 6.7 Conclusions.- 6.8 Acknowledgements.- 6.9 References.- 6.10 Appendix: two-DOF H2 optimal control problem.
Bibliographische Angaben
- 1996, X, 255 Seiten, 45 Abbildungen, Maße: 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3540760776
- ISBN-13: 9783540760771
Sprache:
Englisch
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