H ∞ control design for an adaptive optics system

Nikolaos Denis; Douglas Looze; Jim Huang; David Castañon

Kybernetika (1999)

  • Volume: 35, Issue: 1, page [69]-81
  • ISSN: 0023-5954

Abstract

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In this paper we first present a full order H ∞ controller for a multi- input, multi-output (MIMO) adaptive optics system. We apply model reduction techniques to the full order H ∞ controller and demonstrate that the closed-loop (CL) system with the reduced order H ∞ controller achieves the same high level of performance. Upon closer examination of the structure of the reduced order H ∞ controller it is found that the dynamical behavior of the reduced order H ∞ controller can be accurately approximated by a single-input, single-output (SISO) transfer function (TF) multiplied by the inverse of the adaptive optics plant dc gain. This observation then leads to a general design methodology which only requires the synthesis of a SISO H ∞ controller and multiplication by constant matrices.

How to cite

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Denis, Nikolaos, et al. "$H_\infty $ control design for an adaptive optics system." Kybernetika 35.1 (1999): [69]-81. <http://eudml.org/doc/33410>.

@article{Denis1999,
abstract = {In this paper we first present a full order $H_\infty $ controller for a multi- input, multi-output (MIMO) adaptive optics system. We apply model reduction techniques to the full order $H_\infty $ controller and demonstrate that the closed-loop (CL) system with the reduced order $H_\infty $ controller achieves the same high level of performance. Upon closer examination of the structure of the reduced order $H_\infty $ controller it is found that the dynamical behavior of the reduced order $H_\infty $ controller can be accurately approximated by a single-input, single-output (SISO) transfer function (TF) multiplied by the inverse of the adaptive optics plant dc gain. This observation then leads to a general design methodology which only requires the synthesis of a SISO $H_\infty $ controller and multiplication by constant matrices.},
author = {Denis, Nikolaos, Looze, Douglas, Huang, Jim, Castañon, David},
journal = {Kybernetika},
keywords = {multi-input; multi-output; adaptive optics system; model reduction techniques; $H_\infty $ control; multi-input; multi-output; -control; adaptive optics system; model reduction techniques},
language = {eng},
number = {1},
pages = {[69]-81},
publisher = {Institute of Information Theory and Automation AS CR},
title = {$H_\infty $ control design for an adaptive optics system},
url = {http://eudml.org/doc/33410},
volume = {35},
year = {1999},
}

TY - JOUR
AU - Denis, Nikolaos
AU - Looze, Douglas
AU - Huang, Jim
AU - Castañon, David
TI - $H_\infty $ control design for an adaptive optics system
JO - Kybernetika
PY - 1999
PB - Institute of Information Theory and Automation AS CR
VL - 35
IS - 1
SP - [69]
EP - 81
AB - In this paper we first present a full order $H_\infty $ controller for a multi- input, multi-output (MIMO) adaptive optics system. We apply model reduction techniques to the full order $H_\infty $ controller and demonstrate that the closed-loop (CL) system with the reduced order $H_\infty $ controller achieves the same high level of performance. Upon closer examination of the structure of the reduced order $H_\infty $ controller it is found that the dynamical behavior of the reduced order $H_\infty $ controller can be accurately approximated by a single-input, single-output (SISO) transfer function (TF) multiplied by the inverse of the adaptive optics plant dc gain. This observation then leads to a general design methodology which only requires the synthesis of a SISO $H_\infty $ controller and multiplication by constant matrices.
LA - eng
KW - multi-input; multi-output; adaptive optics system; model reduction techniques; $H_\infty $ control; multi-input; multi-output; -control; adaptive optics system; model reduction techniques
UR - http://eudml.org/doc/33410
ER -

References

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  6. Francis B., A Course in Control Theory, Springer–Verlag, Berlin 1987 
  7. Huang J., Looze D. P., Denis N., Castañon D. A., Dynamic modeling and identification of an adaptive optics system, In: Proc. 4th IEEE Conf. on Control Applications, Albany 1995 
  8. Huang J., Looze D. P., Denis N., Castañon D. A., Control designs for an adaptive optics system, In: 34th IEEE Conference on Decision and Control Proceedings, New Orleans 1995 
  9. Moore B. C., 10.1109/TAC.1981.1102568, IEEE Trans. Automat. Control AC-26 (1981), No. 2 (1981) MR0609248DOI10.1109/TAC.1981.1102568
  10. Tebo A., Adaptive Optics, OE Reports, No. 96, 1991 
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