| Title:
|
$H_\infty$ control design for an adaptive optics system (English) |
| Author:
|
Denis, Nikolaos |
| Author:
|
Looze, Douglas |
| Author:
|
Huang, Jim |
| Author:
|
Castañon, David |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
[69]-81 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
multi-input |
| Keyword:
|
multi-output |
| Keyword:
|
adaptive optics system |
| Keyword:
|
model reduction techniques |
| Keyword:
|
$H_\infty$ control |
| MSC:
|
93B11 |
| MSC:
|
93B15 |
| MSC:
|
93B36 |
| MSC:
|
93C95 |
| idZBL:
|
Zbl 1274.93060 |
| idMR:
|
MR1705531 |
| . |
| Date available:
|
2009-09-24T19:23:22Z |
| Last updated:
|
2015-03-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135268 |
| . |
| Reference:
|
[1] Aubrun J. N., Lorell K. R., Mast T. S., Nelson J. E.: Dynamic analysis of the actively controlled segmented mirror of the W.M. Keck ten meter telescope. IEEE Control Systems Magazine, December 1987 10.1109/MCS.1987.1105386 |
| Reference:
|
[2] Babcock H. W.: Adaptive optics revisited.Science 249 (1990), 253–257 10.1126/science.249.4966.253 |
| Reference:
|
[3] Boyer C.: Adaptive optics for high resolution imagery: Control algorithms for optimized modal corrections.In: Proc. of the SPIE, Vol. 1780, 1992 |
| Reference:
|
[4] Downie J. D., Goodman J. W.: Optimal wavefront control for adaptive segmented mirrors.Appl. Optics 28 (1989), No. 4 10.1364/AO.28.005326 |
| Reference:
|
[5] Ellerbroek B. L., Loan C. Van, Pitsianis N., Plemmons R. J.: Optimizing closed loop adaptive optics performance using multiple control bandwidths.J. Opt. Soc. Amer. A 11 (1994) 10.1364/JOSAA.11.002871 |
| Reference:
|
[6] Francis B.: A Course in Control Theory.Springer–Verlag, Berlin 1987 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[9] Moore B. C.: Principal components analysis in linear systems: controllability, observability, and model reduction.IEEE Trans. Automat. Control AC-26 (1981), No. 2 MR 0609248, 10.1109/TAC.1981.1102568 |
| Reference:
|
[11] Tebo A.: Adaptive Optics.OE Reports, No. 96, 1991 |
| Reference:
|
[12] Tyson R. K.: Principles of Adaptive Optics.Academic Press, San Diego 1991 |
| . |
