# Article

Full entry | PDF   (2.1 MB)
Keywords:
multi-input; multi-output; adaptive optics system; model reduction techniques; $H_\infty$ control
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.
References:
[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 DOI 10.1109/MCS.1987.1105386
[2] Babcock H. W.: Adaptive optics revisited. Science 249 (1990), 253–257 DOI 10.1126/science.249.4966.253
[3] Boyer C.: Adaptive optics for high resolution imagery: Control algorithms for optimized modal corrections. In: Proc. of the SPIE, Vol. 1780, 1992
[4] Downie J. D., Goodman J. W.: Optimal wavefront control for adaptive segmented mirrors. Appl. Optics 28 (1989), No. 4 DOI 10.1364/AO.28.005326
[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) DOI 10.1364/JOSAA.11.002871
[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.: Principal components analysis in linear systems: controllability, observability, and model reduction. IEEE Trans. Automat. Control AC-26 (1981), No. 2 DOI 10.1109/TAC.1981.1102568 | MR 0609248
[11] Tebo A.: Adaptive Optics. OE Reports, No. 96, 1991
[12] Tyson R. K.: Principles of Adaptive Optics. Academic Press, San Diego 1991

Partner of