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Adaptive Optics Feedback Control

Published online by Cambridge University Press:  13 March 2013

J.-P. Folcher ,
M. Carbillet ,
A. Ferrari  and
A. Abelli
J.-P. Folcher
Affiliation:
UMR 7293, Lagrange Université de Nice Sophia-Antipolis/CNRS/Observatoire de la Côte d’Azur, Parc Valrose, 06108 Nice Cedex 2, France
M. Carbillet
Affiliation:
UMR 7293, Lagrange Université de Nice Sophia-Antipolis/CNRS/Observatoire de la Côte d’Azur, Parc Valrose, 06108 Nice Cedex 2, France
A. Ferrari
Affiliation:
UMR 7293, Lagrange Université de Nice Sophia-Antipolis/CNRS/Observatoire de la Côte d’Azur, Parc Valrose, 06108 Nice Cedex 2, France
A. Abelli
Affiliation:
UMR 7293, Lagrange Université de Nice Sophia-Antipolis/CNRS/Observatoire de la Côte d’Azur, Parc Valrose, 06108 Nice Cedex 2, France
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Abstract

This paper concentrates on the control aspects of Adaptive Optics (AO) systems and includes a prior exposure to linear control systems from the “classical” point of view. The AO control problem is presented and the well-established optimized modal gain integral control approach is discussed. The design of a controller from a modern control point of view is addressed by means of a linear quadratic Gaussian control methodology. The proposed approach emphasizes the ability of the adaptive optics loop to reject the atmospheric aberration. We derive a diagonal state space system which clearly separates the dynamics of the plant (deformable mirror & wavefront sensor) from the disturbance dynamics (atmospheric model). This representation facilitates the numerical resolution of the problem. A frequency analysis is carried out to check performance and robustness specifications of the multiple-input multiple-output feedback system. The effectiveness of the approach is demonstrated through numerical experiments.

Type
Research Article
Information
European Astronomical Society Publications Series , Volume 59: New Concepts in Imaging: Optical and Statistical Models , 2013 , pp. 93 - 130
Copyright
© EAS, EDP Sciences 2013

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References

Anderson, B., & Moore, J.B., 1990, Optimal Control: Linear Quadratic Methods (Prentice-Hall)
Astrom, K.A., & Wittenmark, B., 2011, Computer-Controlled Systems: Theory and Design (Dover Publications)
Bitmead, R.R., Gevers, M., & Wertz, V., 1990, Adaptive Optimal Control: the Thinking Man’s GPC (Prentice Hall Englewood Cliffs, NJ)
Bitmead, R.R., & Gevers, M., 1991, Riccati Difference and Differential Equations: Convergence, monotonicity and stability, In The Riccati equation, ed. S. Bittanti, A.J. Laub & J.C. Willems (Springer Verlag)
Boyd, S., 1993, Lecture Notes for E105, Introduction to Automatic Control (Stanford University)
Burg, J.P., 1975, Ph.D. Thesis, Maximum Entropy Spectral Analysis (Stanford University)
Born, M., & Wolf, E., 1999, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of light (Cambridge University Press)
Carbillet, M., Vérinaud, C., Femenía, B., Riccardi, A., & Fini, L., 2005, MNRAS, 356, 1263 CrossRef
Carbillet, M., Desiderà, G., Augier, A., et al., 2010, Proc. SPIE, 7736, 773644 CrossRef
Conan, J.M., Raynaud, H.F., Kulcsár, C., Meimon, S., & Sivo, G., 2011, Are Integral Controllers Adapted to the New Era of ELT Adaptive Optics? In AO4ELT2, Victoria, Canada, September
Dorato, P., & Levis, A., 1971, Optimal Linear Regulators: the Discrete-time Case, IEEE Transactions on Automatic Control, 613
Dorf, R.C., & Bishop, R.H., 1998, Modern Control Systems, Eight edition (Addison-Wesley Longman Publishing Co., Inc., Boston, MA, USA)
Demerle, M., Madec, P.Y., & Rousset, G., 1994, Servo-Loop Analysis for Adaptive Optics, In NATO Meeting, Cargèse, France, June 29-July 9, 1993, ONERA, TP, Vol. 423, 73
Dessenne, C., Madec, P.Y., & Rousset, G., 1998, Appl. Opt., 37, 4623 CrossRef
Franklin, G.F., Powell, J.D., & Emami-Naeni, A., 1991, Feedback Control of Dynamic Systems, Second edition (Addison-Wesley)
Franklin, G.F., Powell, J.D., & Workman, M.L., 1990, Digital Control of Dynamic Systems, Second edition (Addison Wesley)
Gendron, E., & Léna, P., 1994, A&A (ISSN 0004-6361), 291
Kulcsár, C., Raynaud, H.F., Petit, C., Conan, J.M., & de Lesegno, P.V., 2006, Appl. Opt, 39, 2525
Kwakernaak, H., & Sivan, R., 1972, Linear Optimal Control Systems (John Wiley & Sons)
Laub, A.J., 2004, Matrix Analysis for Scientists and Engineers, Society for Industrial Mathematics
Looze, D.P., 2005, Realization of Systems with CCD-based Measurements, Automatica, 41
Looze, D.P., 2006, J. Opt. Soc. Am., 23, 603 CrossRef
Looze, D.P., 2007, J. Opt. Soc. Am., 9, 2850 CrossRef
Noll, R.J., 1976, J. Opt. Soc. Am., 66, 207 CrossRef
Paschall, R.N., & Anderson, D.J., 1993, Linear Quadratic Gaussian Control of a Deformable Mirror Adaptive Optics System with Time-delayed Measurements, Appl. Opt., 32
Paschall, R.N., Von Bokern, M.A., & Welsh, B.M., 1991, Design of a Linear Quadratic Gaussian Controller for an Adaptive Optics System, In Proceedings of the 30th IEEE Conference on Decision and Control, 1761
Roddier, F., 1999, Adaptive Optics in Astronomy (Cambridge University Press)
Skogestad, S., & Postlethwaite, I., 2007, Multivariable Feedback Control: Analysis and Design