Discrete-time model for an adaptive optics system with input delay

The standard adaptive optics (AO) system can be viewed as a sampled-data feedback system with a continuous-time disturbance (the incident wavefront from the observed object) and discrete-time measurement noise. A common measure of performance of AO systems is the time average of the pupil variance of the residual wavefront. This performance can be related to that of a discrete-time system obtained by lifting the incident and residual wavefronts. This article derives the corresponding discrete-time model and the computation of the AO system residual variance based on that model. The predicted variance of a single mode of an AO system is shown to be the same as that obtained via simulation.

[1]  Douglas P Looze.  Linear-quadratic-Gaussian control for adaptive optics systems using a hybrid model. , 2009, Journal of the Optical Society of America. A, Optics, image science, and vision.

[2]  Michel Verhaegen,et al.  Adaptive optics Η2-optimal control design applied on an experimental setup , 2006, SPIE Astronomical Telescopes + Instrumentation.

[3]  M. Kasper,et al.  Adaptive Optics for Astronomy , 2012, 1201.5741.

[4]  Pramod P. Khargonekar,et al.  H 2 optimal control for sampled-data systems , 1991 .

[5]  Tongwen Chen.  A simple derivation of the H2-optimal sampled-data controllers , 1993 .

[6]  D.P. Looze.  Minimum variance control structure for adaptive optics systems , 2005, Proceedings of the 2005, American Control Conference, 2005..

[7]  Bassam Bamieh,et al.  The 2 problem for sampled-data systems , 1992, Systems & Control Letters.

[8]  Laurent M. Mugnier,et al.  Optimal control law for multiconjugate adaptive optics , 2003, SPIE Astronomical Telescopes + Instrumentation.

[9]  Jin Bae Park,et al.  Design of H2 Controllers for Sampled-Data Systems with Input Time Delays , 2004, Real-Time Systems.

[10]  Jean-Pierre Véran,et al.  Optimal modal fourier-transform wavefront control. , 2005, Journal of the Optical Society of America. A, Optics, image science, and vision.

[11]  B. Francis,et al.  H/sub 2/-optimal sampled-data control , 1991 .

[12]  Huibert Kwakernaak,et al.  Linear Optimal Control Systems , 1972 .

[13]  Astrom.  Computer Controlled Systems , 1990 .

[14]  J. Hardy,et al.  Adaptive Optics for Astronomical Telescopes , 1998 .

[15]  B. Welsh,et al.  Imaging Through Turbulence , 1996 .

[16]  C. Loan.  Computing integrals involving the matrix exponential , 1978 .

[17]  Katsuhiko Ogata,et al.  Discrete-time control systems , 1987 .

[18]  Jean-Marc Conan,et al.  Optimal control, observers and integrators in adaptive optics. , 2006, Optics express.

[19]  Yutaka Yamamoto,et al.  New approach to sampled-data control systems-a function space method , 1990, 29th IEEE Conference on Decision and Control.

[20]  Bassam Bamieh,et al.  A general framework for linear periodic systems with applications to H/sup infinity / sampled-data control , 1992 .

[21]  Geir E. Dullerud,et al.  An LMI solution to the robust synthesis problem for multi-rate sampled-data systems , 2001, Autom..

[22]  Leonid Mirkin,et al.  Some Remarks on the Use of Time-Varying Delay to Model Sample-and-Hold Circuits , 2007, IEEE Transactions on Automatic Control.

[23]  D.P. Looze.  Discrete-Time Model of an Adaptive Optics System , 2007, 2007 American Control Conference.

[24]  C. Kulcsár,et al.  Optimal control law for classical and multiconjugate adaptive optics. , 2004, Journal of the Optical Society of America. A, Optics, image science, and vision.

[25]  J. Y. Wang,et al.  Modal compensation of atmospheric turbulence phase distortion , 1978 .

[26]  Gene H. Golub,et al.  Matrix computations , 1983 .

[27]  Douglas P. Looze.  Structure and approximations of LQG controllers based on a hybrid AO system model , 2009, 2009 European Control Conference (ECC).

[28]  Douglas P. Looze,et al.  Optimal Compensation and Implementation for Adaptive Optics Systems , 1999 .

[29]  Bi Zhen.  H_2-optimal sampled-data control with pole placement constraint , 2000 .

[30]  E. Fridman,et al.  Sampled-data H ∞ control and filtering : Nonuniform uncertain sampling , 2007 .

[31]  Bruce A. Francis,et al.  Optimal Sampled-Data Control Systems , 1996, Communications and Control Engineering Series.

[32]  Hannu T. Toivonen,et al.  H∞ and LQG control of asynchronous sampled-data systems , 1997, Autom..

[33]  Emilia Fridman,et al.  Sampled-data Hinfinity control and filtering: Nonuniform uncertain sampling , 2007, Autom..

[34]  Shinji Hara,et al.  A hybrid state-space approach to sampled-data feedback control , 1994 .

[35]  R. Vaccaro.  Digital control : a state-space approach , 1995 .