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Article Dans Une Revue International Journal of Robust and Nonlinear Control Année : 2011

Minimum-variance control of astronomical adaptive optic systems with actuator dynamics under synchronous and asynchronous sampling

Résumé

Adaptive optic (AO) systems are now routinely used in ground-based telescopes to counter the effects of atmospheric turbulence. A deformable mirror (DM) generates a correction wavefront, which is subtracted from the turbulent wavefront using measurements of the residual phase provided by a wavefront sensor (WFS). Minimizing the variance of the residual phase defines a sampled data control problem combining a continuous time minimum-variance (MV) performance criterion with a discrete-time controller. For a fairly general class of linear time-invariant DM and turbulence WFS models, this control problem can be transformed into an equivalent discrete-time LQ optimization problem involving a set of (discrete-time) control-sufficient statistics of the incoming continuous-time turbulence. This paper shows how to constructively solve this MV problem in the presence of DM's dynamics, starting from continuous-time models of DM and turbulence. This result is extended to the case of asynchronous DM/WFS sampling. An illustrative application to optimal control of tip-tilt turbulent modes for the European extremely large telescope in the presence of first-order DM's dynamics is presented.

Dates et versions

hal-01590239 , version 1 (19-09-2017)

Identifiants

Citer

Henri-François Raynaud, C. Correia, Caroline Kulcsár, J.-M. Conan. Minimum-variance control of astronomical adaptive optic systems with actuator dynamics under synchronous and asynchronous sampling. International Journal of Robust and Nonlinear Control, 2011, 21 (7), pp.768 - 789. ⟨10.1002/rnc.1625⟩. ⟨hal-01590239⟩
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