Fractional loop delays in adaptive optics modeling and control

Marquis, Lucas; Raynaud, Henri-François; Galland, Nicolas; Marco de la Rosa, Jose; Montilla, Icíar; Tubío Araújo, Óscar; Reyes García-Talavera, Marcos; Kulcsár, Caroline
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Journal of the Optical Society of America A

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This paper revisits the problem of optimal (minimum variance) control for adaptive optics (AO) systems when measurement and command applications are asynchronous, resulting in a non-integer servo loop delay. When not properly accounted for, such fractional delays may severely degrade the AO performance, especially in the presence of high-frequency vibrations. We present evidence of this performance degradation thanks to in-lab experimental measurements on the Gran Telescopio Canarias Adaptive Optics (GTCAO) system controlled with standard suboptimal linear quadratic Gaussian (LQG) controllers. A constructive, easy to implement LQG control design is then proposed and validated in a simulation for vibrations affecting the tip-tilt modes. Our methodology is very interesting because it allows a performance assessment for any linear controller in terms of variance, rejection transfer functions, power spectral densities, and stability margins. We also show how the continuous-time disturbance model can be derived from standard discrete-time disturbance data-based modeling.