Fractional loop delays in adaptive optics modeling and control

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.