Disturbance Modelling for Minimum Variance Control in Adaptive Optics Systems Using Wavefront Sensor Sampled-Data

Modern large telescopes are built based on the effectiveness of adaptive optics systems in mitigating the detrimental effects of wavefront distortions on astronomical images. In astronomical adaptive optics systems, the main sources of wavefront distortions are atmospheric turbulence and mechanical vibrations that are induced by the wind or the instrumentation systems, such as fans and cooling pumps. The mitigation of wavefront distortions is typically attained via a control law that is based on an adequate and accurate model. In this paper, we develop a modelling technique based on continuous-time damped-oscillators and on the Whittle's likelihood method to estimate the parameters of disturbance models from wavefront sensor time-domain sampled-data. On the other hand, when the model is not accurate, the performance of the minimum variance controller is affected. We show that our modelling and identification techniques not only allow for more accurate estimates, but also for better minimum variance control performance. We illustrate the benefits of our proposal via numerical simulations.