An Optimal Integral Controller for Adaptive Optics Systems.

Integral controllers are commonly employed in astronomical adaptive optics. This work presents a novel tuning procedure for integral controllers in adaptive optics systems which relies on information about the measured disturbances. This tuning procedure consists of two main steps. First, it models and identifies measured disturbances as continuous-time-damped oscillators using Whittles´s likelihood and the wavefront sensor output signal. Second, it determines the integral controller gain of the adaptive optics system by minimizing the output variance. The effectiveness of this proposed method is evaluated through theoretical examples and numerical simulations conducted using the Object-Oriented Matlab Adaptive Optics toolbox. The simulation results demonstrate that this approach accurately estimates the disturbance model and can reduce the output variance. Our proposal results in improved performance and better astronomical images even in challenging atmospheric conditions. These findings significantly contribute to adaptive optics system operations in astronomical observatories and establish our procedure as a promising tool for fine-tuning integral controllers in astronomical adaptive optics systems.