Mirrors´ dynamics: A plague for adaptive optics systems performance?

This paper proposes a constructive controller design technique to optimize the closed-loop performance of adaptive optics systems in presence of deformable mirror´s dynamics, based on LTI continuous-time models of the disturbance and mirror. This sampled-data stochastic minimum-variance control problem has an equivalent discrete-time and tractable LQG control formulation. We show that the optimal solution can be obtained in a simpler way than what was proposed previously in the literature, with all control calculations being performed using off-the-shelf state-space control software. The proposed formulation provides an easy tool for performance evaluation of sub-optimal controllers. As an illustrative example, control of the tip-tilt wavefront distortion modes for an Extremely Large Telescope (ELT)-class AO system in presence of poorly damped second order DM´s dynamics well within the disturbance rejection bandwidth is presented. Variance calculations and time-domain simulations show that in this case, infinite actuator bandwidth is not mandatory, on the condition DM´s dynamics be adequately accounted for.