Optimal control strategy to reduce the temporal wavefront error in AO systems

An Adaptive Optics (AO) system for astronomy is analysed from a control point of view. The focus is put on the temporal error. The AO controller is identified as a feedback regulator system, operating in closed-loop with the aim of rejecting wavefront disturbances. Limitations on the performance of feedback regulator systems are discussed. The concept of optimal control is proposed to minimise the temporal error. The issue of closed-loop feedback controller design is made transparent by using the principle of Internal Model Control. The central issue in reducing the temporal wavefront is the design of a feedforward prediction filter. In three separate tests - a numerical simulation example, measured data from an AO test bench and open-loop telescope data - the advantage of optimal control over the common approach of integral control is demonstrated. Optimal control of the temporal error yields a smaller temporal error, enables a longer integration time in the wavefront sensor, or the use of fainter natural guide stars.