Distributed Force Control of Deformable Mirrorsg

Large (>1 m) deformable mirrors are attractive for adaptive optics on ground-based telescopes; the mirrors typically have hundreds or thousands of actuators. The use of force actuators instead of position actuators has the potential to significantly reduce total system cost. However, the use of force actuators results in many lightly-damped structural resonances within the desired bandwidth of the control system. We present a robust control approach for this problem and demonstrate its performance in simulation. First, we demonstrate that high-bandwidth active damping using velocity feedback from mirror sensors that are not quite collocated with the actuators can be robustly implemented, because at sufficiently high frequencies the structural dynamics enter an “acoustic” limit, where the half power bandwidth of a mode exceeds the modal spacing. This is important, because the system can be made less expensive using sensors placed in between actuators rather than collocated with each actuator. Introduction of active damping leads to a much easier problem for subsequent position control. It is known that a position control system in which each of the actuators is controlled using feedback from a collocated sensor can be made robustly stable. However, the resulting performance at high spatial frequencies is poor because there is no shared information between neighbouring actuators. In contrast, global control gives excellent performance but lacks robustness to model uncertainty. We introduce an innovative local control approach, which significantly improves the high spatial frequency performance without the robustness challenges associated with a global control approach. The overall approach is demonstrated