Hysteresis Modeling and Go-To Control of Deformable Mirrors in Adaptive Optics

We propose a model-based approach to provide "open-loop" control, or precise go-to capability, for piezo actuated deformable mirrors (DMs) used in adaptive optics. Our DM model consists of a two-dimensional, linear partial differential equation known as the thin plate equation to describe the DM facesheet which is coupled to nonlinear scalar ordinary differential equations to describe the hysteretic actuators. Our control approach is carried out in two stages. In the first stage we compute actuator loads that drive the DM facesheet to a prescribed shape. The second stage involves the solution of "inverse" ordinary differential equations that provide the command voltages that induce actuator loads computed in the first stage. This work is significant in that it may enhance predictive and feed-forward control schemes in adaptive optics. Standard integral controllers, operating in closed loop, may also benefit since the gain may be increased.