Large-displacement Electrostatic Actuation of Membrane Reflectors through Mechanical Control of Electrode-membrane Gap

Several applications of deformable mirrors in adaptive optics and beam shaping rely on electrostatic actuation to provide the required deformation. In the case of membrane mirrors, the actuation force is frequently controlled via the potential difference across the gap between the metallized membrane and the electrode substrate. In our previous work we studied an alternative approach using a constant voltage and variable area, accomplished with appropriately centered clusters of switchable area segments. Here, we investigate controlling the force by driving the electrode substrate in a direction perpendicular to the actuator/ membrane surface. Using a single-mode non-linear model and the Lyapunov potential method, a closed-loop controller is designed for tracking a trajectory derived to meet prescribed performance criteria (such as steady deflection, bandwidth, and damping ratio). The velocity-observer input is derived from beam response measurements obtained using a quad cell beam position finder. The controller is found to be robust to a class of measurement errors affecting the quad cell output and a class of membrane velocity errors arising from platform vibrations, where both types of error are modeled as first-order Markov processes. The analytical results are confirmed using numerical simulations, showing the technique to be fairly successful at meeting the prescribed performance requirements for large deflections at moderate voltages and areas.