Model-Based Feedforward Control of Large Deformable Mirrors

In this paper, a model-based feedforward control concept for fast set-point changes of large deformable mirrors is proposed. It takes into account local position control loops of excited actuators and mode-dependent stiffness variations of the mirror shell. Based on partial differential equations for the temporal and spatial behavior of the deformable mirror, a modal approximation of the mirror dynamics is performed. It is shown that a second order approximation of the eigenmode dynamics is appropriate for low-order modes even when additional system components as delays, digital-to-analog converters, current drivers, actuator-magnet efficiencies, capacitive sensors, and analog-to-digital converters are included. In particular, appropriate transfer functions with identified coefficients of the proposed modal models are presented for a 45-actuator prototype of the Large Binocular Telescope adaptive secondary mirror (P45). Additionally, experimental results with model-based feedforward control are presented. The identified dynamic model of the P45 is finally used to derive flatness based feedforward commands for chopping.