Large-displacement Closed-loop Control of Variable Area Electrostatic Actuation for Membrane Reflectors

Membrane mirrors may be attractive in some space applications where light weight, deployability, and conformability are desired. This article investigates large-displacement closed-loop control of electrostatically driven mirrors being used in focusing and steering of laser beams. The required transient response characteristics for the membrane response are achieved using a variable area, constant voltage actuation method, which may be advantageous in some applications. Our previous work on variable area control was restricted to membrane deflections not exceeding 1/3 (the available gap size), and assumed that a continuous area variation was available. In this article, the controller design is extended to enable deflections approaching the entire available gap size, which would help to bring down the voltage requirement for a prescribed deflection range. A Lyapunov function-based approach is used here along with a fully nonlinear dynamic model. Although a single-mode lumped parameter model is used, a feedforward technique to compensate for a class of residual modes is investigated in this paper. Also studied in this article is the use of a Lyapunov function-based framework to guide the design of a controller to handle step-wise/discrete area changes. A dynamic observer based on quad-cell beam-position detector measurements and a fully nonlinear plant model is also studied. The article discusses numerical simulation results, which show that the controllers under study are fairly successful at providing closed-loop deflections approaching the full gap size at the required bandwidth.