Studies on Area-controlled Electrostatic Actuation of Small Membrane Reflectors

Abstract

Membrane mirrors are advantageous in several applications due to their light weight and potential for deployability. Desired optical performance often requires dynamic actuation, however, and electrostatic actuators are frequently employed for this purpose. This paper investigates a variable area/constant voltage method for electrostatic actuation of small circular membrane mirrors designed to meet specified performance requirements for a beam steering and focus/defocus application. The proposed technique involves selective application of a constant voltage to area segments that together make up an electrode pad. The paper shows that a lumped parameter model for this system also has the property of differential flatness (similar to variable voltage/constant area systems), based on which the reference trajectory for membrane deflection can be specified in phase space. The phase space trajectory is derived from the required transient response characteristics (rise time, settling time, etc.). A closed loop system comprised of a controller and an observer is devised using a Lyapunov function-based approach. A `quad cell' beam position finder is used to detect the beam angular deflection and intensity. The overall system is simulated numerically in this paper. The control system is found to provide efficient trajectory tracking for both symmetric and antisymmetric mode excitation. Although the area changes for the proposed system are discrete, the present simulations only consider continuously-variable area actuation.