Flatness-Based Control of Electrostatically Actuated MEMS With Application to Adaptive Optics: A Simulation Study

Abstract

Typical adaptive optics (AO) applications require continual measurement and correction of aberrated light and form closed-loop control systems. One of the key components in microelectromechanical system (MEMS) based AO systems is the parallel-plate microactuator. Being electrostatically actuated, this type of devices is inherently instable beyond the pull-in position when they are controlled by a constant voltage. Therefore extending the stable travelling range of such devices forms one of the central topics in the control of MEMS. In addition, though certain control schemes, such as charge control and capacitive feedback, can extend the travelling range to the full gap, the transient behavior of actuators is dominated by their mechanical dynamics. Thus, the performance may be poor if the natural damping of the devices is too low or too high. This paper presents an alternative for the control of parallel-plate electrostatic actuators, which is based on an essential property of nonlinear systems, namely differential flatness, and combines the techniques of trajectory planning and robust nonlinear control. It is, therefore, capable of stabilizing the system at any point in the gap while ensuring desired performances. The proposed control scheme is applied to an AO system and simulation results demonstrate its advantage over constant voltage control