A general geometric framework for control of electrostatically-actuated mems and nems

This paper presents a geometric framework for the modeling and stabilization of a general class of electrostatically-actuated mechanical systems. The class of devices under study consists of a movable, rigid, grounded electrode, with a variety of allowable rotational and/or translational degrees of freedom, and a set of multiple, fixed, independently-addressable, drive electrodes. Previous work has placed the general electrostatic forces and the electrical system in a framework suitable for passivity-based control. This paper generalizes this result further by allowing the electrical part of the model to incorporate current leakage between electrodes. With respect to this model a stabilizing dynamic feedback control laws is derived in terms of coordinate-independent geometric formulas. To obtain controllers for a specific device it is then necessary only to evaluate these formulas. Appropriate approximations may be applied to make the computations more tractable. Performance may be improved using dynamic output feedback, but additional information is needed, typically in the form of a model relating electrode capacitances to the system configuration. We demonstrate the controller computations on a representative MEMS, and validate performance using ANSYS simulations.