A general modelling and control framework for electrostatically actuated mechanical systems

This paper presents a geometric framework for the stabilization and control of a general class of electrostatically actuated mechanical systems. Microelectromechanical systems (MEMS), such as micromirrors, are one motivating application for this work. There wavelengths of applications of interest lead to positioning requirements on the order of 40-100 nm. Furthermore, electrostatic actuation is poised to be the method of choice for the emerging field of nanoelectromechanical systems (NEMS), and the approach presented should be applicable there as well. 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. A key contribution of this paper places general electrostatic forces in a framework suitable for passivity-based control. The configuration space of the movable body is assumed to have the structure of a simple mechanical system on a Lie group, and stabilizing static and dynamic feedback control laws are derived in terms of co-ordinate-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. The static output feedback controller requires only measurement of the charge and voltage on each drive electrode to provide almost-global stabilization of a desired feasible configuration, but performance is limited by the natural dynamics of the mechanical subsystem. 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. Copyright (c) 2005 John Wiley & Sons, Ltd.