Passivity-Based Control of Electrostatic MEMS in the Presence of Parasitics

We present an integrated approach to modeling and control of electrostatically-actuated MEMS in the presence of parasitics. The model consists of a set of fixed or movable electrodes, each coupled to the others through a resistor and capacitance, and to ground through a capacitance and a voltage or current source. This formulation incorporates movable structures, control electrodes, sense electrodes, and parasitic capacitances. The resulting dynamic equations are directly incorporated into a control framework for stabilization and tracking. Based on the parameters of the model, formulas for two controllers are presented, one requiring measurement of electrode voltage and charge, the other requiring additionally measurement or estimation of the movable electrode velocities. In the absence of parasitics, both controllers provide almost-global stabilization of any equilibrium configuration. When parasitics are present, the approach must be modified to prevent the "charge pull-in" bifurcation. The paper presents an explicit design for the 1 degree-of-freedom case