Capacitive stabilization of an electrostatic actuator: output feedback viewpoint

With constant voltage control, use of the entire capacitive gap in analog operation of electrostatically-actuated MEMS devices is restricted by a bifurcation phenomenon known as "pull in" or "snap through." It is well known that a properly-sized series capacitor will eliminate this bifurcation. We re-visit this result from the viewpoint of control theory, and show that the series capacitor implements static charge feedback, and can semi-globally stabilize any position in the gap. In fact, with charge as output, the system is relative degree one, and input-output linearizable with asymptotically stable zero dynamics, suggesting that more general compensation schemes may be fruitful. In fact, the system may be input-output linearized using only the voltage across the electrodes. We show that any position in the gap may be globally asymptotically stabilized with output feedback of voltage and charge.