Passivity-Based Stabilization of a 1-DOF Electrostatic MEMS Model With a Parasitic Capacitance

Feedback control of electrostatic microelectromechanical systems (MEMS) is significantly complicated by the presence of parasitics. This paper considers the stabilization of a one-degree-of-freedom (1-DOF) piston actuator under the influence of a capacitively coupled parasitic electrode. Previous work by the authors has shown that, in the absence of parasitics, passivity-based control may be used to make any feasible equilibrium point of this system globally asymptotically stable. However parasitics may destabilize the nominal closed-loop system by inducing multiple equilibrium points, causing a saddle-node bifurcation called
charge

pull-in
. This note shows how the nominal passivity-based control formulation may be modified to eliminate the multiple equilibria and prevent charge pull-in. As in previous work, we consider both static and dynamic output feedback controllers, with the dynamic controller providing additional control over transient performance.