A passivity-based controller for an electrostatic MEMS model in the presence of parasitics

Feedback control of electrostatic microelectromechanical systems (MEMS) is significantly complicated by the presence of parasitic surfaces. This note considers the stabilization of a one-degree-of-freedom (1-DOF) piston actuator with capacitively-coupled parasitics. Previous work by the authors has shown how, in the absence of parasitics, any feasible equilibrium point of this system may be made globally asymptotically stable using passivity-based control. However if parasitics are present this nominal closed-loop system may be destabilized by capacitive coupling, through a phenomenon called charge pull-in. This note shows how the nominal controller formulation may be modified to eliminate multiple equilibria. If the movable electrode is completely screened from the parasitic electrode by the control electrode, the unique equilibrium is globally asymptotically stable. Otherwise, though the desired equilibrium is still unique, its region of attraction may be finite and the equilibrium may lose stability through a Hopf bifurcation. Furthermore in the second case the output feedback controller cannot be implemented using feasible measurements. the controller obtained by neglecting the unmeasurable quantities still eliminates charge pull-in, but the region of attraction may be reduced still further.