Passivity-based stabilization of a 1-DOF electrostatic MEMS model with a parasitic capacitance
This thesis addresses the problem of stabilizing 1-DOF piston mode electrostatic actuator in the presence of parasitic capacitance due to conductive substrate. The current study makes use of passivity-based control technique to formulate controllers. The static and dynamic controller schemes based on total charge can result in a unique equilibrium, however, their region of attraction may be small and the equilibrium may lose stability through Hopf bifurcation for certain configurations. A new charge quantity Qcc is introduced and used to derive static and dynamic feedback controllers in order to resolve issues encountered in the controllers based on total charge. The controllers based on Qcc are proved to be capable of globally asymptotically stabilizing the unique feasible equilibrium point for the configurations where the movable electrode is screened from the parasitic electrode by the control electrode. When the movable electrode and the parasitic electrode are directly coupled to have a mutual capacitance, numerical simulations show that the region of attraction of the closed-loop equilibrium is large. The effects of the infinite parallel plate approximation inherent in the formulation on the controller performance are investigated.