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The objective of this paper is to present a supervised multi-level fuzzy controller to control the deflection of an electrostatically actuated microplate within and beyond its pull-in range. The mode shapes of the microplate are derived using Extended Kantorovich Method (EKM) which are shown to be in great agreement with finite element results. Using open loop simulations, it is shown that the first mode shape is effectively the dominant one. Then by utilizing a single mode approximation along with employing the Lagrange equation, the dynamic behavior of the microplate is described in modal space by an ordinary differential equation. By static and dynamic simulations, dependence of the plate deflection on the applied voltage is identified linguistically. Then based on the linguistic description of the system, a fuzzy controller is designed to stabilize the microplate at desired deflections. To improve the performance specifications of the closed-loop system, another fuzzy controller at a higher level is proposed to adjust the parameters of the main controller in real time. To guarantee the stability of the closed-loop system, a non-fuzzy supervisory unit is attached to the control architecture. The simulations results reveal that by using the presented single level and supervised adaptive controllers, the control objective is met effectively with good performance specifications. It is also observed that adding a second level and a supervisory unit to the main controller can reduce the overshoot and the settling time for within and beyond pull-in stabilization of electrostatically actuated microplates in following the step commands. Excellent performance of the system in the presence of the proposed controller is further demonstrated using multiple step and also sinusoidal commands. The qualitative knowledge resulting from this research can be generalized and used for development of efficient controllers for N/MEMS actuators and electrostatically actuated nano/micro positioning systems.
Radgolchin et al. (Mon,) studied this question.