Optimal Control of Electrostatically Actuated Micro-Plate Attached to the End of Microcantilever

An optimal control is designed for damping the unwanted vibrations of an electrostatically actuated micro-system. The goal is using feasible methods to decrease the settling time and overshoot of the response. This configuration consists of an electro-statically actuated micro-plate attached to the end of a micro-cantilever. The DC voltage is applied between the micro-plate and the opposite electrode micro-plate. This DC voltage causes an electrostatic force. In this model micro cantilever is considered as a continuous medium for which Euler-Bernoulli beam theory can be implemented. The plate is considered as a rigid body, and the electrostatic force is a nonlinear function of the displacement and the applied voltage underneath the micro-plate. The equation of motion is derived using Newton’s second law. In order to extract the corresponding state space and control the system in a closed loop way, exact method is used to reduce related partial differential equation of the systems into a set of two ordinary differential equations and the resultant state space is linearized about the operating point. The linearized state space is then optimized using the linear-quadrant regulator. Efficiency and applicability of the mentioned controller is investigated using comparative analyzing method.