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

Document Type : Research Article

Authors

1 Mechanical Engineering Department, Faculty of Engineering, Kharazmi University, Tehran, Iran

2 Mechanical Engineering Department, Faculty of Engineering, Kharazmi University, Tehran, Iran ABSTRACT:

Abstract

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.

Keywords

Main Subjects

References

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Amirkabir Journal of Mechanical Engineering
Volume 49, Issue 4
March 2018
Pages 805-818

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