Application of quadratic controller to control the pull-in instability of a micro-resonator

This study is on the nonlinear dynamics of a clamped–clamped electro-statically actuated capacitive micro-beam. The micro-resonator is composed of silicon and PZT as a piezoelectric material. PZT is functionally distributed along the height of the micro-beam according to the power law distribution law. The micro-resonator is simultaneously subjected to DC piezoelectric and AC harmonic actuations. The governing equation of the motion is derived by the minimization of the Hamiltonian and generalized to the viscously damped systems. The static and dynamic analysis of an electrostatically actuated micro beam with and without controller is presented. The results depict that by adding the controller we can increase the pull-in voltage of micro-resonator and consequently prevent the pull-in phenomena in micro-beam. The effect of varies controllers are discussed and changing the coefficients of quadratic controller are presented. Using frequency response curves, the effect of adding controller in the vicinity of primary resonance is presented.