The Control Of Pull-in Instability Of A Typal Electrostatic Double-side Micro Resonator Via Delayed Velocity Feedback

As a typal microinertial sensor in microelectromechanical system(MEMS),electrostatic microresonator has been widely used in autonomous vehicles.However,due to its non-linear electrostatic force and other reasons,the microresonator structure presents a complex nonlinear dynamic behavior,such as chaos and pull-in instability cause the direct failure of the microresonator sensor,which is also one of the main reasons for the frequent accidents of autonomous vehicles.Therefore,it is of great practical significance to propose an effective control method for the nonlinear dynamic characteristics of electrostatic microresonators.In this paper,a class of electrostatic driven double-side capacitive microresonators is studied.First,the dynamic modeling of the microresonators is carried out.By introducing the nonlinear time transformation function,the exact analytical solution of the heteroclary orbits for the system without time delay is obtained.Then,based on bifurcation theory and using Melnikov method,the critical conditions of the design parameters of the pull-in instability of the micro resonator are obtained,and the linear delay velocity feedback control is introduced in the DC bias voltage of the system drive circuit to suppress the pull-in instability.By comparing the safe domain method with the numerical simulation,it is proved that the delay velocity feedback control can effectively restrain the complex dynamic behavior(pull-in instability and chaos)of this kind of double-sided capacitive microresonator.