The Control Of Complex Dynamics Of A Typical Double-side Micro Resonator Via Delayed Position Feedback

A type of electrostatic double-side capacitive micro resonator is considered,and time-delayed position feedback on the DC voltage of its driven circuit is applied to control the complex dynamic behaviors of the microstructure,such as chaos and pull-in instability.Firstly,based on the theory of global bifurcation,the necessary conditions for homoclinic bifurcation and heteroclinic one in a time-delay position feedback control system are discussed;thus,the control mechanism of the chaotic motion and pull-in instability is analyzed.Then the validity of theoretical prediction is verified by the agreement between numerical results and theoretical ones.It follows that when the coefficient of the gain is positive,the delayed position feedback can be applied to effectively suppress the two complex dynamic phenomena i.e.chaos and pull-in instability which can be attributed to the global bifurcation but with totally different mechanism.This paper has some potential value of application in ensuring the dynamic integrity of the micro-resonator vibration systems and the design of the microstructures.