Nonlinear Dynamics Of Folded-MEMS Comb Drive Resonators With Time–Delayed Control

As one of the most critical and most widely used in micro electro mechanical system,the promotion of micro comb actuator in the performance,manufacturing and application range is very important for the development of the whole industry.Due to the structure and size of the micro computer system,the complex dynamic characteristics of the nonlinear electrostatic driving force will be generated.The nonlinear vibration of the micro comb structure under some conditions limits the stability of the drive and reduces the reliability of the drive.Even very small physical parameters change,may also make the static electric power driving comb drives have a greater impact,and cause even pull in phenomenon,resulting in instability of the system.In this paper,the nonlinear vibration of a single degree of freedom model of micro comb actuator is analyzed,the equivalent stiffness and amplitude frequency response of the system are obtained by the perturbation method and Fourier integral equation.Comprehensive analysis on the two aspects of the electrostatic driving force parameters and structural physical parameters,which can achieve the purpose of expanding the normal working range of the driver,controlling the output of the driver,improving the sensitivity of the reaction and improving the service life.Because of the delay of the system response,the characteristics of the structure and the speed limit of the signal transmission,the time delay phenomenon exists in all kinds of micro electro mechanical systems.But in the actual design of the system,the effective control of the system is almost not considered.After analysis,static electricity of electrostatic driven micro comb structure is a kind of feedback effect.It is very easy to cause the pull in effect,result in system instability.However,the time delay can be used to control the whole system.The control of the system with time delay has the advantages of low cost,low driving voltage,high quality factor and high stability.The time delay can be used to stabilize the system output,compensate system parameters change,improve the overall performance of the drive.Time-delayed velocity feedback and time-delayed displacement feedback are taken into consideration in the DC and AC driving voltage of the folded-MEMS comb drive resonators and the single degree of freedom model of the folded-MEMS comb drive resonators under the influence of time-delayed control is presented.This paper feedback from the velocity and displacement with small vibration amplitude to the electricity driving force and approximate the expression with the Taylor expansion.The method of multiple-scales is used to obtain the amplitude-frequency response equation of the system under the influence of time-delay parameters.The change of time-delayed parameter in the system nonlinear resonance result in jumping phenomena when the driving frequency is in the vicinity of resonance frequency.The resonance frequency and nonlinear characteristics of softening or hardening vary under conditions with different physical parameters such as DC and AC voltage.Stability region and vibration amplitude of the system with different physical parameters can be controlled by changing the time-delay parameters After calculation and using numerical method,the conclusion is verified,and the comparison of two different time delayed feedback control methods is obtained.the positive velocity time-delayed control gain make the system instable and the negative velocity time-delayed control gain lead to the disappearance of jumping phenomena.the negative Displacement time-delayed control gain make the system instable and the positive Displacement time-delayed control gain lead to the disappearance of jumping phenomena.This provides theoretical reference.to compensate the change of system parameters and improve the performance of comb and stabilize the system output.