Stability Analysis And Time Delay Feedback Control Of Micro/Nano Electromechanical System

Due to the small scale and small damping,the micro/nano electromechanical system can easily enter the nonlinear vibration state,and thus has a particularly rich nonlinear dynamic behavior,such as snap-through,hysteresis,nonlinear soft/hard characteristics,bifurcation and chaos.Therefore,the research on the comprehensive performance of micro/nano electromechanical system has important theoretical exploration value and engineering application prospect for in-depth discussion on the vibration mechanism of micro/nano electromechanical system,reasonable guidance for the optimal design of electromechanical system,and reliable vibration control measures for electromechanical system.In this paper,the delay feedback control method is applied to several kinds of micro/nano electromechanical system,and the effects of feedback gain coefficient and time delay on the vibration characteristics of these nonlinear systems are studied.The main contents and research results are as follows:(1)The amplitude frequency response characteristics of the primary/secondary resonance of a high-order nonlinear mass microcantilever coupled system with time delay are systematically discussed.By using the multiple scales method,the conditions for the super-harmonic and sub-harmonic resonance of the system with time delay are obtained,and the optimization method of the optimal delay value and control parameters of the controlled system is given.It is found that the time delay control parameters only change the critical point or vibration position of the system amplitude frequency curve for sub-harmonic;for the case of primary resonance and super harmonic,the time delay control parameters weaken the amplitude,hardening characteristics and multi-value region of the system,and enhance the stability of the system.(2)The effect of velocity delay feedback control on the vibration characteristics of nonlocal nano beam is studied innovatively.The multiple scales method and integral iteration method are used to obtain the approximate analytical solution of the system.The attenuation rate is taken as the objective function,the stable vibration condition and the optimal time delay condition are taken as the constraint conditions.At the same time,the effects of small scale effect,wave number,Winkler foundation modulus,axial load and aspect ratio on the amplitude frequency curve of the primary resonance with or without time delay are systematically studied.It is found that the length of the slender nano beam is relatively short,and the influence of nonlocal effect on the system can be effectively reduced by selecting appropriate delay parameters,Moreover,the aspect ratio can effectively adjust the soft and hard characteristics of time-delay systems.Various parameters(such as wave number,Winkler foundation modulus,axial load and aspect ratio)can effectively affect the peak value,amplitude and corresponding bandwidth of the system.(3)The chaotic vibration characteristics of micro resonators with time delay are studied.At present,there is no complete analysis on the static driven micro/nano resonators with fixed ends and initial deflection.In this paper,the time delay control of micro/nano resonators with AC and DC current simultaneously is carried out,and the nonlinear and chaotic vibration control of the system is studied by introducing different time delay parameters.The amplitude frequency response equation and stability conditions of the system under the influence of time delay parameters are obtained.The critical value of time delay and the analytical conditions of chaotic motion are obtained.The results show that the increase of AC driving voltage will cause chaos of the system,and the displacement and velocity delay can effectively suppress the chaotic motion of the system.In this paper,the feedback gain coefficient and time delay are used to suppress the vibration of the system.This method has a wide space for design and adjustment,which is helpful to promote the application of delay feedback control in the field of micro/nano electromechanical system.The theoretical research work in this paper will provide necessary theoretical guidance and engineering application basis for the device design and performance optimization of micro/nano electromechanical system.