Dynamics And Time Delay Control Research Of Electrically Driven Exponential Beam Nonlinear Micro-gyroscope

With the increasingly extensive application of gyroscopes,different application scenarios and consumer markets put forward higher requirements for the development and innovation of gyroscopes.The complex and changeable working environment and incomplete processing technology will lead to complex nonlinear behavior of the gyroscope system,which will lead to problems such as reduced sensitivity,reduced bandwidth area and poor stability of the gyroscope.Therefore,it is of great significance to eliminate or make use of the influence of system nonlinearity to improve the output performance of the gyroscope and enhance the stability of the system.In this paper,the exponential beam is introduced into the gyroscope.After considering the influence of curvature nonlinearity and inertia nonlinearity on the system,a new type of variable cross-section beam nonlinear micro gyroscope is designed.The linear motion control equation,boundary condition and nonlinear discretization model of exponential variable cross-section beam type nonlinear gyroscope are established by using the extended Hamilton principle,single mode approximation method and Lagrange differential equation.The static structure of gyroscope system with different section change factors is calculated and solved by ADM method.The nonlinear discrete model of the system is analyzed by using the multi-scale method,and the dynamic structure is solved and calculated.Using the hardening nonlinear characteristics of the gyroscope system,by adjusting the static bias DC voltage and the change factor of the exponential beam section,the difference between the corresponding frequency of the peak value of Coriolis force and the peak value of the detection peak in the system response can be controlled.Compared with linear systems,adjusting the frequency difference between the two peaks can obtain higher sensitivity and greater bandwidth.In addition,due to the particularity of exponential beam structure,when AC voltage acts on the beam thickness and width in two different directions,different performance advantages in the same system can be obtained to meet the needs of different working scenarios.Through the perturbation analysis of the nonlinear dynamic equation,the influence of the exponential section change factor,AC voltage,damping ratio and external input angular velocity on the dynamic output response of the gyroscope system is discussed.The results show that the bandwidth of the exponential beam gyroscope can be further widened by adjusting the damping ratio and AC voltage in the driving and detection directions after selecting the appropriate section change factor;The output performance advantages of gyroscopes vary with the direction of action of AC voltage.When AC voltage is applied in the thickness direction,the exponential beam gyroscope system can obtain better bandwidth performance;When the AC voltage is applied in the width direction,selecting an appropriate section change factor can not only obtain higher system sensitivity performance,but also increase the linear measurable range of the gyroscope to the external input angular velocity.Based on the exponential beam gyroscope model,this paper introduces a timedelay speed controller and a time-delay displacement controller,and discusses the influence of the gain parameters and time delay parameters of two different control systems on the output response of the system.By adjusting the parameters of the system under the time-delay speed control,the output bandwidth of the exponential beam nonlinear gyroscope is further improved.By adjusting the system parameters in time domain under time-delay displacement control,the response speed of the exponential beam nonlinear gyroscope is improved.