Research On Segmented Modeling Method Of MEMS Electromagnetic Micromirror

In recent years,with the development of MOEMS technology,MEMS electromagnetic micromirrors have gradually been widely used.Micro-mirrors are integrated with micro-optical mirrors and micro-electro-mechanical drivers.The basic principle is to rotate or translate the active micro-mirrors through electrostatic action,so as to change the propagation direction or phase of the input light.Therefore,MEMS electromagnetic micromirrors and their arrays can be widely used in optical communication optical exchange,spectral analysis instruments,astronomy,virtual reality imaging,laser radar and other fields,so it has become a hot topic in the world.For a long time,MEMS electromagnetic micromirror has been regarded as a linear system in the working state.However,with the increasing requirements on the performances of application products,the influence of the inherent hysteresis nonlinear characteristics in the electromagnetic micromirror cannot be ignored,which will greatly affect the positioning accuracy of the electromagnetic micromirror and even lead to the instability of the whole system.At present,it is an effective method to remove hysteresis nonlinear characteristics by designing controller based on system model.Therefore,it is significant to study how to establish an accurate mathematical model to describe the characteristics of MEMS electromagnetic micromirrors.This is also the main task of this thesis,that is,to establish a mathematical model of MEMS electromagnetic micromirrors with hysteresis characteristics by using the idea of segmented modeling method.In this thesis,by analyzing the working principle and experimental data of MEMS electromagnetic micromirror,it is found that the hysteresis characteristics exist in the system,and the hysteresis is input rate-dependent.Moreover,the width of hysteresis loop will increase obviously with the frequency of input increasing,while the maximum output value will decrease gradually.the input rate-depended hysteresis sometime is called as dynamic hysteresis.The main contents of this paper is listed as follows.（1）In this thesis,a new segmented PI model is proposed to describe dynamic hysteresis by analyzing the data of hysteresis test platform.Experimental results show that the proposed segmented PI model is superior to the traditional hysteresis model in describing dynamic hysteresis characteristics.（2）It is important for the proposed model to obtain the input signal frequency,but it is difficult to get signal frequency on line in application.Thus,the Hilbert transform is introduced to acquire input signal instantaneous frequency.Thus,a frequency recognitor is designed.In addition,another novelty is PSO algorithm is employed to estimate the number of PI operators in the segmented PI model,and namely,the optimal number of PI operators for each sub-model is obtained.（3）Based on the analysis of the MEMS electromagnetic micromirror,the highly underdamped characteristics and input rate-dependent hysteresis both exist in the system,so the block modeling idea is applied to build the system.Namely,a segmented Hammerstein model with the proposed segmented PI hysteresis model is used to describe the MEMS electromagnetic micromirror.Next,PSO algorithm is employed to estimate the number of PI operators in Hammerstein model,and Least Square method is used to identify the parameters of the model.Compared experimental results show that the proposed model better describe the characteristics of MEMS electromagnetic micromirror.