Research On Hysteresis Modeling And Control Of Piezoelectric Two-dimensional Micro-operation Stage

With the rapid development of micro-nano technology,piezoelectric micro-operation technology has gradually become one of the key research contents in the field of high-performance precision processing equipment.It has been widely used in semiconductor technology,optical micro-processing,medical technology science,micro electromechanical precision system,aerospace precision equipment manufacturing and other frontier technology fields.However,as the core driving element of the multi-dimensional micro-positioning stage,the inherent hysteresis non-linearity of the piezoelectric ceramic actuator causes the nonlinear problem of the stage,and the coupling effect exists between the outputs of the multi-dimensional stage,which seriously affects the positioning accuracy and tracking performance of the stage.Aiming at the main problems existing in the piezoelectric multi-dimensional micro-positioning stage,this paper takes the piezoelectric two-dimensional micro-positioning stage as the research object and studies the hysteresis nonlinear modeling and motion tracking control of the stage respectively.The main contents are as follows:In order to describe the rate-dependent hysteresis nonlinearity of piezoelectric two-dimensional micro-positioning stage and improve its control accuracy,a Hammerstein modeling method based on PI model is proposed.Hammerstein model-based piezoelectric micro-positioning stage is composed of static hysteresis nonlinear part and linear dynamic part in series.Modified Prandtl-Ishlinskii(MPI)model which can describe the static hysteresis part of the stage and Autoregressive model with exogenous input(ARX)model which can describe the linear dynamic part are adopted.The experimental stage was set up for the experiment,and the method for calculating model parameters was given to obtain the parameters.The experimental results showes that the relative error range of the established model is from 1%to 5%,indicating that the rate-dependent hysteresis model could accurately describe the dynamic hysteresis nonlinear characteristics of the stage.Due to the inherent hysteresis of the piezoelectric ceramic actuator and the coupling effect of the two-dimensional micro-positioning stage,the motion tracking accuracy of the stage will be affected.In order to solve these problems,a compound control strategy based on MPI inverse model compensation feedforward control and H? robust control is proposed.The control strategy using MPI inverse model as the feedforward compensation stage hysteresis characteristics,using ARX model and its inverse model tracking precision of the control system of target displacement,which the MPI inverse modeling error compensation error and ARX model inverse model is contained in the ARX model uncertainty in the model,output as the coupling effects between the external disturbance.By transforming the control structure into the standard H? tracking control form,the controller is calculated to eliminate the error caused by model uncertainty and external disturbance.Through experimental analysis,the control strategy can achieve good tracking of target displacement of the stage,and with the gradual increase of tracking signal frequency,the tracking error range of the stage stabilizes between-2 ?m and 2 ?m,which proves that the control strategy is feasible and effective.In the motion tracking control of micro-positioning stage,the inverse model is often established to compensate the hysteresis nonlinearity,so as to improve the tracking accuracy of the stage.Therefore,in order to improve the tracking accuracy of the stage and avoid the inverse model,a tracking control strategy of RBF neural network based on PI-BP model is proposed.The PI-BP model is composed of a Prandtl-Ishlinskii(PI)model which can convert multi-mapping hysteresis into one-to-one mapping and a Back Propagation(BP)neural network with strong approximation ability to one-to-one mapping in series,where BP is a three-layer network structure.The PI model is obtained by weighted superposition of a number of play operators,and its weight parameters are obtained by particle swarm optimization.Then,the difference between the output displacement of the PI-BP model and the actual output displacement of the stage is taken as the adjustment parameter of the RBF neural network controller to adjust the deviation of the tracking target displacement of the stage.Experimental results show that the error range of RBF neural network tracking control based on PI-BP model is from-4?m to 6?m,and the maximum relative error is 0.1201,indicating that this control can effectively improve the tracking accuracy of the stage and is feasible.In order to solve the problem of poor generalization ability of the hysteresis model of piezoelectric micro-positioning stage,a method for modeling the hysteresis of convolutional neural network(CNN)based on PI model obtained by combining the output of the rate-dependent hysteresis model layer with the output dot product of the convolutional network layer for a two-dimensional micro-positioning stage.The rate-dependent hysteresis model layer is composed of the PI model layer and the nonlinear term,where the input signal frequency obtained through the Fourier transform layer is take as the input of the nonlinear term and the output of the nonlinear term is take as the weight parameter of the PI model.The convolutional network layer is established by using CNN with deep learning ability to extract the characteristic information of input voltage.Through the experiment shows that,in the case of different frequency,accuracy of the proposed method is compared with traditional PI model accuracy is higher.Meanwhile,using untrained data for analysis,the standard error of the proposed model to predict displacement increased for 18.74%to 36.75%,and that the proposed model not only has high precision,but also has strong learning ability and generalization ability.