Research On Hysteresis Modeling And Compensation Method Of Piezoelectric Micro-motion Platform

Piezoelectric actuators have the advantages of high stiffness,fast frequency response,high displacement resolution,etc.It is an ideal actuator in the field of precision positioning and has been successfully applied in micro-nano-scale measurement,MEMS,biomedical engineering and other fields.However,there is a complex hysteresis nonlinearity between the input and output of the piezoelectric actuator,which will reduce the accuracy of the system and affect its stability.In this paper,the piezoelectric micro-motion platform is taken as the research object,and the hysteresis nonlinearity of the piezoelectric actuator is taken as the entry point.The modeling method of hysteresis nonlinearity and the corresponding compensation method are deeply studied to suppress and eliminate the influence of hysteresis nonlinearity on the accuracy of piezoelectric actuator,and realize the precise positioning and position tracking of the micro-motion platform.The main contents of this paper are as follows:(1)Research on hysteresis modeling methods.Firstly,a rate dependent PMPI model(Polynomial Modified Prandtl-Ishlinskii,PMPI)is proposed,which can describe both the static and dynamic hysteresis characteristics,and the symmetric and asymmetric hysteresis characteristics,Then the essential wiping-out and congruency properties of the proposed model are proved by an example and mathematical derivation.Secondly,the experimental system of the piezoelectric micro-motion platform is built,and the hybrid algorithm(NM-DE algorithm)combined with the differential evolution algorithm and the simplex method is used to identify the model parameters.The experimental results show that after the feedforward inverse compensation of the rate-dependent PMPI model,the tracking error is reduced by nearly an order of magnitude compared with no control.(2)Research on feedforward inverse compensation method based on hysteresis model.Based on the PMPI model,three inverse model compensator construction methods are proposed:direct inverse(D-I),integral inverse(I-I)and iterative inverse(I-M).Through the performance comparison of the three kinds of inverse compensators by simulation,the best inverse compensators with the best comprehensive performance are selected and verified by the experiment platform.The experimental results show that after the feedforward inverse compensation of the rate-dependent PMPI model,the tracking error is reduced by nearly an order of magnitude compared with no control.(3)Design a robust adaptive controller for piezoelectric micro-motion platforms.Firstly,the dynamics modeling of the piezoelectric micro-motion platform,namely the hysteretic nonlinear-linear dynamic system series structure model.Then the parameters of the nonlinear and linear links of the dynamic model are separately identified.Secondly,combined with the advantages of feedforward control,sliding mode control and adaptive control,a robust adaptive control algorithm with disturbance estimation is proposed.The global stability of the closed-loop system is analyzed by Laypunov function.Finally,the experimental results show that the proposed robust adaptive controller can effectively reduce the influence of hysteresis nonlinearity and system uncertainty on the platform control,and achieve fast nano-precision motion control of the micro-motion platform.