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

As a precision motion actuator,piezoelectric actuators have the advantages of high displacement resolution,fast frequency response,and small thermal deformation,and are widely used in the fields of micro-nano manufacturing and precision measurement.However,the inherent hysteresis and nonlinearity of piezoelectric actuators seriously affects the positional accuracy of the system.In addition,when the frequency of the input signal increases,the hysteresis curve becomes more complicated and difficult to describe.Therefore,this paper focuses on the piezoelectric micro-motion platform,analyzes the singular hysteresis characteristics of the piezoelectric actuator,establishes the corresponding model and compensator,and aims to solve the dynamic hysteresis problem of the piezoelectric actuator and realize the High-precision trajectory tracking control of the piezoelectric micro-motion platform.The main research contents of the paper are:(1)Aiming at the difficult to describe the singular hysteresis of piezoelectric actuators,a simple and accurate mathematical model is proposed.First,build a data acquisition system for the piezoelectric micro-motion platform to test and study the singular hysteresis characteristics of the piezoelectric actuator.Then,based on the classic Play operator,the rising delay coefficient and the falling delay coefficient are introduced,and the Delay Prandtl-Ishlinskill(DPI)model that can accurately describe the dynamic hysteresis is proposed.The effect of the two delay coefficients on the Delay Play(D-Play)operator is analyzed through simulation.Finally,the Differential Evolution(DE)algorithm is used to identify the unknown parameters of the model,and to compare and verify the performance of the DPI model.Experimental results show that the proposed model can accurately describe the dynamic hysteresis characteristics of piezoelectric actuators.It provides a basis for the next study of dynamic hysteresis compensation.(2)In order to suppress the dynamic hysteresis characteristics of piezoelectric actuators,two feedforward inverse compensators are designed.First,an inverse DPI model based on the Delay Stop(D-Stop)operator is established to design a Direct Inverse(D-I)compensator.Then,aiming at the problem that the DPI model cannot solve the analytical inverse model,the simplified form of DPI model — Time-dependent PrandtlIshlinskill(TPI)model and its inverse solution are deduced,so as to design the Analytical Inverse(A-I)compensator.Finally,the performance of the two compensators is verified through simulation and experiment.Experimental results show that both compensators can effectively suppress the dynamic hysteresis characteristics of piezoelectric actuators,which lays the foundation for the next design of feedback controllers.(3)In order to solve the problem that the parameters of the compensator cannot match the application conditions or the real-time modification of the reference trajectory,a parameter tuning controller is designed.First,establish a comprehensive electromechanical dynamic model of the piezoelectric micro-motion platform,and design a parameter tuning controller that can update the parameters in real time.Then,it is verified by simulation,and the result shows that the parameter tuning controller can realize the real-time modification of the parameters under the high-frequency signal.Finally,the performance of the controller is verified through comparative experiments.Experimental results show that the parameter tuning controller can effectively reduce the impact of dynamic hysteresis and parameter mismatch on positional accuracy,and realize high-precision positioning of the piezoelectric micro-motion platform.