Modeling And Control Of Micro-nano Positioning Platform Based On Piezoelectric Ceramic Actuator

Micro-nano positioning system based on piezoelectric ceramic actuator has the advantages of low energy consumption,fast response speed and no friction,and can achieve micro-nano level positioning accuracy,so it is widely used in various precision manufacturing and micro-nano positioning technology and other fields.However,the nonlinear characteristics such as hysteresis and creep in the nature of the positioning system will directly affect the performance of the piezoelectric driven positioning system,reduce its control precision,and even lead to the instability of the whole system in serious cases.Therefore,how to accurately establish the mathematical model and compensate the positioning system based on the characteristics of the piezoelectric driving positioning system has become a hot issue in the research of modern precision positioning technology.To solve the above problems,a nonlinear mathematical model combining the nonlinear characteristics of hysteresis and creep with the linear characteristics of mechanical dynamics is proposed in this paper,and an adaptive inverse model compensation control is designed for the positioning system.The main research contents are as follows.(1)The main characteristics of the piezoelectric driven positioning system are analyzed,and the characteristics of nonlinear characteristics such as hysteresis and creep as well as the nature of mechanical and dynamic characteristics are elaborated in detail.The basic structure of the positioning system used in this study is also given.(2)According to the theoretical analysis of the piezoelectric driven positioning system,a nonlinear mathematical model is proposed,which combines the nonlinear characteristics such as hysteresis and creep and the linear characteristics of mechanical dynamics.The coupling model is a series combination of the classical Hammerstein structural model and the fractional operator model.Among them,the Hammerstein structural model is generally composed of two sub-modules.The first static nonlinear sub-module in the Hammerstein structural model in this paper uses the classical P-I model to describe the hysteretic nonlinear characteristics of the piezoelectric driven positioning system.The second dynamic linear submodule uses the second order transfer function to represent the mechanical and dynamic characteristics of the piezoelectric driven positioning system.Then,based on Hammerstein structural model,the fractional operator model is series,which mainly represents the creep nonlinear characteristics of the piezoelectric actuated positioning system.Finally,an experimental platform was built to verify the accuracy of the proposed coupling model.Under the action of sinusoidal signal of 1-100 Hz,compared with Hammerstein model,the root mean square error of the coupling model proposed in this paper is reduced by 27%-61%from 0.1195?m to 0.4610?m.The relative error is reduced from 2.12%-4.79% to 1.16%-2%,which indicates that the designed coupling model can better describe the characteristics of the piezoelectric driven positioning system.(3)The adaptive inverse model compensation based on the on-line adjustment of LMS algorithm was applied to the control of the hysteresis nonlinear characteristics of the piezoelectric actuated positioning system.The creep nonlinear characteristics were linear compensated by the inverse of the fractional creep model,and the dynamic adjustment control of the positioning system was carried out by the incremental PID control algorithm.In the simulation experiment,compared with the traditional PID control and the inverse model compensation compound control,The data show that the root mean square error is reduced by 30%-60% and the relative error is reduced by 0.1%-2.5% under the action of sinusoidal input,the effectiveness of the incremental PID control and the adaptive inverse model compensation compound control designed in this paper is verified.