Research On Modeling And Compensation Method For Hysteresis Nonlinear Characteristics Of Piezoelectric Actuator

Piezoelectric ceramic actuator exhibits nonlinear characteristics dominated by hysteresis due to material properties.The Prandtl-Ishlinskii(PI)model is built for feedforward control compensation in tradition phenomenological method,but it cannot achieve sufficiently ideal output results.The dissertation takes piezoelectric ceramic driven nanopositioning stage as the experimental object.Firstly the causes of nonlinear characteristics are analyzed from the perspective of the material itself.Secondly the nonlinear characteristics is compared with the mathematical features of the Play operator,which is the element of PI model,to improve the commonly used classical PI model from different indicators in feedforward control.The dissertation aims to eliminate the influence of the hysteresis and nonlinear characteristics of the piezoelectric ceramic driver,and improve the control accuracy of the nanopositioning stage.The main research of the dissertation are as follows:(1)The reasons for the nonlinear characteristics of piezoelectric ceramics are studied from the micro-polarization mechanism,and the formula for the deformation speed is deduced,as well as a reasonable conclusion made for the three major nonlinear causes of inverse piezoelectric effect,ferroelectric effect and electrostrictive effect.The relationship between crystal polarization and displacement is explained,and the Physical Nonlinear Characteristics(PNC)model is established.This model determines the main source of nonlinear characteristics,namely hysteresis characteristics,and proposes a multi-stage model establishing method for solution.On this basis,according to its nonlinear characteristics,a three-stage PI model is used to model the hysteresis loop,which verifies the general law of deformation rate derived.The compensation control experiment proved that the three-stage PI inverse model compensation greatly reduces the error of the classical PI inverse model.(2)The segmented modeling method for describing piezoelectric nonlinear characteristics is improved.In view of the significantly different hysteresis characteristics of the two stages of boost phase and back phase,the concept of hysteresis tangent slope for segmentation is proposed.The experimental data is collected by processing the characteristics,and the value jumping points are found as the basis for the analysis: segment marker points.Therefore,the complex hysteresis characteristics of multiple loops can be modeled based on reasonable segmentation using segment marker points,and be reconstructed into a complete Mark Segmented PI(MSPI)model.The inverse model compensation control experiment proves that the total compensation accuracy of the MSPI model can achieve the same results as the threestage PI compensation control.Moreover,it solves the high error problem in the inner loop modeling of the classical PI model.(3)The segmented modeling method is improved continuously.In a more level-loop hysteresis characteristics,the multi-use of segmentation methods produces lower connectivity and a larger amount of redundant modeling,which apparently affects the efficiency of the modeling algorithm and causes unequal modeling errors between inner loops of different levels.By analyzing the hysteresis characteristics and symmetry of the Play operator that constitutes the PI model,a Separated Level-loop PI(SLPI)model is proposed,which uses an inner-loop separation logic algorithm to combine complex nonlinear features.The algorithm decomposes into multiple single-loop hysteresis characteristics,simplifies the complex hysteresis feature,and obtains its vertexes and level information,and then uses the PI model to independently model the hysteresis characteristics of each single loop,and reconstructs each segment to complete the inverse model.The feedforward compensation control experiment proved that the SLPI inverse model can improve the compensation accuracy of complex hysteresis characteristics,and reduce the compensation accuracy difference between each hysteresis single loop.(4)A real-time compensation control method is proposed in the way of calling the modeling library on demand.In the past,the feedforward control methods are often used in the control of disturbance-known system,and cannot compensate the real-time requirement as feedback control closed loop.Therefore,it is necessary to collect the outer loop characteristic and the creep characteristics of the piezoelectric actuator,and establish a hysteresis modeling library that can represent all real-time compensation possibilities after resolution segmentation.Based on the hysteresis characteristic law provided by the Madelung principle,the corresponding feature modeling is called in the modeling library to complete the real-time feedforward compensation control.The proposed method enables feedforward control to apply real-time compensation,retains the advantages of simple and effective feedforward control,and avoids problems such as response in feedback control.The dissertation mainly proposes the modeling method of hysteresis nonlinear characteristics of piezoelectric actuators based on feedforward control compensation.It proves that the segmented model is a simple and effective strategy to improve the modeling accuracy.Corresponding to different accuracy requirements,different segmented methods can be used to improve the feedforward control results.The dissertation also includes the necessary steps for designing and processing precision mechanical equipment,as well as setting up an experimental verification stage,and identifying model parameters using algorithms such as secondary programming.