Dynamic Modeling For Cross-coupling Hysteresis Effect Of Multi-axis Piezoelectric Actuated Stages

These years have witnessed the tremendous development of nano-positioning systems widely used in modern nanometer measurement and manufacturing equipments,e.g.scanning tunneling microscopes(STMs),atomic force microscopes(AFMs)and micro-robot arm,etc.The piezoelectric motor shows the great superiorities in micro/nano positioning field due to its converse piezoelectric effect.However,the piezoelectric ceramic suffers from complex nonlinear effects such as hysteresis and creep,which have the adverse effect on the positioning precision of the stage,and the cross-coupling occurs while the two axis of the multi-axis piezoelectric actuated stage are moving together,meanwhile,the vibration deforms the outputs of the piezoelectric actuator at the high frequencies.Thus,it is an urgent challenging task to develop an effective modeling method to approximate the nonlinear dynamic of the hysteresis and spatial/temporal cross-coupling of the piezoelectric actuated stages.To fulfill such a task,in this thesis,we have proposed a traditional Hammerstein modeling to approximate the hysteresis nonlinearity of the single axis piezoelectric actuated stage,which is cascaded a static nonlinear block with a dynamic linear model.Afterwards,the effectiveness of the method is verified through a plenty of experiments.Meanwhile,the wildly used Bouc-Wen and Preach models are conducted to make a comparison with the proposed approach,which shows the superiorities of the Hammerstein model in a further step.Subsequently,we have developed a pure data-driven distributed multi-channel Hammerstein model to identify the X-Y cross-coupling hysteresis of a piezoelectric actuated stage.The present model is a cascade connection of a static nonlinear block and a dynamic spatial/temporal linear block.Therein,orthonormal functional series and polynomials are used as the basis series functions of the linear and nonlinear blocks,respectively.By feeding a periodical exciting signal to the Y-axis,the spatial/temporal data is gathered at different X-Y axes contacting positions.Accordingly,a multi-channel identification scheme is derived to guarantee high modeling precision without any prior-knowledge about the mid-output.Afterwards,matrix spectrum analysis is used to prove the convergence of the proposed Hammerstein modeling method.Finally,the Hammerstein modeling results based on experimental data are provided to verify the effectiveness and superiority of the model.