Research On Hysteresis Compensation And Motion Control Of Piezoelectric Nanopositioners

The high-precision piezoelectric micro-motion platform is widely used in advanced manufacturing and processing,biotechnology,medical engineering and automation technology,nanometer measurement and other micro-nano technologies,which plays a vital role in ultraprecision processing,micro-operation and testing.The piezoelectric micro-motion platforms are most designed on the basis of piezoelectric ceramics actuators and flexure hinge mechanism.However,the inherent hysteresis and creep phenomena of the piezoelectric actuator and the vibration caused by the light damping characteristic of the flexible hinge mechanism affect the output positioning accuracy significantly.In addition,in the multi-dimensional motion,the cross-coupling and synchronization between the axes also reduce the accuracy of contour tracking.Therefore,based on the flexure-hinge piezoelectric micro-motion platform,this dissertation focus on two issues: hysteresis nonlinear compensation and motion control,and various control strategies,including hysteresis feedforward compensation,disturbance suppression,cross-coupling suppression and synchronization,are studied and designed.For the hysteresis nonlinear compensation,feedforward control based on the hysteresis model is a direct and effective method,but the accuracy of the hysteresis model directly affects the compensation effect.Therefore,an improved BW model is propesed to improve the modeling accuracy of static hysteresis.The nonlinear hysteresis component is decomposed from the static hysteresis curve of the piezoelectric micro-motion platform.The hysteresis loop is asymmetric and its maximum and minimum points have the same changing trend as the input signal speed.The proposed model combines the BW model with the asymmetric component and the cubic polynomial of the input signal velocity,which greatly improves the modeling accuracy,especially at the maximum and minimum points.Based on the established model,a feedforward hysteresis compensator is designed to realize the quasi-static hysteresis nonlinear compensation by using open-loop control.When it comes to reference signals with large strokes and frequencies,the hysteresis is rate-dependent,and the feedforward compensation based on the static hysteresis model cannot meet the requirements of precise tracking.Considering the coupling of rate-dependent hysteresis and dynamic characteristics of the flexure hinge transmission mechanism,a cascaded model is adopted to describe the piezoelectric system,consisting of a rate-independent P-I operator hysteresis sub-model and linear dynamics sub-model.The hysteresis compensator based on the inverse multiplication structure and model predictive feedback tracking controller are designed respectively,and the integral term is introduced to improve the steadystate tracking accuracy.Without the complicated rate-dependent hysteresis modeling,this control strategy has a simple structure and is easy to be applied in practice.The tracking tests of multiple reference trajectories show that the platform with this control method realizes the precise motion under the influence of dynamic hysteresis.Besides,in order to maintain the motion accuracy under the influence of external interference,a robust model predictive controller based on disturbance compensation is proposed.By treating the external interference,hysteresis and model uncertainty as the total disturbance,the DOB is designed based on the nominal model to remove the it.Then,inspired by UDE,the residual disturbance is calculated and used to correct the reference trajectory in real time,and the feedback control adopts the model predictive control with integral term.This method has strong robustness to unknown interference and can also compensate for hysteresis.Tracking results of multiple reference trajectories under 0-150 g variable load demonstrate the proposed controller has stable tracking performance,and the root mean square error of tracking reference signals within 50 ?m and below 20 Hz is below 0.8 ?m.Finally,in order to ensure the accuracy of contour tracking in multi-dimensional motion,a synchronous multiple-input multiple-output model predictive control method is proposed.The coupling dynamic model is established and the multi-input multi-output model predictive control is used to deal with the influence of cross-coupling.Based on the expression in position domain,the synchronization error is calculated and introduced into the cost function to improve the synchronization performance.In addition,for commonly used periodic scanning signals,repeated control is designed to suppress periodic errors.The proposed control strategy ensures the synchronization to improve the accuracy of contour tracking,and the tracking results of circular,spiral,and Lissa two-dimensional contour signals verify its satisfied tracking performance.This dissertation proposes corresponding control methods to deal with hysteresis compensation,disturbance suppression,cross-coupling suppression and synchronization.The researches in this thesis have reference significance for the development and practical application of precision motion systems.