Study On Modeling And Control Of The Nonlinearity Of Piezoelectric Actuator

With the development of modern industry and precision manufacturing,researches inmore and more fields step into the stage of miniaturization.Micro/nano machining and positioning technology is a type of key technology in modern scientific research and industrial technology.Piezoelectric ceramics,with advantages of fast response,good dynamic performance,nanoscale resolution and susceptible to electromagnetic interference,is widely implemented in various fields for nano-scale processing and positioning.However,problems still exist,the nonlinear characteristics of the piezoacuator,such as hysteresis and creep can cause serious interference and influence to the system performance and positioning precision,which will limit its application.This thesis conductesstudies on modeling and solving intrinsicnolinearproblems of the piezoelectric actuator for precisely driving the nanopositioning stage designed in the project"Research on high precision positioning table and the key techniques of its measurement and control system",which is partially supported by "Science and Technology Foundation Project of Shenyang(No.F13-316-1-74)".First of all,we conduct comprehensive theoretical analysis,experimental measurements and mechanical principle summary of the hysteresis,creep and temperature characteristics of the piezoelectric actuator,which providnecessary basis for the modeling and control of those nonlinear characteristics.Secondly,to eliminate the bad effect,which the piezoelectric hysteresis brings to the system,this thesis studies the classical Prandtl-Ishlinskii model.Since the classical Prandtl-Ishlinskii model is not suitable for asymmetric hysteresis representing,we improve the Prandtl-Ishlinskii model by replacing the traditional play operatorwith the ladder operator,and complete its adaptive online identification by using the LMS algorithm,which is able to complete the identification of piezoelectric hysteresis curve better.However,the improved PI model is still found cannot representminor hysteresis loopswell,additionaly,its inverse is hard to be built.Therefore,this thesisgoes ahead to study the classical Preisach model,since it is one type universal hysteresis model.Based on its discrete model,we propose a type of improved Preisach model based on the erasure feature by using BP neural network,and complete the adaptive online identification of its inverse model.This model avoids the acumulated error of the traditional discrete Preisach model and the complexity of inversebuilding,which is practical and easy to understand.Thirdly,in order to reduce the creep effect of piezoelectricactuators,this thesisstudies the creep's logarithm model and operator superposition model under the open-loop condition.By comparing the models,a better basic operator superposition model is chosen and the model's parameters areestimated using RWLS algorithm.Laplace transform is proposed to establish the inverse creep model.The designed inverse creep model is cascaded to the front of the improved Preisach adaptive inverse model to compensate the creep effect.Experimental results show that the creep is greatly reduced.Then,this thesis studies many different control schemes for regulating piezoelectric actuator hysteresis,creep nonlinearity.A piezoelectric actuator test system is utilized to conduct experiments for comparing performances of different cotrolschemes.By comparing the tracking results and tracking errors of different schemes,finally the improved Preisach adaptive inverse model feedforward control based PID feedback control scheme is proposed.This scheme can greatly eliminate hysteresis,creep and influences brought by exogenous distrubances.Finally,for regulating a piezoelectric actuator driven nanopositioning stage,a control scheme is studied.Simulations ofdifferent signals' tracking tests for the stage's mechanical part and the entireintegrated system are carried outusing ADAMS and MATLAB.Experiments on the nanopositioning stage have been conducted and the results confirm the effectiveness of the proposed improved Preisach adaptive inverse model feedforward control based PID feedback control scheme.