Hysteresis Dynamic Modeling And Control Method For Piezo-driven Micro-positioning Stage

The arrival of the microscopic nanometer era promotes the rapid development of the nano-driven positioning technology.The piezo-driven micro-positioning stage is composed of the piezoelectric ceramic actuator,which is widely used in nanoscale positioning fields because of its micro-nanoscale displacement resolution and fast frequency response.However,the inside piezoelectric material of the piezo-driven micro-positioning stage will be accompanied by complex hysteresis effect during the polarization process.As a result,the positioning accuracy of the stage is greatly reduced and the positioning performance is seriously damaged,which ultimately limits its application in the nanometer precision drive system.In this thesis,the piezo-driven micro-positioning stage is taken as the research object,whose internal hysteresis nonlinearity is deeply studied.The purpose is to describe the hysteresis characteristic accurately and eliminate the effect of hysteresis effectively,furthermore,to achieve high-precision drive positioning control of the stage and extend its application foreground.The main research content of the thesis is as follows:Considering that the change of the input direction of Duhem differential equation will affect its output characteristic and cause the difficulty of parameter identification,a Duhem static model based on the interior point algorithm is proposed to characterize the static hysteresis characteristic of the piezo-driven micro-positioning stage by introducing a linear part.To further describe the dynamic hysteresis characteristic of the stage,the diagonal recurrent neural network and the Duhem static model are connected in series to establish an online Duhem dynamic model based on the gradient descent algorithm.The results of comparative modeling experiments under different driving signals verify the effectiveness of the Duhem dynamic model.In order to eliminate the complex hysteresis nonlinearity of the piezo-driven micro-positioning stage,the open-loop inverse compensation control method is designed based on the corresponding hysteresis model.Due to the separate hysteretic structure of the Duhem static model,a static feedforward inverse compensation controller based on the inverse multiplication structure is proposed through direct inverse derivation to compensate the static hysteresis of the stage effectively.Combined with the idea of the inverse control and based on the Duhem dynamic model,a dynamic feedback inverse compensation controller with online parameter adjustment is propsed to improve the robustness and self-adaptive ability of the control system and solve the problem of high-frequency trajectory tracking control.The convergence of the dynamic inverse compensation controller is analyzed by the Lyapunov stability theorem,and the availability of the dynamic inverse compensation controller is verified by comparative tracking experiments under different trajectory signals.In view of the problem that the performance of the open-loop inverse compensation controller is affected by the accuracy of the hysteresis inverse model and external perturbation,an equivalent sliding mode closed-loop control strategy with perturbation estimator is proposed without hysteresis inverse model.Taking the unmodeled dynamic,parameter uncertainty and external perturbation of the stage system into account,a perturbation estimator is introduced into the design of the controller.To reduce the steady-state error and speed up the response,the equivalent control term and the low pass filter-based robust term are designed by using the proportional integral sliding surface switching function,realizing the chatter-free sliding mode control for the complex hysteresis of the stage system.The stability of the control system is strictly proved by the Lyapunov stability theorem.The results of repeated positioning experiments of different trajectory signals certificate that the sliding mode controller is effective and chatter-free,and has better control accuracy than the dynamic feedback inverse compensation controller.The comparison experimental results between no-load and on-load under different trajectory signals show that the sliding mode controller has loading capability and can ensure stable tracking performance of control system.