Data-driven Control Method With An Observer For Piezoelectric Micro-positioning Stage

The piezoelectric micro-positioning control system is widely used in various fields,such as large-scale integrated circuit manufacturing,aerospace equipment,laser communication,and semiconductor technology,due to its miniaturization,strong driving force,high resolution,and fast response speed.However,piezoelectric micro-positioning stage has complex mechanical structure and nonlinear characteristics,multi-parameter coupling,and is very sensitive to the disturbance such as noise.It is difficult to establish an accurate mechanism or mathematical model,even if the established model can accurately describe the complex nonlinear behavior of the stage.And the uncertainty of the model parameters and disturbance severely affect the control performance of the system,such as positioning accuracy and response speed.In order to avoid creating this sort of problem,this paper takes the piezoelectric micro-positioning stage as the research object,and aims to design the data-driven control(DDC)strategy that does not depend on the precise mechanism or mathematical model information of the controlled plant to achieve high-precision trajectory tracking control of piezoelectric micro-positioning stage.Firstly,the experimental setup of piezoelectric micro-positioning stage control system is constructed,and its components and working process are introduced.And the input and output characteristics of stage are studied.The open-loop test results of piezoelectric micro-positioning stage show that there is an obvious and complex nonlinearity between the input voltage signal and the output displacement signal of the stage.It is difficult to obtain the physical parameters of the control system,which makes it difficult to obtain an accurate mathematical model of the system by methods such as mechanistic analysis.Therefore,the control method that does not depend on the accurate model information of the controlled plant,and only uses the input and output measurement data of the system is studied to achieve high-precision control for the stage.The control performance of data-driven control methods for piezoelectric micro-positioning stage based on different dynamic linearization is studied.The theoretical analysis and comparison experiments verify the applicability and superiority of the DDC method based on full form dynamic linearization(FFDL).In order to suppress or eliminate the adverse effects of the disturbance on the performance of the control system,piezoelectric micro-positioning stage is described as the nonaffine nonlinear discrete-time system considering the disturbance.The discrete-time extended state-like observer(DESLO)is designed to observe and compensate for unknown disturbance in the system based on the discrete-time extended state observer(DESO)and the deviation control principle,and then the observed value is introduced into the DDC algorithm based on FFDL to design a DESLO-based DDC method,and the convergence of the designed controller is proved by the principle of contraction mapping.In order to verify the feasibility of the proposed control method,the proposed control method is applied to the stage under different types of desired signals,and comparative experimental results show that the proposed control method can achieve greater control for piezoelectric micro-positioning stage and has strong rejection ability to the disturbance,which further improves the control performance of the system and effectively improves the trajectory tracking effect of the stage.Finally,hysteresis nonlinearity is one of the most obvious nonlinear characteristics of piezoelectric micro-positioning stage.In order to avoid the influence of inherent hysteresis nonlinearity of piezoelectric micro-positioning stage on the control accuracy of the system,the play operator is introduced as the exogenous variable function to describe the hysteresis nonlinearity characteristics.The system is equivalent to a dynamic linearization data model with some play operators.A DDC controller based on hysteresis observer is designed,and the Lyapunov theory is used to prove the stability of the designed controller.The proposed method gives physical meaning to some pseudo partial derivative(PPD)of the data model,and it can effectively reduce the complexity of PPD and the estimation complexity of control parameters.By comparing the experimental results,it can be seen that the designed controller effectively improves the dynamic performance of the system while ensuring the steady-state performance,which further demonstrates the effectiveness of the proposed controller.