Data-driven Adaptive Control Method For Piezoelectric Micro-nano Positioning Systems

By the principle of the inverse piezoelectric effect,piezoelectric micro-nano positioning systems constructed of piezoelectric materials can produce micro-nano displacement under the voltage signal,which have characteristics of fast response and miniaturization.The performance of piezoelectric micro-nano positioning systems is not easily affected by changes in temperature and magnetic field,such that they are more and more widely applied to the advanced manufacturing industry.Based on two piezoelectric micro-nano positioning systems,namely the piezo-actuated stage and the piezoelectric linear motor,as the research objects,this study aims to meet the demand of high precision positioning control and design controllers to reduce or eliminate the influence of complex hysteresis on the positioning accuracy of the controlled systems.This provides the theoretical and experimental basis for the further application of piezoelectric micro-nano positioning systems in the field of advanced manufacturing.The main research content of this thesis is as follows:Firstly,the experimental platform of a piezo-actuated stage and that of a piezoelectric linear motor are built,respectively,and their working principles are introduced.Considering that the displacement of piezoelectric micro-nano positioning systems is sensitively affected by the amplitude and frequency of voltage signals,the two experimental platforms are driven by a series of voltage signals with different amplitudes and frequencies,the open-loop characteristics of which are analyzed,respectively.The amplitude correlation and rate correlation in the hysteresis of the experimental platforms are discussed by observing their input-output curves.The necessity of designing data-driven adaptive control(DDAC)methods for the piezoactuated stage and the piezoelectric linear motor is illustrated.It provides an important experimental basis for the selection and design of controllers for the piezoelectric micro-nano positioning system.Due to the complex hysteresis of the piezo-actuated stage,it often takes a complicated structure and cumbersome modeling process to build an accurate offline model of the piezo-actuated stage.And the performance of the offline model-based control methods highly depends on the precision of the offline model.To address the above issue,a neural network-based DDAC is proposed in this study.The piezoactuated stage is described as an equivalent compact format dynamic linearization(CFDL)prediction model under the Lipschitz condition using the measurable input and output data of the controlled system.Then,a model-free adaptive predictive controller(MFAPC)is established by the weighting optimal algorithm.Next,a neural network is adopted to estimate the dynamic pseudo-partial derivatives of the prediction model,such that the unknown parameters of the controller can be adjusted online.The key factors that give the proposed controllers advantages over the classical MFAPC are the neural network,improving the adaptive performance of the controller.The tracking performance,disturbance rejection behavior and robustness of the proposed control method are demonstrated via tracking control experiments.The CFDL model has a simple structure,but the complex nonlinear of the piezoactuated stage is represented by the pseudo-partial derivative of the compact format dynamic linearization model.To obtain the ideal control effect,adjusting the adaptive parameters of the CFDL model-based DDAC online will cause a great computational burden.In addition,the above control method may lead to low precision or even instability of the closed-loop control system,because some states that are not contained in the CFDL model may affect the performance of the system.To solve this problem,an estimator-based DDAC is proposed for the piezo-actuated stage.First,the piezoactuated stage is described as a non-affine nonlinear discrete system with a hysteresis input.Then,a DDAC is designed based on an equivalent model established via the dynamic linearization technique.To adjust the adaptive parameters of the proposed controller online,a Hopfield neural network(HNN)-based estimator is proposed,which can not only update the adaptive parameters of the controller but also estimate the output of the piezo-actuated stage to ensure the validity of the controller’s parameters.Stability analysis and experimental results verifiy the effectiveness of the proposed control method for the piezo-actuated stage.The above two control methods are designed in the circumstances that the controlled system meets the generalized Lipschitz condition.Although this condition is a common restriction assumption for many systems to design the controller,it is usually an ideal state for the actual system to satisfy the generalized Lipschitz condition.Therefore,to address this issue,a direct DDAC method is designed in this study.First,a modular model consisting of a linear sub-model,hysteresis sub-model,and lumped uncertainties is established to describe the piezo-actuated stage,where the adaptive parameters of this model are identified by an HNN estimator online.To realize the highprecision tracking control of the piezo-actuated stage,a direct adaptive controller is designed using a time delay recursive neural network(TDRNN).The stability of this method is studied.Furthermore,the performance of the above three control methods proposed for the piezo-actuated stage in this study is analyzed according to the experimental results,and the application of these methods for tracking control of the piezo-actuated stage is discussed and summarized.Finally,to achieve precise motion control for a piezoelectric linear motor,a corrective control-based composite adaptive control method is proposed.In this study,a corrective controller is employed based on the dynamic linear sub-model of the piezoelectric linear motor to improve its dynamic and static characteristics.Then,to avoid the influence of unmodeled dynamics,such as inherent nonlinearity and external vibration,a composite adaptive control consisting of a model-free adaptive controller(MFAC)and a low-pass filter is established,where the demand for precision tracking control can be realized without establishing the overall model of the piezoelectric linear motor.The low-pass filter is adopted to eliminate high-frequency measurement noise in the system,thus improving the transient response of the classical MFAC method.In addition,theoretical analysis and experimental results show that the corrective controlbased composite adaptive control method exhibits the good performance of the piezoelectric linear motor to realize point-to-point positioning and third-order S-curve tracking,which indicates that the proposed controller is suitable for engineering applications.