Control Of Piezo-driven Nanopositioning Stag With Hysteresis Compensation

With the advantages of small size,fast response and high driving force,piezo-driven nanopositioning system has been used in many fields,such as microelectronics and ultra precision machining.Due to the hysteresis nonlinearity of the piezoelectric ceramics,the precision and stability of the nanopositioning system are seriously affected.Therefore,the processing and controlling methods for the hysteresis nonlinearity system are one of the critical problems to be solved in the application of the nanopositioning system.Taking the piezo-driven nanopositioning system as the controlled plant,this paper studies high precision control methods for hysteresis nonlinear systems based on the active disturbance rejection control(ADRC).By improved ADRC method,the performance of disturbance rejection is improved and the effective hysteresis compensation is achieved,satisfying the requirement of high positioning precision.The main research contents are listed as follows.Firstly,for the piezo-driven nanopositioning system,the phenomena of hysteresis are revealed and the characteristics are analyzed through the experiment method.The causes and the forms of nonlinearity such as hysteresis and creep properties are analyzed through experiments.The series dynamic model is proposed to characterize the dynamic behaviors of the system,and the parameters of linear system are obtained by dynamic identification,providing a foundation for controller design.Secondly,a robust guaranteed cost design method of ADRC is proposed.An integral action is added in the framework of ADRC to describe integral of error quantificationally.A robust stability condition of closed-loop is presented according to Lyapunov stability theory,and a quadratic cost index where the tracking error is appearing explicitly is used for ADRC performance assessment.The cost bound is optimised to obtain controller parameters to avoid trial and error in tuning,improving the control performance in presence of multifarious uncertainties without increasing the difficulty of controller design.The good disturbance rejection performance is demonstrated through the simulations and experiments.Then,a compound ADRC based on the differential-estimation of the extended state observer(ESO)is proposed.Based on the principle of DOB that disturbance observation is observed by the inverse nominal model,combing with the idea of regarding the series integral system as the standard plant while the rest as disturbance in ADRC,a differential-estimation method by ESO for system output is developed in order to establish the inverse model of a series integral system.The disturbance observation method based on ESO differential-estimation is designed to achieve a more accurate disturbance observation.Furtherly,the compound ADRC based on ESO differential estimation is proposed,which is implemented in the piezo-driven nanopositioning system.The experiment results show that the compound ADRC effectively improves the dynamic and disturbance rejection performance of ADRC.Finally,a repetitive control method for periodic disturbance is proposed for the application requirement for periodic scanning.The improved ADRC is transformed into a two-degree-of-freedom structure,and is inserted by a repetitive controller.The closed loop stability conditions are obtained by the small gain theorem,and the parameter of the repetitive controller satisfying the stability conditions is obtained according to the separation principle.The experiment is carried out for the piezo-driven nanopositioning system,which exhibits good control performance for the periodic signal.