Modeling And Control Methods For 2-DOF Nanopositioning Systems Based On Piezoelectric Actuators

With the rapid development of nanomaterials and high-precision positioning,high precision positioning technology based on piezoelectric actuators is widely used in many fields.However,the non-linear characteristics of piezoelectric actuators can seriously affect their accuracy in tracking and positioning,with the most significant impact being the hysteresis characteristics,and the coupling effect exhibited by the two-dimensional piezoelectric actuated micro and nano positioning platform,which also has a serious impact on the platform output accuracy and increases the difficulty of platform control.In this paper,a high-precision hysteresis model is developed to compensate for the hysteresis characteristics and to design an effective control strategy for a two-dimensional piezo-actuated micro-and nano-positioning platform.In this paper,a fractional-order Duhem model(FODuhem)is proposed to describe the rate-dependent hysteresis nonlinearity of piezoelectric actuators.The fractional order operator is introduced on the basis of the conventional Duhem model and a differential evolutionary algorithm is used to identify the parameters of the fractional order Duhem model.Finally,the experimental results clearly show that the fractional-order Duhem model can better describe the rate-dependent hysteresis non-linearity of the piezoelectric actuator than the conventional Duhem model.In this paper,an open-loop control method based on fractional-order Duhem inverse model compensation is firstly proposed.Since the open-loop control compensation method is sensitive to external disturbances,an integral-type sliding-mode control method is proposed as a feedback controller to form a closed-loop control system based on fractional-order Duhem inverse model compensation.Finally,the stability of the control system is proved by Liapunov’s stability criterion,and then the proposed closed-loop control method is experimentally verified on a piezoelectric actuated micro and nano positioning platform.In this paper,an adaptive backstepping control method is proposed to solve the problem of inaccurate positioning of a two-dimensional piezoelectric-actuated micro and nano-positioning platform due to the coupling effect.