Hysteretic Nonlinearity Modeling And Control Of Micro-positioning Stage Driven By Piezoelectric Actuators

Micro-positioning stage driven by piezoelectric actuators has many advantages,such as low energy consumption,large driving force,high positioning accuracy and fast re-sponse speed.It is widely used in the field of high precision micro-nano processing and manufacturing.However,because of the rate-dependent hysteresis characteristic of piezo-electric actuators,the control accuracy of the system will be seriously reduced,and even the system will be unstable,which limits its application.It is of great significance to study how to eliminate the rate-dependent hysteresis characteristics of piezoelectric actuators.Based on Matlab/Simulink real-time workspace(RTW)and Beijing Advantech's PCI-1710 data acquisition card,a semi-physical experimental platform for rapid control pro-totype was built in the laboratory.The experimental platform was used to realize exper-imental data acquisition and control algorithm verification.The Hammerstein model consists of a linear dynamic module connected by a static nonlinear function in series.The Bouc-Wen model is used in the static non-linear part.Its parameters are identified by particle swarm optimization(PSO).The identification results show that the Bouc-Wen model can well simulate the actual control object in the low frequency band.The linear dynamic part of the Hammerstein model is equivalent to a linear second-order system,whose parameters are obtained by the identification toolbox of matlab.By comparing the simulation results of Hammerstein rate-dependent hysteresis model with the experimental results,it can be seen that the model can well describe the hysteresis characteristics of the actual control object.In order to eliminate the hysteresis of the micro-positioning stage driven by Piezo-electric actuators,this chapter adopts the compound control mode of feedforward and feedback.The feed-forward controller uses the inverse model of Bouc-Wen model.Be-cause the feed-forward control is very sensitive to disturbances and the parameters of the model,it is easy to be affected by disturbances.The H_?feedback controller is designed to suppress these disturbances.The experimental results show that the designed feed-forward and feedback control method can track the reference input signal of any frequencyAnother control strategy for eliminating hysteresis is the hysteresis linearization con-trol object.A hysteresis compensator is constructed to connect the hysteresis compensator in series at the front end of the piezoelectric micro-positioning stage to linearize the control object.The designed hysteresis compensator is the inverse model of Bouc-Wen.The hys-teresis compensator is connected in series at the front end of the control object to linearize the control object.The linearized control object is equivalent to a linear time-invariant second-order system.Considering the inverse compensation error and model error,a s-liding mode control strategy based on disturbance observer is designed.The disturbance observer uses a nonlinear extended state observer,which has higher estimation accuracy than the linear extended state observer.In order to overcome the shortcomings of slow convergence and severe chattering of traditional sliding mode control,a non-singular fast terminal sliding mode surface is adopted,and a fast power reaching law with disturbance compensation is adopted to make the designed controller continuous and non-singular.The experimental results show that the non-singular fast terminal sliding mode control can achieve better tracking effect for reference input signals of single frequency and com-posite frequency than the traditional sliding mode control.