Modeling And Control Of High-precision Micro-displacement Piezoelectric Positioning Platform

With the rapid development of modern ultra-precision machining and precision manufacturing technology,micro/nano drive control technology is widely used in many fields such as micro positioning and microelectronics.Among them,the micro positioning platform with piezoelectric ceramic material as driving element has many advantages,such as low power consumption,fast response,large output force,etc.,but in practical application,the positioning accuracy and control accuracy of the positioning platform by piezoelectric ceramic become poor due to the hysteresis nonlinear phenomenon.Therefore,in order to eliminate the influence of hysteresis nonlinearity on the positioning accuracy and control accuracy of the piezoelectric micro positioning platform,and achieve high-precision control,this paper takes the piezoelectric micro positioning platform as the research object,and carries out two aspects of research,including the establishment of high-precision hysteresis model and the design of controllerThe hysteresis nonlinearity in the whole working range of piezoelectric ceramics often leads to the decrease of the system precision,the oscillation,and even the instability of the system.For periodic sinusoidal input signals,Improved hysteretic modeling method for enhanced prandtl-ishlinskii model(EPIM).Firstly,based on the analysis of the piezoelectric characteristics and the characteristics of the traditional prandtl-ishlinskii model,an improved enhanced prandtl-ishlinskii model was used to describe the hysteresis characteristics of piezoelectric ceramics,the experimental platform of piezoelectric micro-displacement positioning based on dSpace was built.Finally,based on the enhanced prandtl-ishlinskii model method,the hysteresis nonlinear characteristics of piezoelectric ceramics were identified in the piezoelectric driven micro-displacement positioning platform.Experimental results show that in low frequency band,the root mean square error of the traditional prandtl-ishlinskii hysteresis model and the enhanced prandtl-ishlinskii hysteresis model is not much different.As the input signal frequency increases,the advantages of the enhanced prandtl-ishlinskii hysteresis model become more and more obvious.When the input signal frequency is 50Hz,the RMSE accuracy of the enhanced prandtl-ishlinskii hysteresis model is 13.47%higher than that of the prandtl-ishlinskii hysteresis model.When the input signal frequency is 150Hz,the RMSE accuracy of the enhanced prandtl-ishlinskii hysteresis model is 27.09%higher than that of the prandtl-ishlinskii hysteresis model.It is proved that the enhanced prandtl-ishlinskii hysteresis model has greater advantages in describing hysteresis characteristics than the traditional prandtl-ishlinskii hysteresis model.A parameter identification method for the hysteresis nonlinear system of piezoelectric platform is proposed.First,through the enhanced prandtl-ishliskii model direct inverse model modeling method,the hysteresis inverse model feedforward controller for piezoelectric ceramics is constructed.Then,the linear identification of the piezoelectric platform system compensated by the feedforward controller is carried out:After the constructed inverse model is concatenated in front of the controlled object for feedforward inverse compensation,the input voltage of the piezoelectric platform system with a small value is linearly identified.Finally,the experiment proves that the inverse model constructed by the identification results can significantly improve the input and output linearity of the piezoelectric positioning platform.In terms of hysteresis compensation control,two control experiments of feedforward controller and PID controller based on the enhanced prandtl-ishliskii hysteresis inverse model were set.Displacement tracking experiments are carried out on two reference displacements of sine wave and triangular wave of the same frequency.Experimental results show that the feedforward controller can further improve the displacement tracking accuracy than the PID controller,meanwhile,the feasibility and effectiveness of the hysteresis compensation control method for the enhanced prandtl-ishliskii model are verified.Due to the poor anti-interference capability of open loop feed-forward controller,the inverse model modeling error cannot be eliminated.In this paper,propose two feedback control schemes based on feed-forward.The first control method combines the feed-forward control and proportional integral(PI)feedback control of the enhanced Prandtl-Ishliskii inverse model to obtain a composite control,which further improves the control accuracy and anti-interference ability.The second method is the combination of enhanced PI inverse model feed-forward control and fractional order feedback control.The experimental verification shows that the displacement tracking accuracy can be further improved by the combination of fractional order feedback control and PI inverse model feed-forward control.