Research Of Robust Adaptive Control Method For Piezoelectric Micro-positioning Platform

Micro-nano drive control technology is widely applied in the fields of micro-positioning and microelectronics with the rapid development of modern ultra-precision machining and precision manufacturing.Because of the advantages of low power consumption,fast response speed and high output power,the micro positioning platform which is drived by the piezoelectric ceramic has become an important device for realizing micro-nano drive.However,in actual positioning application,the hysteresis nonlinearity and the rate-dependent characteristics of piezoelectric ceramic will lead to the decrease of positioning accuracy and the reduction of control accuracy.Therefore,in this paper,we take the piezoelectric micro-positioning platform as the research object and study from two aspects of the establishment of high-precision hysteresis model and the design of effective controller to achieve high-precision control and eliminate the influence of hysteresis nonlinearity on the positioning accuracy and control accuracy of piezoelectric micro-positioning platform.First of all,aiming at the shortage of the rate-independent characteristic and symmetric characteristics in traditional Prandtl-Ishlinskii(PI)model,the modified rate-dependent PI(MRPI)hysteresis model with rate-dependent and asymmetrical characteristics is proposed by introducing the dynamic input function and polynomial input function into the traditional PI model.The improved genetic algorithm is used to identify the model parameters.The rate-dependent and asymmetric characteristics of the proposed model are verified by simulation.An experimental platform is built to verify the effectiveness and feasibility of the MRPI model.Unlike the compensation method of solving the inverse hysteresis model,in this paper,the hysteretic characteristics are compensated by using the direct inverse hysteresis compensation control method based on the MRPI model.The feedforward controller with the same form of MRPI model is used to describe the inverse hysteresis characteristics of piezoelectric micro-positioning platform.The feedforward controller and the platform are connected in series to achieve the inverse hysteresis compensation control.The displacement tracking experiments are carried out under two reference trajectories of sine wave and triangle wave at different frequencies.The experimental results show that the feedforward control method can effectively compensate the hysteresis nonlinearity.A hybrid control method combining fuzzy self-tuning PID and feedforward is designed based on the feedforward control.Experimental results prove that the hybrid control method combining fuzzy self-tuning PID and feedforward can further improve the displacement tracking accuracy.In order to further improve the positioning accuracy and eliminate the uncertainty of system parameters,this paper proposes a robust adaptive control method without an inverse model to improve the positioning accuracy of the piezoelectric micro-positioning platform.The second-order ordinary differential equations are selected to represent the dynamic model of the piezoelectric micro-positioning platform system,and the hysteresis characteristics of the platform are expressed by the MRPI model.The intermediate variables and robust adaptive control laws are designed so that the output displacement of the system can well track the reference displacement signal,and the influence of hysteresis on the control accuracy can be eliminated.Then the global stability of the control system is proved by Lyapunov function.The displacement tracking experiments are performed under various desired trajectories.The effectiveness of the proposed robust adaptive controller is verified by experiments.The experimental results show that compared with feedforward control and hybrid control,the robust adaptive control scheme can effectively eliminate the hysteresis nonlinearity and further improve the displacement tracking precision of the piezoelectric micro positioning platform.