| As a new kind of smart material,piezoelectric materials can achieve the efficient conversion between electrical energy and mechanical energy.Compared with traditional electromagnetic motors,piezoelectric actuators based on piezoelectric materials can achieve micro/nano-level precision actuating,and have fast response speed,high power density,and strong anti-electromagnetic interference ability,which has a wide range of applications in the fields of precision actuating,optical instruments and large scale integrated circuit manufacturing.However,there is a strong hysteresis nonlinearity characteristic existing in the material,and the hysteresis characteristic is also coupled with the input signal frequency and the external load,which causes the loss of the actuating accuracy of the piezoelectric actuator,and may even lead to the instability of the actuating system.In this paper,piezoelectric actuators is selected as the research object.Considering the hysteresis characteristics of piezoelectric actuators,an improved Rate-dependent Prandtl-Ishlinskii(RDPI)hysteresis modeling method is proposed.Based on this model,a prescribed performance controller is designed to ensure the stability of the closed-loop system,which achieves the trajectory tracking of piezoelectric variable load actuating platform.The main research works of this paper are as follows:1)Implement of the variable load output characteristic test under the condition that the input signal changes with a wide range of frequencies.In order to study the hysteretic nonlinear characteristics of the piezoelectric actuator,considering the influence of the input signal frequency and the external load,the input and output characteristic test of the piezoelectric variable load actuating platform under variable frequency variable load condition is tested in this paper.The experiment result shows that there is a frequency-dependent and load-dependent hysteresis characteristic inside the piezoelectric actuator.2)An improved RDPI hysteresis modeling method is proposed.Based on the electromechanical characteristics of the piezoelectric variable load actuating platform,a hysteresis modeling method of connecting the improved RDPI model and a second-order system is proposed.By introducing a threshold function related to the input signal frequency and external load into the Play operator,the hysteresis characteristics of the piezoelectric variable load actuating platform is accurately described.Combined with piezoelectric variable load actuating platform,the experimental verification under the condition of 0.1kg～0.5kg external load in a wide frequency range of 1Hz～80Hz is completed,which verifies the effectiveness of this modeling method.3)Design and experimental verification of the prescribed performance controller.Based on the established model,this paper adopts the prescribed performance control method to design the controller.The design method based on the Lyapunov stability ensures the stability of the closed-loop system,and considering the influence of external unknown interference,the tracking performance of the piezoelectric variable load actuating platform has been improved effectively.At the same time,the experimental result under the condition of variable frequencies and variable loads proves the effectiveness of the proposed control method.The modeling method proposed in this paper can accurately characterize the hysteresis nonlinear characteristics of the piezoelectric variable load actuating platform,and a prescribed performance controller is designed to improve its actuating accuracy.The research results provide a theoretical basis for the application of piezoelectric actuators in micro-nano precision actuating platform. |
