Research On Nonlinear Modeling And Control Method Of Piezoelectric Actuator

Piezoelectric actuators can convert electrical energy into displacement,utilize the inverse piezoelectric effect of ceramic materials,it is widely used in high-precision positioning control and microscopic measurement and operation.However,the piezoelectric actuator shows severe hysteresis between the input voltage and the output displacement,due to the structure and material properties.The hysteresis characteristics can seriously affect their applications in tracking and positioning systems,which not only reduce the positioning accuracy but also cause system instability.Therefore,in this paper,the piezoelectric actuator is used as the research object to establish a high-precision hysteresis nonlinearity model and design an effective control strategy to eliminate the influence of hysteresis nonlinearity on the positioning system.(1)The Simulink/xPC Target real-time simulation environment is introduced to study the key factors affecting the system real-time,reliability and stability indexes from the perspective of hardware equipment selection and software environment requirements of the simulation system.The piezoelectric actuator tracking and positioning system is built based on the Simulink/xPC Target real-time simulation environment,and the semi-physical simulation system is initialized and tested to eliminate the zero bias and drift problems of the system under zero input response.(2)A Hammerstein rate-dependent hysteresis model is developed,which is composed of an improved Bouc-Wen model and a second-order transfer function model in series.Since the traditional Bouc-Wen model has redundant parameters and the hysteresis curve of the model is symmetric about the origin,the traditional Bouc-Wen model is simplified to obtain a standardized Bouc-Wen model,and a polynomial function is introduced on the basis of the standardized model to describe the asymmetric hysteresis curve and use the artificial bee colony algorithm to identify the model.Compared with the classic Bouc-Wen model,the improved model can describe the hysteresis of the piezoelectric actuator more accurately;the proposed Hammerstein model can describe the hysteresis curves at different frequencies.(3)Design a feedback control method based on inverse model compensation.A hysteresis compensator based on the Bouc-Wen inverse model is used.Due to the problems of compensation errors and sensitivity to external disturbances of the system in the open-loop compensation strategy,a sliding-mode control strategy based on a sliding-mode state observer is designed.The sliding-mode state observer is used to obtain the full state quantity of the system and feed the velocity state of the system to the sliding-mode controller to form a closed-loop control system.The stability of the whole closed-loop system is proved.Finally,the designed control strategy is applied to the piezoelectric actuator tracking and positioning system and its effectiveness is verified.