Research On Dynamic Asymmetric Hysteresis Modeling And Compensation Of Piezoelectric Micro-nano Positioning Platform

In recent years,with the rapid development of nanomanufacturing technology,researchers have studied piezoelectric actuators in depth.Compared with traditional actuators,piezoelectric actuators convert voltage signals into mechanical signals directly,which not only reduces energy loss,but also has higher positioning accuracy.However,piezoelectric actuators have asymmetrical hysteresis characteristic,which is difficult to be predicted and has a great influence on the accuracy of the positioning system.In particular,this characteristic becomes more complicated and difficult to describe under high frequency input.In order to solve the above problems,this dissertation takes the micro-displacement platform driven by piezoelectric actuator as the research object,and researches asymmetric hysteresis and dynamic hysteresis in-depth.Then the related hysteresis models and hysteresis compensators are established to realize the high precision positioning of the platform.(1)Due to the low precision and complex structure of the existing asymmetric hysteresis models,this dissertation proposes an accurate and simple asymmetric hysteresis model based on the classic Prandtl-Ishlinskii(PI)model.First,the classic Play operator is modified to the Asymmetric Play(A-Play)operator to enhance its flexibility,and the influence of parameters on the new operator is analyzed.Then based on the A-Play operator,an Asymmetric Prandtl-Ishlinskii(API)model is proposed.Next,the erasure characteristic and the sub-loop consistency of the API model are verified through theoretical derivation and simulation analysis.Finally,the performance of the API model is verified through experiments.Compared with other models,the API model is simpler and more accurate under the same modeling conditions.This provides a theoretical basis for compensating the asymmetric hysteresis characteristic of piezoelectric actuators.(2)Because the API model is difficult to establish an analytical inverse model,this dissertation studies two methods of inverse solution:the direct inversion and the PID-type iterative inversion.First,in order to reduce their number,the parameters of the memory function in the API model are optimized.Then the influence of the order on accuracy is discussed,and a guidance for selection of the order is provided.Next,the Direct Inverse(D-I)compensator and the PID-type Iterative Inverse(I_PID-I)compensator are designed based on two methods,and the effectiveness of the two compensators is verified by simulation.Finally,it is verified by experiments that both compensators can effectively suppress the asymmetric hysteresis characteristic of piezoelectric actuators.This lays the foundation for the research and compensation of the dynamic hysteresis characteristic of piezoelectric actuators.(3)Through experiments,the dynamic hysteresis characteristic of piezoelectric actuators is deeply studied.First,the dynamic hysteresis law is quantitatively analyzed,and the internal connection is explored between it and the Lissajous curve.Then using the principle of Lissajous curve,a Dynamic Asymmetric Prandtl-Ishlinskii(DAPI)model is proposed based on the A-Play operator and API model.In addition,the Dynamic Direct Inverse(D-D-I)compensator and the Dynamic PID-type Iterative Inverse(D-I_PID-I)compensator are designed based on two static compensators.Finally,it is verified by experiments that the DAPI model can accurately describe the dynamic hysteresis of piezoelectric actuators.Both the D-D-I and D-I_PID-I compensators can effectively suppress the dynamic hysteresis characteristic of piezoelectric actuators.