Hysteresis Modeling And Control Method Of Piezoelectric Actuator Based On Madelung Model

As an ideal new motor,piezoelectric ceramic actuator is widely used in many high-end disciplines such as beam control,ultra-precision machining,biomedicine and so on.It has promoted the continuous development of nanotechnology,microscopic materials and ultra-precision processes.It has the advantages of high positioning accuracy,fast response speed,high reliability,no friction,small size and so on,which has been attached great importance by industry and academia.However,the inherent hysteresis nonlinear effect of the piezoelectric ceramic actuator seriously affects the positioning accuracy of the system and even leads to the instability of the closed-loop system.In addition,the hysteresis characteristics of piezoelectric ceramic actuators are very complex.Although the existing hysteresis models can describe the hysteresis characteristics,the modeling accuracy needs to be improved and it is difficult to expand and improve.For example,the existing directly constructed hysteresis trajectory model loses the important information of turning points,and the classical subclass model requires a lot of computation and is not easy to improve,which greatly hinders the research and application of hysteresis modeling and control methods for piezoelectric ceramic actuators.At the beginning of the 20th century,the German physicist Madelung proposed three rules to describe hysteresis phenomenon,known as Madelung rules,which is often used to verify the correctness of new hysteresis models,but it is not used to build hysteresis models.This thesis takes the piezoelectric ceramic actuator platform as the research object,aiming at the problem that the inherent hysteresis nonlinearity of piezoelectric ceramic actuator greatly affects the tracking accuracy.The hysteresis nonlinear modeling and control methods are studied deeply.In this thesis,based on Madelung rule,a clear and easy to understand nonlinear hysteresis theoretical framework and a stable controller are established to realize the high-precision tracking control of piezoelectric ceramic actuator.The main research contents are as follows:A hysteresis theoretical framework based on Madelung rule is proposed,which is referred to as Madelung model.The model is divided into two parts.The first part is the implementation of the wiping-out mechanism of turning point,and the second part is the construction of the CHC（current hysteresis curve）description method.The wiping-out mechanism of turning point can record all the inflection point information,and its function is to determine which hysteresis curve is CHC.The information of turning point contains all the historical motion information of hysteresis model,which is of great significance to describe hysteresis characteristics.Based on the binary search method,a concrete implementation method of the wiping-out mechanism of turning point is given.After transforming the Madelung model into an algorithm that can be run by a digital processor,the spatial complexity and time complexity analysis are given,which verifies the effectiveness of the proposed method.Based on the relationship between the internal secondary loop hysteresis curve and the external primary loop hysteresis curve,two specific CHC implementation methods were proposed.The symmetric hysteresis CHC description method is derived based on the center symmetry relation,and the asymmetric hysteresis CHC description method is established based on the similarity scaling relation.For more complex hysteresis,in order to get a better modeling effect,a more effective CHC description method can be established according to the actual situation and replace the two CHC description methods proposed in this thesis at any time,without any influence on the other parts of the Madelung model.In addition,the static hysteresis Madelung inverse model is established for symmetric hysteresis and asymmetric hysteresis respectively,and the static feedforward inverse compensation controller is designed based on it.The experimental results show that the Madelung model based on CHC description method and the corresponding static Madelung inverse model have good results for symmetric hysteresis and asymmetric hysteresis.In order to describe the dynamic characteristics and hysteresis nonlinearity of piezoelectric ceramic actuator,two dynamic hysteresis models were proposed based on the static Madelung model.The first is to regard the hysteresis of piezoelectric ceramic actuator as two parts of static hysteresis nonlinear and linear dynamic.Therefore,the dynamic hysteresis model based on Hammerstein is established.The second is to introduce the unique delay response law of the data acquisition system into the static Madelung model,and put forward the dynamic hysteresis model based on the characteristic of signal delay response,which has the advantages of clear structure and easy to understand.Based on the dynamic hysteresis model of signal delay response characteristics,the dynamic Madelung inverse model is established,and then the dynamic feedforward inverse compensation controller is designed.Experiments show that the two dynamic hysteresis models can effectively characterize the dynamic and asymmetric characteristics of piezoelectric ceramic actuators.The designed dynamic feedforward inverse compensation controller effectively improves the tracking and positioning accuracy of the piezoelectric ceramic actuator.Based on the established dynamic and static hysterical Madelung inverse model,two composite control strategies are proposed to eliminate the modeling residuals and improve the robustness of the system.The first composite control strategy uses the static Madelung inverse model as the feedforward controller to linearize the static nonlinear hysteresis.A discrete proportional integral differential controller with l₂performance is designed to compensate the residual linear dynamics and external disturbances.A cone-complement linearization algorithm is proposed to obtain the optimal control parameters.The second composite control strategy directly uses the dynamic Madelung inverse model as the feedforward controller to realize the static nonlinear hysteresis and linear dynamic compensation simultaneously.The proportional integral differential controller is used to eliminate the remaining modeling errors and external interference.The effectiveness of the two composite control strategies is verified by design experiments.