Modeling Of Hysteresis Based On Describing Function Of Backlash

Now, with the rapid development of high-tech, smart devices and high-precisionmicro-positioning devices have been a large number of applications. All these devicesare inseparable from the "smart materials". However, a major limitation ofpiezoceramic actuators is their lack of accuracy due to hysteresis. The existence ofhysteresis severely limits system performance, giving rise to undesirable inaccuracy,oscillations, or even leading to instability. Hence, in the design of the controller,reliable modeling and predictions of hysteresis would be a valuable tool. However, dueto inherent characteristics of hysteresis nonlinearity, traditional control method hasbeen difficult to establish an accurate dynamic model.The main task of the paper is to propose a simple and novel method to create ahysteresis nonlinear model, and test to verify the validity of this method.Because Preisach model has good accuracy and ease of use, this article is mainlybased on the Preisach method to create hysteresis model. Backlash is considered as thesimplest and most effective tool in establishing Preisach hysteresis model. Byimproving the describe function of backlash, we give out a function formula. Based onthis function, we established hysteresis model. This paper is mainly uses the method oftheoretical analysis and experimental verification to study the mechanism and processof modeling hysteresis. First of all, we apply the method of mathematical reasoning toprove the important properties of the function and the role of its arguments in thefunction. And using the method of geometric analysis, we give out the building hysteresis model process with apply the function, and then analyze the role of theseparameters in building the hysteresis model. Finally, since the wide application of asingle hidden layer of neural network on the nonlinear and its powerful approximationcapability, we have built the neural network hysteresis model based on the abovefunction model. Some experiments verify that the neural network hysteresis model havethe ability to simulate the given actual data model in high accuracy.The paper has a clear mathematical expression in modeling hysteresis, and theprinciple is simple and easy to understand. But now the application of this method islimited to the input are trigonometric functions. To non-Preisach hysteresis model, it isnot applicable, and in the controller design, it is not yet complete. These deficiencieswill be the direction of future work.