Application of geometry based hysteresis modelling in compensation of hysteresis of piezo bender actuator

Abstract

This paper presents results of studies of an application of a new method of piezo bender actuators modelling. A special hysteresis simulation model was developed and is presented. The model is based on a geometrical deformation of main hysteresis loop. The piezoelectric effect is described and the history of the hysteresis modelling is briefly reviewed. Firstly, a simple model for main loop modelling is proposed. Then, a geometrical description of the non-saturated hysteresis is presented and its modelling method is introduced. The modelling makes use of the function describing the geometrical shape of the two hysteresis main curves, which can be defined theoretically or obtained by measurement. These main curves are stored in the memory and transformed geometrically in order to obtain the minor curves. Such model was prepared in the Matlab–Simulink software, but can be easily implemented using any programming language and applied in an on-line controller. In comparison to the other known simulation methods, the one presented in the paper is easy to understand, and uses simple arithmetical equations, allowing to quickly obtain the inversed model of hysteresis. The inversed model was further used for compensation of a non-saturated hysteresis of the piezo bender actuator and results have also been presented in the paper.