Development of a combined Prandtl Ishlinskii–Preisach model

Abstract

The Prandtl-Ishlinskii (PI) model and the Preisach model are commonly used models to predict the hysteretic behaviors in smart materials-based actuators. The advantages of the PI model are that (1) the structure of the model is simple, which facilitates the implementation of the model; (2) the analytical inverse of the model is available. The disadvantage of the PI model is that it can only describe the symmetric hysteresis effects. For the Preisach model, it is capable of describing various types of hysteretic behaviors, however, the model is too complicated to implement numerically. To merge the advantages of both models, a combined Prandtl Ishlinskii–Preisach (CPIP) model is proposed in this paper. The CPIP is not a simple combination of the two models. The discrete empirical interpolation method (DEIM) is applied to determine the structure of the CPIP model by selecting the dominated elementary operators. The CPIP model preserves the advantages of the PI model and the Preisach model, and is easy to implement numerically in the Matlab/Simulink environment. Experimental results validate the proposed CPIP model.