Convex identification of models for asymmetric hysteresis

The generalized Prandtl-Ishlinskii model (GPI) of hysteresis has a wide applicability, partly because of its capability of modelling highly asymmetric hysteresis. A disadvantage of the GPI models compared to, for example the Modified Prandtl-Ishlinskii models, has been that they have had to be identified using parametric non convex methods. Recently though, a method for non-parametric convex identification for an extended and more general GPI model was described, giving all model functions. Here, the method, which was based on input discrete equations, is briefly presented in terms of the corresponding input continuous equations. This extended model corresponds to a Preisach model and an explicit expression for this relation is derived. The method is directly applicable to data consisting of first order reversal curves, but in an application to an electrical substation equipment, it is shown that other kinds of data can also be used. The method gives significantly closer fit to this data than previous studies, and it demonstrates that non-equal left and right envelope functions are optimal.