The generalized Prandtl-Ishlinskii model: Relation with the preisach nonlinearity and inverse compensation error

The generalized Prandtl-Ishlinskii model and its inverse have been recently used in different micro-positioning applications to model and to compensate for the symmetric and asymmetric hysteresis loops. The Preisach model is one the most popular hysteresis models that used to characterize hysteresis in different materials and smart actuators. The inverse Preisach model has been used to compensate for the hysteresis nonlinearities in different micro-positioning applications. In this study, we use the inverse generalized Prandtl-Ishlinskii model which is exact and can be obtained analytically to compensate for Preisach hysteresis nonlinearity. We approximate general Preisach densities by the ones corresponding to the generalized Prandtl-Ishlinskii model, and show that the resulting compensation error is an L-bounded signal.