Comparison of Two Rate-Independent Hysteresis Models With Application to Piezoceramic Transducers

Abstract

The applicability of and relationship between two rate-independent hysteresis models that have been used to describe hysteresis in piezoceramic transducers are investigated. It is shown that the generalized Maxwell resistive capacitor hysteresis model is a particular case of the classical Preisach hysteresis model. The Preisach function that reduces the Preisach model to the Maxwell resistive capacitor model is derived. It is also shown that the inverse of the Maxwell model is this same particular case of the classical Preisach model. A Maxwell model identification procedure based on Preisach identification principles is formulated. The applicability of the classical Preisach and Maxwell hysteresis models for identifying and simulating piezoceramic dielectric behavior is investigated experimentally via studies on a 1-3 piezoceramic composite. Results indicate that both hysteresis models can accurately represent piezoceramic hysteresis. It is noted that the identified relationship between Preisach and Maxwell hysteresis models may prove useful in a wider range of hysteresis applications than just those involving piezoceramics.

Modeling and Compensation of Hysteresis in Piezoceramic Transducers for Vibration Control

“…In a previous article (Royston et al, 1999) it has been proven that the Maxwell resistive capacitor (MRC) hysteresis model and its inverse are in fact a form of the classical Preisach model (CPM). In that article the particular Preisach model for the MRC was derived and an online identification routine based on Preisach principles was formulated.…”

“…The authors have established that the MRC hysteresis model and its inverse are particular cases of the classical Preisach hysteresis model (Royston et al, 1999). [Indeed, the basic MRC unit or operator is an elementary stop hysteron, as defined in the magnetics literature (Visintin, 1994;Miano et al, 1996;Bobbio et al 1997); hysterons are also the basic building blocks of the Prandtl-Ishlinskii hysteresis models.…”

Piezoceramic Hysteresis in the Adaptive Structural Vibration Control Problem

“…Before stating the objective of the present study, some prior research is summarized that offers background and a theoretical, computational and experimental foundation. In previous work a constitutive model for PZT transducer nonlinearity was developed and experimentally verified (Royston et al, 1998(Royston et al, , 1999Lee et al, 2001). Specifically, the applicability of a rate-independent discretized Ishlinskii (IM) hysteresis model was established.…”