Analytical Characterization of Hysteresis Loops Described by the Bouc-Wen Model

Abstract

The Bouc-Wen model is able to capture, in an analytical form, a range of shapes of hysteretic cycles which match the behavior of a wide class of nonlinear systems. The obtained models have been used either to predict the behavior of the physical hysteretic elements or for control purposes. The Bouc-Wen model belongs to a class of smooth analytical models described by differential equations. This gives an appropriate mathematical framework to develop analytical knowledge on relevant properties, which can be exploited for a better practical use, in particular for identification and control purposes. In this context, recent papers have studied input-output and dissipative properties and obtained analytical expressions for hysteretic limit cycles and parameter identification formulae. In this direction, this paper presents new results in the form of analytical expressions which allow to understand the direct influence of the model parameters in the shape of the hysteretic loops, thus giving a theoretically based insight for a precise use of the model in practical applications.

Keywords:

• Bouc-Wen model
• hysteresis
• parameters
• hysteresis loop

ACKNOWLEDGEMENTS

Supported by CICYT through grant DPI2005-08668-C03-01. The first author acknowledges the support of the Spanish Ministry of Education and Science through the “Ramón y Cajal” program.