Models for hysteresis and application to structural control

Abstract

Hysteresis is a phenomenon common to a broad spectrum of physical systems. As such, it is often present in plants for which controllers are being designed, where it introduces a problematic nonlinear multivalued behavior. Continuing research into nonlinear systems is generating an increasing interest in the control of hysteretic plants. Herein, there is a broad twofold focus: to obtain general and tractable models of hysteresis capable of accurately describing a variety of hysteretic phenomena, and then to derive corresponding control designs and supporting analytical results. This paper presents mathematical definitions and illustrative descriptions of four general hysteresis models: the hysteron, Bouc-Wen, Chua-Stromsmoe and Preisach models. Each model is capable of representing a great many forms of hysteretic behavior, and is also mathematically tractable enough for control design. As an example, the Bouc-Wen model is used to develop a semi-active structural control model for a magnetorheological damper attached to a three-story scaled building.