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Why are some hysteresis loops shaped like a butterfly?

Authors
Journal
Automatica
0005-1098
Publisher
Elsevier
Publication Date
Volume
47
Issue
12
Identifiers
DOI: 10.1016/j.automatica.2011.08.027
Keywords
  • Hysteresis
  • Butterfly Hysteresis
  • Unimodal Transformation
  • Prandtl–Ishlinskii Model
Disciplines
  • Design

Abstract

Abstract The contribution of this paper is a framework for relating butterfly-shaped hysteresis maps to simple (single-loop) hysteresis maps, which are typically easier to model and more amenable to control design. In particular, a unimodal mapping is used to transform simple loops to butterfly loops. For the practically important class of piecewise monotone hysteresis maps, we provide conditions for producing butterfly-shaped maps and examine the properties of the resulting butterflies. Conversely, we present conditions under which butterfly-shaped maps can be converted to simple piecewise monotone hysteresis maps to facilitate hysteresis compensation and control design. Examples of a preloaded two-bar linkage mechanism and a magnetostrictive actuator illustrate the theory and its utility for understanding, modeling, and controlling systems with butterfly-shaped hysteresis.

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