Journal
AUTOMATICA
Volume 47, Issue 12, Pages 2658-2664Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2011.08.027
Keywords
Hysteresis; Butterfly hysteresis; Unimodal transformation; Prandtl-Ishlinskii model
Funding
- Directorate For Engineering [0758363] Funding Source: National Science Foundation
- Div Of Civil, Mechanical, & Manufact Inn [0758363] Funding Source: National Science Foundation
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [824830] Funding Source: National Science Foundation
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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. (C) 2011 Elsevier Ltd. All rights reserved.
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