Dual input–output pairs for modeling hysteresis inspired by mem-models

We call attention to a dual-pair concept for modeling hysteresis involving instantaneous switching: Specifically, there are two input–output pairs for each hysteresis model under one specific input, namely a differential pair and an integral pair. Currently in engineering mechanics, only one pair is...

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Bibliographic Details
Published in:Nonlinear dynamics 2017-06, Vol.88 (4), p.2435-2455
Main Authors: Pei, Jin-Song, Gay-Balmaz, François, Wright, Joseph P., Todd, Michael D., Masri, Sami F.
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Control
Dynamical Systems
Engineering
Hysteresis models
Mechanical Engineering
Memristors
Modelling
Original Paper
Switching
System theory
Systems theory
Vibration
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Summary:We call attention to a dual-pair concept for modeling hysteresis involving instantaneous switching: Specifically, there are two input–output pairs for each hysteresis model under one specific input, namely a differential pair and an integral pair. Currently in engineering mechanics, only one pair is being recognized and utilized, not the other. Whereas this dual-pair concept is inherent in the differential and algebraic forms of memristors and memcapacitors, the concept has not been carried over to memristive system theory, nor to memcapacitive system theory. We show that the “zero-crossing” feature in memristors, memcapacitors, and memristive/memcapacitive models (i.e., the “mem-models”) is also a feature of the differential pairs of well-known non-mem-models, examples of which are Ramberg–Osgood, Bouc–Wen, bilinear hysteresis, and classical Preisach. The dual-pair concept thus connects mem-models and non-mem-models, thereby facilitating the modeling of hysteresis, and raising a set of scientific questions for further studies that might not otherwise come to awareness.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-017-3388-2