On the Passivity of Hysteretic Systems with Double Hysteretic Loops

Abstract

The Bouc–Wen hysteresis model is widely employed to mathematically represent the dynamical behavior of several physical devices, materials and systems such as magnetorheological dampers, lanthanide zirconium or aluminum oxides, mechanical structures or biomedical systems. However, these mathematical models must account for different properties such as the bounded-input bounded-output stability, asymptotic motion, thermodynamic admissibility or passivity in order to be physically consistent with the systems they represent. The passivity of a system is related to energy dissipation. More precisely, a system is passive if it does not generate energy but only dissipates it. The objective of this paper is to prove that two different double-loop Bouc–Wen models are passive under a particular set of model parameters.

On the characterization of butterfly and multi-loop hysteresis behavior

“…8 illustrates this weighting function with the region Ω c indicated by a dashed line. It follows that the hysteresis loop obtained from a Preisach operator with a weighting function µ defined by (20) and whose input u has one maximum u max = β 1 and one minimum u min = −β 1 has a crossover point with coordinates (u c , y c ) = (0, 0), where y c is computed using ( 16) or (17). Nevertheless, by simple inspection of the phase plot include in Fig.…”

“…Using Lemma 4.3 with the region Ω α1 defined in (21), the hysteresis loop H u,y has a crossover point (u c , y c ) with u c = u(τ 1 ) = u(τ 2 ) = α 1 and where y c = y(τ 1 ) = y(τ 2 ) is given by ( 16) or (17).…”

“…Firstly, in [16] a modified Bouc-Wen is studied which can describe a particular class of asymmetric double hysteresis loop behavior by introducing position and/or acceleration information into the model equation. Moreover, when the parameters of the model satisfy particular conditions, it has been shown that passivity property holds [17]. Secondly, in [18], a framework to transform butterfly loops to singleoriented loops is proposed.…”

On the Characterization of Butterfly and Multiloop Hysteresis Behavior

“…First, in [22], a modified Bouc-Wen is studied, which can describe a particular class of asymmetric double hysteresis loop behavior by introducing position and/or acceleration information into the model equation. Moreover, when the parameters of the model satisfy particular conditions, it has been shown that passivity property holds [23]. Second, in [24], a framework to transform butterfly loops to single-oriented loops is proposed.…”

Distributed actuation systems for adaptive optics: from structural modeling to design optimization

“…It was validated using a magnetostrictive actuator system. Another approach for modeling butterfly hysteresis behavior relies on a modified Bouc-Wen model [58,59] which incorporates either acceleration or position information. Numerical simulations have been performed to validate the framework.…”