Extension of hysteresis operators of Preisach-type to real, Lebesgue measurable functions

Iyer, Ram; Ekanayake, Dinesh B.

doi:10.1016/j.physb.2007.08.069

Cited by 4 publications

(8 citation statements)

References 2 publications

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“…The intuition leading to the play operator may be stated as follows: for a given input function, we look for an output function, starting value of which is given, and we do not change its value as long as the difference between input and output stays within a given boundary region. Several definitions of the play operator are possible, depending on the regularity of the input, the space in which the input and output attain their values and the boundary conditions (characteristics) , , , . It may be defined for sufficiently regular inputs and boundary conditions (characteristics), for example, with the Young or Kurzweil integral formalism , .…”

Section: Introductionmentioning

confidence: 90%

“…Another extensions, for much more general inputs— L ∞ or Lebesgue measurable inputs, but only for constant, symmetric boundaries—were given in and .…”

Section: The Generalised Play Operatormentioning

confidence: 99%

“…The play operator may be also defined for time‐dependent characteristics (which we will call sometimes boundary conditions or boundaries) , or for more general inputs, such as L ∞ ([ a ; b ]) or even Lebesgue measurable functions , , where the Kurzweil integral formalism can not be applied in a straightforward way.…”

Section: Introductionmentioning

confidence: 99%

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The play operator, the truncated variation and the generalisation of the Jordan decomposition

Łochowski

Ghomrasni

2014

Math Methods in App Sciences

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The play operator minimalizes the total variation on intervals [0, T ], T > 0, of functions approximating uniformly given regulated function with given accuracy and starting from a given point. In this article we link the play operator with so called truncated variation functionals, introduced recently by the second-named author, and provide a semi-explicit expression for the play operator in terms of these functionals. Generalisation for time-dependent boundaries is also considered. This gives the best possible lower bounds for the total variation of the outputs of the play operator and its Jordan-like decomposition.

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Section: Introductionmentioning

confidence: 90%

“…Another extensions, for much more general inputs— L ∞ or Lebesgue measurable inputs, but only for constant, symmetric boundaries—were given in and .…”

Section: The Generalised Play Operatormentioning

confidence: 99%

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The play operator, the truncated variation and the generalisation of the Jordan decomposition

Łochowski

Ghomrasni

2014

Math Methods in App Sciences

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“…In particular we also need an approximation property of BV with respect to the convergence defined in (1.2). Let us remark that the problem of extending a hysteresis operator to spaces of non regular functions was dealt by several authors: see, e.g., the monographs [7,16,8,4], the papers [9,12,6,10] and the references therein. In most of these references the extension was obtained for particular cases of hysteresis operators or for scalar hysteresis operators.…”

Section: Introductionmentioning

confidence: 99%

Extending vector hysteresis operators

Recupero

2011

J. Phys.: Conf. Ser.

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In some recent papers we studied how to extend to BV a hysteresis operator defined on Lipschitzian inputs, preserving suitable continuity properties. More precisely we considered the so called strict metric defined by means of the essential variation. This approach may have some drawbacks from the physical point of view, therefore in the present paper we show how to extend a general hysteresis operator with respect to a notion of convergence which takes into account of the pointwise variation rather than the essential variation.

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“…The observed complex hysteretic behavior is typically modeled by physical-oriented complex models, able to describe the physics of the system (especially the phase changes) on an elementary level. The focus of the actual and typical related model development is the representation of the hysteretic effects by implementing internal memory using Preissach operators [7,8] or other suitable approaches. The validation of the models shows that the material behavior can be expressed and mathematically expressed.…”

Section: Introductionmentioning

confidence: 99%

Mathematical models of shape memory alloy behavior for online and fast prediction of the hysteretic behavior

Shibly

Söffker

2010

Nonlinear Dyn

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In this contribution, a new closed form of a mathematical model of Nickel-Titanium (NiTi) shape memory alloy (SMA) and its thermo-mechanical wire hysteresis behavior is developed. The approach is based on experimental data. The behavior of the heated and naturally cooled wire is modeled by mathematical expression. The cycle of heating and cooling is performed under a constant load. The prediction of the hysteretic behavior is realized through models adaptation, as predetermination, or real time determination of the models values, is developed and presented in detail. Simulations for position control using PID controller is shown for comparison purposes. The developed approach is incorporated in a feed forward control scheme. A comparison between the actual position and the predicted models position shows promising results.Keywords SMA hysteric behavior · Hysteresis prediction of SMA wire · Real time modeling of SMA hysteresis · Testing and simulation of shape memory alloy phenomenological behavior

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Extension of hysteresis operators of Preisach-type to real, Lebesgue measurable functions

Cited by 4 publications

References 2 publications

The play operator, the truncated variation and the generalisation of the Jordan decomposition

The play operator, the truncated variation and the generalisation of the Jordan decomposition

Extending vector hysteresis operators

Mathematical models of shape memory alloy behavior for online and fast prediction of the hysteretic behavior

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