A generalization of a piece-wise linear circuit model of hysteresis

Cannas, B.; Cincotti, Silvano; Daneri, I.

doi:10.1109/20.996232

Cited by 15 publications

(4 citation statements)

References 13 publications

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“…A piecewise linear function can be based on hysterons that both resembles the Preisach model and the play model by Cannas et al [ 250 , 251 ] and Cincotti et al [ 252 ] resembling the classical play and stop models but with the hysteresis area limited to a certain interval as seen in Figure 42 . The advantage relative the play model is that it has saturation levels included in the model, which the play model is lacking.…”

Section: Alternative Hysteron Modelsmentioning

confidence: 99%

Review of Play and Preisach Models for Hysteresis in Magnetic Materials

Mörée

Leijon

2023

Materials

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This paper studies the properties of the Preisach model and the play model, and compare their similarities. Both are history-dependent hysteresis models that are used to model magnetic hysteresis. They are described as discrete sums of simple hysteresis operators but can easily be reformulated as integral equations of continuous distribution functions using either a Preisach weight distribution function or a play distribution function. The models are mostly seen as phenomenological or mathematical tools but can also be related to friction-like pinning of domain-wall motions, where Rayleigh’s law of magnetic hysteresis can be seen as the simplest case on either the play model or the Preisach model. They are poor at modeling other domain behavior, such as nucleation-driven hysteresis. Yet another hysteresis model is the stop model, which can be seen as the inverted version of the play model. This type of model has advantages for expressions linked to energy and can be related to Steinmetz equation of hysteresis losses. The models share several mathematical properties, such as the congruency property and wiping-out property, and both models have a history of dependence that can be described by the series of past reversal points. More generally, it is shown that the many models can be expressed as Preisach models, showing that they can be treated as subcategories of the Preisach type models. These include the play model, the stop model and also the alternative KP-hysteron model.

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Section: Alternative Hysteron Modelsmentioning

confidence: 99%

Review of Play and Preisach Models for Hysteresis in Magnetic Materials

Mörée

Leijon

2023

Materials

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“…A dynamic Preisach hysteron will have switching points that depend on the frequency. Another way is to base the model on the alternative Play model that uses the KPhysterons, as studied by Cannas et al [492]. These could be adopted with a rate-dependency in the same way as a dynamic Preisach hysteron, as seen in Figure 38.…”

Section: Dynamic Preisach Model With Frequency-dependent Hysteronmentioning

confidence: 99%

Review of Hysteresis Models for Magnetic Materials

Mörée

Leijon

2023

Energies

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There are several models for magnetic hysteresis. Their key purposes are to model magnetization curves with a history dependence to achieve hysteresis cycles without a frequency dependence. There are different approaches to handling history dependence. The two main categories are Duhem-type models and Preisach-type models. Duhem models handle it via a simple directional dependence on the flux rate, without a proper memory. While the Preisach type model handles it via memory of the point where the direction of the flux rate is changed. The most common Duhem model is the phenomenological Jiles–Atherton model, with examples of other models including the Coleman–Hodgdon model and the Tellinen model. Examples of Preisach type models are the classical Preisach model and the Prandtl–Ishlinskii model, although there are also many other models with adoptions of a similar history dependence. Hysteresis is by definition rate-independent, and thereby not dependent on the speed of the alternating flux density. An additional rate dependence is still important and often included in many dynamic hysteresis models. The Chua model is common for modeling non-linear dynamic magnetization curves; however, it does not define classical hysteresis. Other similar adoptions also exist that combine hysteresis modeling with eddy current modeling, similar to how frequency dependence is included in core loss modeling. Most models are made for scalar values of alternating fields, but there are also several models with vector generalizations that also consider three-dimensional directions.

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“…Unfortunately, this behaviour often leads to severe inaccuracy in positioning and deteriorated performance in transient response when the piezoelectric actuators are operated in an open-loop mode. Moreover, there have been many modelling techniques in hysteresis behaviours [3]- [7], such as the Preisach function studied in [3]- [5] and the nonlinear piece-wise circuit description investigated in [6], [7]. However, these modelling techniques were either complicated or impractical for control design and implementation.…”

Section: Introductionmentioning

confidence: 98%

Adaptive Tracking Control of a Piezoelectric Micropositioner

Shieh

Huang

2006

2006 1ST IEEE Conference on Industrial Electronics and Applications

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In this study, an adaptive tracking control is proposed for trajectory tracking of a piezoelectric micropositioner which is often used to trajectory scanning applications in microscopy. To describe the dynamics of motion of a single-axis piezoelectric micropositioner approximately, a mathematical model composed of a linear differential equation about motion of mechanical systems and a specified hysteresis function is developed. Then, an adaptive tracking control based on this developed model is proposed. The main purpose of the linear differential equation is to describe the motion dynamics of the mechanical component and the specified hysteresis function is to emulate the hysteresis behaviour due to the stacked piezoelectric actuators built-in inside the micropositioner. To validate the proposed control approach, a PC-based control system which uses a laser interferometer as the displacement sensing detector is implemented. Experimental results illustrate the feasibility of the proposed controller for practical applications in trajectory tracking.

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A generalization of a piece-wise linear circuit model of hysteresis

Cited by 15 publications

References 13 publications

Review of Play and Preisach Models for Hysteresis in Magnetic Materials

Review of Play and Preisach Models for Hysteresis in Magnetic Materials

Review of Hysteresis Models for Magnetic Materials

Adaptive Tracking Control of a Piezoelectric Micropositioner

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