Modeling of Magnetic Hysteresis Using Student Distribution
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ORIGINAL PAPER
Modeling of Magnetic Hysteresis Using Student Distribution Mourad Dafri 1 & Abdelaziz Lajimi 1
&
Sofiane Mendaci 2 & Abdesselam Babouri 1
Received: 9 July 2020 / Accepted: 18 August 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, the phenomenon of magnetic hysteresis is modeled by the Preisach model. In the literature, several distribution functions have been used as a distribution function, among which there are some functions that pose precision problems. In this work, we propose the use of the Student function as a distribution function. However, two parameters, a and b, are integrated into this function to improve the accuracy and to model a large category of experimental hysteresis loops. A study of the effect of each parameter on the shape of the hysteresis loop will be presented. Finally, the simulation results are compared with the experimental results for two types of ferromagnetic materials. These results show that the proposed model gives a good approximation of the experimental loops. Keywords Ferrite sheets . Ferromagnetic materials . Hysteresis . Preisach model . Student function
1 Introduction Preisach model of hysteresis phenomenon requires the use of the refinement of elementary loop type [1, 2] and the distribution function of elementary loops [3]. This last not only can be identified from a single or a set of experimental loops [4–7] but also can be approached by an analytical function, such as Lorentz or Cauchy function [8, 9], Gaussian function [10], and the modified Lorentz function [11]. Usually, the two Gaussian and Lorentz functions are unable to correctly reproduce too stiff loops [11]. The modified Lorentz function gives good results in soft ferromagnetic materials [12], but it is unable to correctly generate hysteresis loops with a low slope in the proximity of the coercive field Hc. In this work, we have studied the effect of the introduction of two parameters a and b in the Student distribution function. A comparison between the hysteresis loops generated by the Preisach model associated with the Student distribution function and the measured loops allows us to evaluate the impacts
* Abdelaziz Lajimi [email protected] 1
Laboratoire de Génie Electrique (LGEG), Université 8 Mai 1945 Guelma, BP. 401, 24000 Guelma, Algeria
2
Laboratoire d’Automatique et Informatique (LAIG), Université 8 Mai 1945 Guelma, BP. 401, 24000 Guelma, Algeria
and the benefits of these two parameters on the shape of magnetic hysteresis loops.
2 Student Function Preisach mathematical model of hysteresis is given by [13]: M ðt Þ∫∫ρðα; βÞγ αβ ½H ðt Þdαdβ
ð1Þ
where γαβ[H(t)] γαβ[H(t)] is the elementary hysteresis operator (hysteron) which can only take the discrete values − 1 and 1. ρ (α, β) is the student distribution function given by:
pffiffiffi ρðα; βÞ ¼ ka a a þ
a −b Hc
2 ! −32
aþ
β þb Hc
2 ! −32
ð2Þ where k is the parameter of regulation, Hc is the coercive field, a∈IR*þ , ∈IR*þ b∈ H c H s ; H s H c , and Hs i
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