Preisach Plane Research Articles

Combination of hysteresis models for accuracy improvement and stabilised electromagnetic calculations

An interpolation strategy based on pre-evaluated integrals of the first-order reversal curves is presented. The proposed approach allows the seamless integration of different hysteresis models into a single calculation in a way that the most appropriate curve is picked up for particular subdomains of the Preisach plane. It can be shown that this approach can contribute to the stabilisation of numerical field calculations.

Data based constitutive modelling of rate independent inelastic effects in composite cables using Preisach hysteresis operators

AbstractThis contribution aims at introducing first steps to develop hysteresis operator type inelastic constitutive laws for Cosserat rods for the simulation of cables composed of complex interior components. Motivated by the basic elements of Cosserat rod theory, we develop a specific approach to constitutive modelling adapted for this application. Afterwards, we describe the hysteretical behaviour arising from cyclic bending experiments on cables by means of the Preisach operator. As shown in pure bending experiments, slender structures such as electric cables behave inelastically, and open hysteresis loops arise with noticeable difference between the first load cycle and the following ones. The Preisach operator plays an important role in describing the input-output relation in hysteresis behaviours, and it can be expressed as a superposition of relay operators. Hence, a mathematical formulation of the problem is introduced, and a first attempt is made to determine the hysteresis behaviour that describes the relation between curvature and bending moment. Therefore, a suitable kernel function is identified in a way that its integration over the Preisach plane results in the bending moment of the specimen, and a comparison between different kernel functions is performed.

Study of bistable behaviour in interacting Fe-based microwires by first order reversal curves

Amorphous ferromagnetic Fe-based microwires (MWs) have a magnetic structure consisting mainly of a single longitudinal domain and small closure domains at both ends. A rectangular hysteresis loop is then observed according to the fast domain wall propagation along the microwire. This type of material is a good physical example of the idea of a magnetic relay hysteron as described in Preisach model of hysteresis. The hysteron was defined as a mathematical operator acting on the field and producing rectangular loops whose superposition gives out the hysteresis loop. The hysteron idealization is frequently used to describe and interpret FORC (First Order Reversal Curve) diagrams by comparison with Preisach plane. The central idea of this work is to study the FORCs of a real physical sample that behaves closely to the ideal hysteron, both isolated and interacting with a twofold aim. On one hand, providing a better understanding of FORC measurements, and, on the other, analyzing the magnetization reversal processes in microwires with rectangular hysteresis loops. While for a single microwire the behaviour is that expected for a hysteron, both in the hysteresis loop and in the FORC diagram, the magnetostatic interaction between two microwires breaks with the ideal behaviour due to the change in the domain wall mobility at the end of the wires.

Nonlinear hysteresis identification and compensation based on the discrete Preisach model of an aircraft morphing wing device manipulated by an SMA actuator

The conception of aircraft morphing wings thrives in aeronautics since the appearance of shape memory alloys (SMAs). An aircraft morphing wing device, manipulated by an SMA actuator, inherits the intrinsic nonlinear hysteresis from the SMA actuator, ending up with control disadvantages. Conventionally, systems with SMA actuators are constrained to bi-stable states to bypass the hysteresis region. Rather than retreating a morphing wing device to bi-stable states, this paper is dedicated to transcend the morphing wing device beyond the customary limit. A methodology of discrete Preisach modeling, which identifies the hysteresis of the morphing wing device, is proposed herein. An array of discrete equal-distance points is applied to the Preisach plane in order to derive the Preisach density over the partitioned unit of the Preisach plane. Discrete Preisach modeling is fulfilled by the discrete first-order reversible curve (DFORC). By utilizing the discrete Preisach model, the aircraft morphing wing device is simulated; the validity and accuracy of discrete Preisach modeling are demonstrated by contrasting the simulated outcome with experimental data of the major hysteretic loop and the wingspan-wise displacement over time; a comparison between simulation and experimental results exhibits consistency. Afterwards, a hysteresis compensation strategy put forward in this paper is implemented for quasi-linear control of the aircraft morphing wing device, which manifests a compensated shrinking hysteresis loop and attains the initiative of extending the morphing range to the intrinsic hysteretic region.

Efficient Deperming Protocols Based on the Magnetic Properties in Demagnetization Process

Recently developed magnetic materials have high coercive force and high squareness ratios to meet the industrial demand. In the electric and electronics industries and in defense development, a deperming procedure is needed to reduce residual magnetization to zero. But the conventional deperming has a limitation of not considering the magnetic hysteresis. To research an efficient and reliable deperming current, this paper proposes a deperming analysis process using the Preisach modeling combined with the finite-elements method, which is verified by magnetic treatment facility experiments. By analyzing the trace on the Preisach plane, flash-D deperm, which leaves a lot of trace remaining on the high-density coercive force, was found to be more effective. Therefore, a method to formulate a flash-D deperm current using Preisach modeling is proposed. Finally, it is expected to obtain the most efficient flash-D deperm current according to the magnetic hysteresis of each ferromagnetic material.

State-space formulation of scalar Preisach hysteresis model for rapid computation in time domain

A state-space formulation of classical scalar Preisach model (CSPM) of hysteresis is proposed. The introduced state dynamics and memory interface allow to use the state equation, which is rapid in calculation, instead of the original Preisach equation. The main benefit of the proposed modeling approach is the reduced computational effort which requires only a single integration over the instantaneous line segment in the Preisach plane. Numerical evaluations of the computation time and model accuracy are provided in comparison to the CSPM which is taken as a reference model.

Nonlinear Control of Systems Preceded by Preisach Hysteresis Description: A Prescribed Adaptive Control Approach

When systems are preceded by hysteresis nonlinearities, many controller strategies have been developed with various hysteresis models, especially in the past decade. Among the hysteresis models, the Preisach model has a very general and well-established mathematical structure. However, designs of controllers that guarantee the closed-loop stability of nonlinear systems having the Preisach hysteresis representation are still a challenging issue in the literature. In this paper, we will attempt to demonstrate a solution in which a stable controller can be designed for nonlinear systems that couple with Preisach hysteresis model. The key is that by utilizing the so-called Preisach plane, the Preisach model is reexpressed into a control-oriented form, in which the input signal is explicitly expressed. It is then possible to fuse available control techniques with the Preisach model designing stable controllers. As an illustration to show the advantage of the developed control-oriented form, a prescribed adaptive control approach is adopted to ensure the transient and steady-state performance of the tracking error. The effectiveness of the control scheme is validated by the experimental results.

The peak in anomalous magnetic viscosity

Anomalous magnetic viscosity, where the magnetization as a function of time exhibits non-monotonic behaviour, being seen to increase, reach a peak, and then decrease, is observed on recoil lines in bulk amorphous ferromagnets, for certain magnetic prehistories. A simple geometrical approach based on the motion of the state line on the Preisach plane gives a theoretical framework for interpreting non-monotonic behaviour and explains the origin of the peak. This approach gives an expression for the time taken to reach the peak as a function of the applied (or holding) field. The theory is applied to experimental data for bulk amorphous ferromagnet alloys of composition Nd60−xFe30Al10Dyx, x = 0, 1, 2, 3 and 4, and it gives a reasonable description of the observed behaviour. The role played by other key magnetic parameters, such as the intrinsic coercivity and fluctuation field, is also discussed. When the non-monotonic behaviour of the magnetization of a number of alloys is viewed in the context of the model, features of universal behaviour emerge, that are independent of alloy composition.

FORC differential dissection of soft biphase magnetic ribbons

The problem of unravelling the information contained in First Order Reversal Curves (FORC) has become in the recent years a discussion matter because the commonly used technique of assimilating the FORC diagrams to the Preisach plane is not satisfactory in many cases. This is particularly so when the magnetic interactions within the system are strong, comparable or larger than the switching fields, as in soft ferromagnets. In this work, the authors present an interpretation of this technique as a differential tool for the study of magnetic interactions without referring to Preisach models. It allows discriminating the magnetic phases of the system as well as the dominant interactions. The proposed FORC differential dissection is applied to partially crystallized ribbons of the Co69B12Si12Fe4Mo2Ni1 alloy, identifying two magnetic phases with close but different magnetic hardness which are positively coupled both internally and mutually.

Memory characteristics of hysteresis and creep in multi-layer piezoelectric actuators: An experimental analysis

In this paper we provide an experimental characterization of creep and hysteresis in a multi-layer piezoelectric actuator (PEA), taking into account their relationships in terms of memory structure. We fit the well-known log-t model to the response of the PEA when driven by piecewise-constant signals, and find that both the instantaneous and the delayed response of the PEA display hysteretic dependence on the voltage level. We investigate experimentally the dependence of the creep coefficient on the input history, by driving the PEA along first-order reversal curves and congruent minor loops, and find that it displays peculiar features like strict congruence of the minor loops and discontinuities. We finally explain the observed experimental behaviors in terms of a slow relaxation of the staircase interface line in the Preisach plane.

Direct recursive identification of the Preisach hysteresis density function

In this paper, a novel direct method of recursive identification of the Preisach hysteresis density function is proposed. Using the discrete dynamic Preisach model, which is a state-space realization of the classical scalar Preisach model, the method is designed based on the output increment error. After giving the general formulation, the identification scheme implemented for a discretized Preisach plane is introduced and evaluated through the use of numerical simulations. Two cases of Gaussian mixtures are considered for mapping the hysteresis system to be identified. The parameter convergence is shown for a low-pass filtered white-noise input. Further, the proposed identification method is applied to a magnetism-related application example, where the flux linkage hysteresis of a proportional solenoid is assumed from the measurements, and then the inverse of a standard demagnetization procedure is utilized as the identification sequence.

An Efficient Inverted Hysteresis Model with Modified Switch Operator and Differentiable Weight Function

This paper proposes a different inverted hysteresis model with modification of the classic Preisach switch operator. By using this new switch operator, the inverted model remains the wiping out and congruency properties. It also guarantees the symmetry and total positiveness of weight function in the Preisach plane. According to the change pattern of H(B) branches, a differentiable weight function is introduced in the inverted model. The weight function performs with good continuity and symmetry. This makes it possible to implement the inverted model in numerical analysis without iterative procedure. The identification work is done by means of the measured major loops. Here the Newton method algorithm is applied to optimize the mean squared error (MSE) between the measured and simulated data. By this way, the limited number of parameters can be determined. The inverted model was verified for both soft and hard magnetic materials. Besides major hysteresis loops, minor loops and first-order reversal curves (FORCs) can also be simulated. By comparison, the simulation results produced by the inverted hysteresis model show good approximation to the measurement data.

Preisach 모델을 이용한 강자성체의 탈자기법 연구

강자성체는 자구들의 상호작용으로 인해 잔류 자화가 남게 되는데, 전자전기 산업 및 국방 피탐지 분야에서는 이러한 잔류 자화량을 정밀하게 0으로 만드는 탈자기법이 요구된다. 하지만 현재 수행되는 탈자기법들은 경험과 실험에 의존한 방법들로, 새로운 재료의 개발에 따른 효율적인 탈자를 위해서는 강자성체의 히스테리시스 곡선을 반영한 탈자기법이 필요하다. 본 논문에서는 자성체의 물성적인 성질을 기반으로 정립된 Preisach 모델링 기법을 이용하여 Anhysteretic Deperm, Deperm-ME, Flash-Deperm에 따른 2차원 유한요소해석을 수행하였다. 탈자 전류에 의한 자기이력궤적의 분석을 통해 강자성체의 히스테리시스 곡선과 탈자 변수의 관계를 고찰하였으며, 이로써 탈자에 효율적인 전류 감소 형태를 제시하였다. Ferromagnetic material's residual magnetization is remained because of the interaction between domains from external apply field, so the electrical and electronic industry and area of defense development request deperm protocol which makes the residual magnetization to 0. But the deperm protocols which are used theses days are developed by using only experience and experiment, so we have to develop deperm protocol considering hysteresis curve. In this paper, Anhysteretic Deperm, Deperm-ME, Flash-Deperm were analyzed using two dimensional finite element method and Preisach model that was formulated by property of magnetic materials. From that analysis, the relations between hysteresis curve and deperm variable are compared by analyzing the trace of Preisach plane. Also, an efficient current ratio of deperm protocol, is proposed.

What does a first-order reversal curve diagram really mean? A study case: Array of ferromagnetic nanowires

The magnetic characterization technique of hysteretic materials based on the measurement of the first-order reversal curves (FORC) is one of the most appealing methods recently introduced in hundreds of new laboratories, but due to the complexity of the FORC data analysis, it is not always properly used. This method originated in identification procedures for the classical Preisach model and consequently often the FORC distribution is interpreted as a slightly distorted Preisach distribution. In this paper, we discuss this idea from two points of view derived from the basic assumptions used in the Preisach model. One is that the interaction field is equivalent with a shift of the rectangular hysteron along the applied field axis without changing the intrinsic coercivity. The other is the direct use of switching fields as coordinates, in fact, the ones defining the Preisach plane. We discuss the compatibility between the experimental FORC distribution and the Preisach model developed on the interaction field hypothesis. As a “toy model,” we are using a system of ferromagnetic nanowires, explaining from the physical point of view the complex FORC diagrams as they are obtained in experiments. This explanation gives a fundament for the correct interpretation of the FORC diagram in order to get “Preisach type” information about the system, mainly about the distributions of coercive and interaction fields within the sample. These results are relevant for many ferromagnetic systems and give a valuable guide for understanding the FORC technique and its fundamental link with the Preisach model.

Characterizing Hysteresis Nonlinearity Behavior of SMA Actuators by Krasnosel’skii-Pokrovskii Model

Krasnosel’skii-Pokrovskii (KP) model is one of the great operator-based phenomenological models which is used in modeling hysteretic nonlinear behavior in smart actuators. The time continuity and the parametric continuity of this operator are important and valuable factors for physical considerations as well as designing well-posed identification methodologies. In most of the researches conducted about the modeling of smart actuators by KP model, especially SMA actuators, only the ability of the KP model in characterizing the hysteretic behavior of the actuators is demonstrated with respect to some specified experimental data and the accuracy of the developed model with respect to other data is not validated. Therefore, it is not clear whether the developed model is capable of predicting hysteresis minor loops of those actuators or not and how accurate it is in this prediction task. In this paper the accuracy of the KP model in predicting SMA hysteresis minor loops as well as first order ascending curves attached to the major hysteresis loop are experimentally validated, while the parameters of the KP model has been identified only with some first order descending reversal curves attached to the major loop. The results show that, in the worst case, the maximum of prediction error is less than 18.2% of the maximum output and this demonstrates the powerful capability of the KP model in characterizing the hysteresis nonlinearity of SMA actuators.In order to have continuous operator rather than jump discontinuities like the Preisach operator, Krasnosel’skii- Pokrovskii[12] allows the Preisach operators to be any reasonable functions. The elementary operator of the KP model which is referred to as the KP kernel, a special case of a so called generalized play operator, is a continuous function on the Preisach plane and has minor loops within its major loop. Let <i>P</i> be the Preisach plane over which hysteresis occurs:

An efficient vector Preisach hysteresis model based on a novel rotational operator

The vectorial modeling of hysteresis phenomena is an important task with respect to precise numerical simulation of ferromagnetic materials. Many vector models are based on extended Preisach models. Approaches are known where the scalar Preisach models are defined in different space directions and the results are calculated by summation or integration. Within this approach, we suggest a Preisach model that uses only one Preisach plane, but an additional rotational plane. This rotational plane practically defines a direction for each Preisach element. Therefore, this operator can be evaluated in a very efficient way.

Application of Support Vector Machines to the Tracking Control of Piezoelectric Actuators

In this paper, a hybrid approach associated the Preisach concept with support vector machines (SVM) is brought forward to identify and predict the nonlinear behavior of piezoelectric actuators (PA). Preisach concept is used to construct mesh nodes in the Preisach plane and determine the final output displacement of PA. SVM is trained based on the mesh nodes and provides favorable generalization ability in the Preisach plane. Experimental results validate the proposed method.

Application of Support Vector Machines to the Tracking Control of Piezoelectric Actuators

In this paper, a hybrid approach associated the Preisach concept with support vector machines (SVM) is brought forward to identify and predict the nonlinear behavior of piezoelectric actuators (PA). Preisach concept is used to construct mesh nodes in the Preisach plane and determine the final output displacement of PA. SVM is trained based on the mesh nodes and provides favorable generalization ability in the Preisach plane. Experimental results validate the proposed method.

ODEs involving the derivative of a Preisach operator with a degenerated density

This paper examines a class of operator–differential equations that contain derivatives of the Preisach operator. We offer a solution for situations where the density function of the Preisach operator is zero in a region bounded by the Preisach plane bi-sector. This solution is relevant for systems in which output remains constant following a change in direction of input. We apply the solution to problems in terrestrial hydrology.

The history of magnetization process influence on FMR response of particle systems

In order to express the history of magnetization process dependence on ferromagnetic resonance (FMR) for a particle system we use a statistical model based on the Preisach model. The precedent magnetization processes define in Preisach plane a configuration of particle magnetization orientations. The particles are considered single domain and saturated and are modeled as Stoner–Wohlfarth particles. The FMR response of the system is computed by summarizing the individual dynamic susceptibility of the particles, keeping account of the initial directions of the particle magnetizations. The FMR spectra of the particle system is determined considering three initial magnetization states: the demagnetized state, the positive saturated state in which all the particles have the magnetization in the static field direction and the negative saturated state when all the particles have the magnetization in the opposite field direction. The static field dependence of the resonance frequency and linewidth are determined as functions of the initial magnetization states.