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A mathematical model of magnetic hysteresis loops for weak ac magnetic fields, which is applicable for both symmetrical hysteresis loops that are described by the Rayleigh law of magnetization and asymmetrical loops that are not, has been formulated. The asymmetrical hysteresis loops take place when the ferromagnet is affected, along with an ac magnetizing field, by a dc field. The frequency spectrum of a ferromagnet magnetization has been analyzed as a time function. A technique for experimental determination of parameters that enter into this model is proposed, which uses amplitudes and phases of the first three magnetization harmonic components (the first, the second, and the third ones).

An identification technique for the parameters of phenomenological models of hysteresis is presented. The basic idea of our technique is to set up a system of equations for the parameters of the model as a function of known quantities on the major or minor hysteresis loops (e.g. coercive force, susceptibilities at various points, remanence), or other magnetization curves. This system of equations can be either over or underspecified and is solved by using the conjugate gradient method. Numerical results related to the identification of parameters in the Energetic, Jiles–Atherton, and Preisach models are presented.

Polycrystalline single phase oxides, La 0.7-x Nd x Pb 0.3) MnO 3 (0.3≤x≤0.7), have been synthesized by a standard ceramic fabrication method. A phenomenological model is proposed to describe the magnetization process, and to fit the experiment data of hysteresis loops under different composition ratio. The magnetic hysteresis behavior can be modeled by the formula of [Formula: see text]. The resulted model can satisfy the experiment data ranging from 0.005T to 5T. Explanations on the fitting coefficients of these compounds are addressed.

This paper generalizes a 2-D isotropic vector hysteresis model represented by the superposition of scalar stop models. Its identification method and property of rotational hysteresis loss are discussed. The generalized vector model can control its rotational hysteresis loss

Analytical approximation of symmetrical and unsymmetrical hysteresis loops is based on the general description of magnetization consisting of the slow reversible process and more violent irreversible process. The coercivity term in the irreversible component generates symmetrical hysteresis loops, which are used for the approximation of first-order reversal curves and their distribution. Model has been applied to materials with typical S-shaped and rectangular hysteresis loops.

By using the concept of online goal adaptation, we develop a new online identification and a robust adaptive control for hysteresis system which is described by discrete Preisach model. The proposed identification requires triangle matrices to simply the calculation for Preisach model. In addition, a robust adaptive control is adopted without inverse Preisach model based on the weighting factor recursive least square (WFRLS) method. A Lyapunov function candidate guarantees the stability of this hysteresis system. Finally, simulations perform on a typical system which clarify the validity of the proposed approach.

Several physical models for simulating the hysteresis loop have been proposed that the implementation of some of these models is very complex and time-consuming and needs much data. In many technical applications, an exact mathematical model of the magnetic characteristics of the magnetic materials B-H is required to calculate the magnetic field in rotating machinery or other electromagnetic systems. Two common methods for simulation of hysteresis loops are Preisach and Jiles-Atherton Models. In this paper, at first we describe them, after that, the two methods are used to simulate the hysteresis loop using Labview software. The results of the simulation clearly show the relative superiority of the Jiles-Atherton's method.

This paper presents an improved approach for simulating magnetic hysteresis, which takes into account the effect of applied stress, based on an extended Stoner-Wohlfarth (S-W) model. Meanwhile, the S-W asteroid rotates and shrinks, and the stable direction of magnetization of the particle can be calculated from the new energy minimum conditions. This developed model is applied to analyze the magnetic hysteresis phenomenon of a soft magnetic composite (SMC) material under different compaction process, and the results of simulations are in good quantitative agreement with experimental data.

U radu smo izvršili mjerenja sa dvi različite zavojnice sa torusnom jezgrom, uključujući promjene frekvencije i broj zavoja na zavojnici, kako bi prikazali utjecaj navedenih veličina na karakteristike tih istih zavojnica dobivenih Preisachovim modelom. Prikazana su mjerenja petlji histereza te razlike između histereza dviju zavojnica kao i razlike petlji histereza istih zavojnica pri utjecaju promjene frekvencije i broja zavoja. Zaključili smo da histereze prve zavojnice, za razliku od petlji histereze druge zavojnice, su uske i njihovi gubitci su jako mali kada uspoređujemo razlike u rezultatima izvođene sa drugom zavojnicom, nevidi se posebna razlika u izgledu histereze promjenom frekvencije ili promjenom broja zavoja zavojnice. Razlog tome je jako mala razlika u promjeni frekvencije i broju zavoja. Estimirani parametri Preisachovog modela pojavljuju se samo iznad glavne dijagonale, i to tako da parametri najveće histereze nalazi na glavnoj dijagonali a parametri najmanje histereze pojavljuju najdalje od glavne dijagonale. In this paper we have conducted the measurements with two different coils containing a toroidal shape core, including changes in the frequency and number of turns of the coil. The paper presents a measure hysteresis loops and the difference between them . We have concluded that the hysteresis of the first coil, unlike the hysteresis loop of other coil, are narrow and their losses are very small and not exist the distinct difference in the appearance of hysteresis when we changing frequency or changing the number of turns of the coil. The reason for this conclusion is very little difference in changing the frequency and the number of turns of the coil. The Estimation parameters of Preisach models appear just above the main diagonal. Parameters of largest hysteresis are located on the main diagonal and the parameters of at least the hysteresis are away from the main diagonal.

Because of hysteresis the perfect modeling of ferromagnetic materials is difficult. The general purpose of Preisach model was applied in this area. The main problem is to determine the weighting function from measurement of hysteresis loops. Another approach, based on the method of trials and errors, was used. According to the nature of a material, the weighting function was searched in the form of normal distribution with constant background. Only several parameters should be found by the best fit with experimental data. The agreement with experiment is acceptable, especially for higher excitations. The numerical model can be used for semi quantitative analysis or simulation of electrical or electronic devices with a ferromagnetic core.

The Preisach model describes the output of a hysteretic system in the form of a history-dependent double integral of the Preisach distribution function [1]. Many efficient numerical implementations have been developed in the literature to compute the output as a function of input, however, inverting the Preisach operator (i.e. computing the input variable as a function of the output) remains a difficult task. A number of authors have proven the existence and continuity of the inverse of the Preisach operator [2, 3], however, the lack of efficient numerical algorithms to invert the operator has limited the area of applicability of the model and made it only sporadically used in the real-time control applications involving optimal design, sensors and actuators, smart materials, and other mechanical systems where it is imperative control the output accurately [4,5,6].

Hysteresis phenomenon is currently met in magnetic materials characterization. From many years this hysteresis had been modeled with different approaches. The aim of this paper is to present a comparison between few sigmoid functions used more often in other research areas. The functions were updated according to the requirements of the magnetic hysteresis and there comparisons for three different magnetic materials were performed. In the last part, hysteresis losses are evaluated using relative errors between experimental loop area and modeled loop area.

This paper presents the scalar dynamic magnetic hysteresis model based on the Preisach theory. The important role in this theory played hysteresis operator states. The changes of these operators' states are not immediate in the dynamic model but they are a function of time and parameter k representing the magnetic properties of the material. In this paper the transient state of the hysteresis operator is defined by the nonlinear first order differential equation. The implementation of the dynamic hysteresis is additionally associated with feedback hysteresis model. This allows for obtaining a more accurate model for low and high magnetization frequencies. The material parameter k was determined for the toroidal tape wound core made of anisotropic sheet steel ET114-27. This paper presents the magnetic hysteresis loop simulation results for the different magnetization frequencies.

This paper presents the thickness effect of hysteresis ring of hysteresis motor using finite element method combined with a vector hysteresis model. From the magnitude and direction of the magnetic field intensity, the magnetization of each ring element is calculated by a vector hysteresis model. The developed torque can be obtained with the vector sum of individual torque of each element on the hysteresis ring. From these calculations, it can be found that the motor torque is not in proportion to the thickness of the ring. As a result, there exists a proper point of thickness and that can be determined using the proposed methoㅇ in this paper.

Macroscopic behavior of ferromagnetic materials can be considered as the resultant of three phenomena: hysteresis, eddy current, and excess loss. Hysteresis is the behavior of the material under quasi-static variation of magnetic field. Eddy-current and excess losses are dependent on the rate of field variation and are evident in the fast variation of the magnetic field, so they are called dynamic effects. This paper presents a simple and practical technique in field analysis of electromagnetic systems having hysteresis and dynamic effects. Based on the Preisach model for hysteresis and existing formulations for eddy currents and excess loss, an equivalent expression for field intensity has been introduced. A new technique has been presented in order to include this expression in the finite-element code. A typical system has been modeled by this code. Effects of relaxation and time step were examined on the stability and the convergence rate of the method. The validity of the proposed model has been checked by comparing its results with experimental measurements

In this paper a new vector hysteresis model is constructed on the basis of a scalar hysteresis model. The advantages of the scalar model are its easy identification, past memory representation and numerical simplicity. The accommodation property of the model comes from the construction philosophy of the model. The feasibility of the extrapolation is defined by the turning points. The convenience of this model is its efficiency in reduction of the calculation time. The model parameters, the modification vector fields, derived from the permeability vector can be determined from the measured data points. The vector model can approximate the behavior of the vector hysteresis characteristics of ferromagnetic materials. In this paper the main question of the vector model, the definition of the initial values of components in the selected directions is solved.

This paper introduces a simplified vector model based on the Preisach approach that intrinsically satisfies loss and saturation properties. It is able to reproduce isotropic and nonisotropic behavior. The main idea is to compute the magnetization vector in two steps independently, amplitude and phase. The first one is computed by means of a scalar Preisach model with a distribution depending on the angle of the applied field with respect to a fixed direction. The phase is computed by means of a phase diagram and a simple function that take into account the history of the angle between magnetization and applied field. The proposed formulation allows fast computation of rotational and alternative vector magnetization, the computational time is of the order of two times the scalar Preisach model

The Preisach distribution function in electrical steel at different magnetizing frequencies has been studied by the combination of the experimental measurements in an Epstein frame and the numerical identification by the method of centered cycles. The dynamic Preisach distribution function is mostly distributed in the discretized elements along the alpha=-beta axis and the neighboring axis of the alpha=beta axis in the Preisach plane. The least-squares method has been employed to determine the dependence of the values of the distribution function in those specific elements on the magnetizing frequency. The simulated results show that the method in this paper provides another way of calculating the dynamic hysteresis loops

Most key elements of ferroelectric properties are defined through the hysteresis loops. For a ferroelectric ceramic, its loop is contributed collectively by its constituent grains, each having its own hysteresis loop when the ceramic polycrystal is under a cyclic electric field. In this paper, we propose a polycrystal hysteresis model so that the hysteresis loop of a ceramic can be calculated from the loops of its constituent grains. In this model a micromechanics-based thermodynamic approach is developed to determine the hysteresis behaviour of the constituent grains, and a self-consistent scheme is introduced to translate these behaviours to the polycrystal level. This theory differs from the classical phenomenological ones in that it is a micromechanics-based thermodynamic approach and it can provide the evolution of new domain concentration among the constituent grains. It also differs from some recent micromechanics studies in its secant form of self-consistent formulation and in its application of irreversible thermodynamics to derive the kinetic equation of domain growth. To put this two-level micromechanics theory in perspective, it is applied to a ceramic PLZT 8/65/35, to calculate its hysteresis loop between the electric displacement and the electric field ( D versus E ), and the butterfly-shaped longitudinal strain versus the electric field relation ( ϵ versus E ). The calculated results are found to be in good quantitative agreement with the test data. The corresponding evolution of new domain concentration c 1 and the individual hysteresis loops of several selected grains—along with those of the overall polycrystal—are also illustrated.

A general model for vector hysteresis is presented. We will show that the model is in agreement with the required thermodynamical properties and with the macroscopic properties observed in the real media. Also the relationship with the Classical Preisach Scalar Model will be discussed.

We prove dissipativity of nonresonant forced non-resonant pendulum with Preisach friction. In a general case we use estimates of the width of hysteresis loop, if the forcing term is quasiperiodic, the equation is always dissipative.

This paper analyzes a non-linear heat diffusion process when the thermal diffusivity behaviour is a hysteretic function of the temperature. Modelling this temperature dependence, the discrete Preisach algorithm as general hysteresis model has been integrated into a non-linear multigrid solver. The hysteretic diffusion shows a heating-cooling asymmetry in character. The presented type of hysteresis speeds up the thermal processes in the modelled systems by a very interesting non-linear way.

A neural network based approach of identification for Preisach-type hysteresis is proposed. In this method, a hysteretic operator is introduced to transform the multi-valued mapping of hysteresis into a one-to-one mapping so that neural networks can be applied to the approximation of the behavior of hysteresis. The proposed model has a simple architecture that simplifies identification procedure and is available to different operating conditions. Finally, an example of simulation and the result of modeling the hysteresis existing in a piezoelectric actuator based on the proposed method are presented.

In this paper a statistical approach of hysteresis phenomenon is presented. Under the assumption that each magnetic domain can be represented by a random variable a very simple model of hysteresis can be built on. In spite of the simplicity of the model it possesses many important properties of hysteretic behaviour.

First-order reversal curves (FORCs) are used to analyze the kinetic effects described by dynamic Preisach models of hysteresis. It is shown that dynamic processes in magnetic materials strongly affect the symmetry of FORC diagrams. The regions that are most strongly affected when the applied magnetic field varies at high speed are located in the proximity of the diagonal of the FORC diagrams. In these regions, the differential magnetic susceptibility can be negative and result into negative values of the FORC diagrams. An identification technique based on the FORC diagrams is presented for the kinetic parameters of the dynamic Preisach model.

The possibility of considering dynamic effects in three vector hysteresis models is investigated. The friction model of oriented Preisach operators which rotate due to the torque exerted by the external field, the coercive spheres model, the 3D analogue of the classical Preisach model, and a further collective model based on micromagnetic analogy are considered. Furthermore, the “external” dynamic generalization of the static hysteresis models is introduced for the vector case.

PurposeTo analyze the Jiles and Atherton hysteresis model used for hysteresis losses estimation in soft magnetic composite (SMC) material.Design/methodology/approachThe Jiles and Atherton hysteresis model parameters are optimized with genetic algorithms (GAs) according to measured symmetric hysteresis loop of soft magnetic composite material. To overcome the uncertainty, finding the best‐optimized parameters in a wide predefined searching area is done with the proposed new approach. These parameters are then used to calculate the hysteresis losses for the modeled hysteresis. The asymmetric hysteresis loops are also investigated.FindingsThe classical GAs are good optimization methods when a pre‐defined possible set of solutions is known. If no assumption on solutions is present and a wide searching area range for parameter estimation is selected then the use of the new approach with nested GAs gives good results for symmetric hysteresis loops and further for the estimation of hysteresis losses.Research limitations/implicationsThe use of the Jiles and Atherton hysteresis model for asymmetric hysteresis must be explored further. Only one set of optimized Jiles and Atherton hysteresis model parameters used for estimation of hysteresis losses gives good results for only symmetric hysteresis loops. These parameters have limitations for asymmetric hysteresis loops.Practical implicationsNested GAs are a useful method for optimization when a wide searching area is used.Originality/valueThe originality of the paper is in the establishment of nested GAs and their application in Jiles and Atherton hysteresis model parameters optimization. Also, original is the use of the Jiles and Atherton hysteresis model for hysteresis loop description of soft‐magnetic composite material.

Currently applied Preisach models enable approximations of hysteresis loops with the use of a variable density of domains and complicated distribution functions. An alternative method presented in this paper uses constant distribution of domains in a new, hyperbolic diagram of hysteresis. Such approach restores the original direct relation between the magnetization and the area enclosed in the diagram by an external field, and enables simpler and more accurate modeling of hysteresis.

We describe an accommodation hysteresis model based on a combination of history-dependent and history-independent models. The amount of accommodation is changed by varying the weights of the models employed in the resulting model. We illustrate the operation of the proposed model with accommodating cycles attached to the major loop. The model can be useful in further investigations of the accommodation phenomenon, as we show by using complex trajectories constructed by it. It can be incorporated in magnetodynamic calculations and circuit analysis.

PurposeThe purpose of this paper is to present a procedure, which determines the magnetic force acting between a soft magnetic cylinder and a coil taking the hysteresis phenomena into account.Design/methodology/approachThe magnetic force is computed replacing the ferromagnetic body with an equivalent magnetic moment distribution. Isotropic vector Preisach model with analytical expressed Everett function describes the magnetic properties of the ferromagnetic material. The magnetization distribution is calculated applying the integral equation method. The Preisach hysteresis model is included in the iteration process based on Picard‐Banach scheme.FindingsIn the case of integral equation method the unknown quantities are the magnetization and the magnetic field intensity. In this way the Preisach hysteresis model can be included in a convenient way in the iteration procedure. Knowing the magnetization distribution the magnetic force can be determined. The developed algorithms can be applied in tubular linear motor design.Originality/valueThe paper presents a new formulation of the Preisach hysteresis model. With the aim of the analytically expressed Everett function a stable and faster algorithm can be realized to determine the magnetic force in arrangements with ferromagnetic parts.

First-order reversal curve (FORC) and remanence-based Preisach diagrams are alternative ways of determining the Preisach distribution of a sample, which incorporates information about the coercivity spectrum and the distribution of interactions and self-demagnetizing fields. We compare results of the two methods for well-characterized synthetic and natural samples containing single-domain (SD) and pseudo-SD (PSD) magnetite, maghemite, titanomagnetite and titanomaghemite. The greater time requirements of remanence as opposed to in-field measurements limited our Preisach diagrams to a few hundred points, compared to several thousand points for the corresponding FORC diagrams. Only minimal smoothing could be applied in order to limit the regions near the axes of the diagrams in which function values must be extrapolated. In spite of these restrictions, we find excellent agreement between the essential features of the distributions determined by the two methods. The main features, the location and spreading of the distribution peak, are very consistent. However, the low-coercivity part of the Preisach distribution is sometimes poorly resolved or not imaged at all for remanence-only measurements. Features in this region can be diagnostic of PSD and multidomain (MD) grains. The essential agreement between our FORC and Preisach diagrams in the region where they overlap justifies using the much faster FORC routine instead of traditional remanence-based Preisach methods to determine the Preisach distribution of palaeomagnetic samples without strong interactions. We propose a symmetric FORC protocol that would permit separation of the irreversible and reversible parts of the Preisach distribution. The irreversible part is what is determined by remanence-only methods and what is desired for characterization of the remanence behaviour of palaeomagnetic samples. The reversible part is most significant in detecting MD behaviour and screening out samples containing large PSD and MD grains.

A new neural networks dynamic hysteresis model for piezoceramic actuator is proposed by combining the Preisach model with diagonal recurrent neural networks. The Preisach model is based on elementary rate-independent operators and is not suitable for modeling piezoceramic actuator across a wide frequency band because of the rate-dependent hysteresis characteristic of the piezoceramic actuator. The structure of the developed model is based on the structure of the Preisach model, in which the rate-independent relay hysteresis operators (cells) are replaced by the rate-dependent hysteresis operators of first-order differential equation. The diagonal recurrent neural networks being modified by an adjustable factor can be used to model the hysteresis behavior of the pizeoceramic actuator because its structure is similar to the structure of the modified Preisach model. Therefore, the proposed model not only possesses that of the Preisach model, but also can be used for describing its dynamic hysteresis behavior. Through the experimental results of both the approximation and the prediction, the effectiveness of the neural networks dynamic hysteresis model for the piezoceramic actuator is demonstrated.

This paper presents a method for modeling symmetric minor loops in hysteretic magnetic media. The method employs symmetric minor loops combined with certain segments of the initial magnetization curve to identify the classical Preisach model. The proposed method is simple and effective. It exploits the symmetric positions of the reversal points lying on the initial magnetization curve and, therefore, guarantees monotonic symmetric change of the Preisach model input used in the calculation of the Everett function. A further advantage of the method is that it permits the use of the numerical Preisach model and omits the need of higher-order reversal curves. The method is applied to the prediction of symmetric minor loops of semi-hard magnetic material by using the classical scalar Preisach model. The simulation and measurement results show the high accuracy of the method and validate the proposed approach.

Many systems with hysteresis are adequately represented by the Preisach model. Hysteresis in these systems can be very effectively reduced using the “phaser”, an ideal frequency domain operator, in a feedback connection. The position stability of this type of control has not yet been established in spite of the experimental evidence that the resulting systems are stable. This paper shows the dissipativity for the relay operator, for the Preisach model, and then for the lead approximation to the phaser. We then give a proof of stability for the feedback connection of this phaser approximation with systems represented by the Preisach model of hysteresis.

Hysteresis poses a challenge for control of smart actuators. A fundamental approach to hysteresis control is inverse compensation. For practical implementation, it is desirable for the input function generated via inversion to have regularity properties stronger than continuity. In this paper, we consider the problem of constructing right inverses for the Preisach model for hysteresis. Under mild conditions on the density function, we show the existence and weak-star continuity of the right-inverse, when the Preisach operator is considered to act on Holder continuous functions. Next, we introduce the concept of regularization to study the properties of approximate inverse schemes for the Preisach operator. Then, we present the fixed point and closest-match algorithms for approximately inverting the Preisach operator. The convergence and continuity properties of these two numerical schemes are studied. Finally, we present the results of an open-loop trajectory tracking experiment for a magnetostrictive actuator.

The relaxation dynamics of collections of interacting, thermally activated, two-level subsystems are shown to be characterized by nonequilibrium ageing and memory effects which are analogous to those observed in magnetic systems where randomness and frustration yield a collectively frozen magnetic state with spin-glass-like correlations. Numerical simulations of these nonequilibrium relaxation effects are presented and compared with measurements performed on assemblies of nanodimensional magnetic particles, and their physical origins, as well as their relationship to genuinely collective nonequilibrium relaxation phenomena, are discussed within a theoretical framework based on the Preisach model of hysteresis.

The perovskite (La0.2Nd0.8)0.67Pb0.33MnO3 (LNPMO) with a Curie temperature TC=220K is characterized by measuring the zero field cooled (ZFC) and field cooled (FC) moments over a wide range of temperature 2K

The Jiles–Atherton and the Preisach models are extended and employed in the rate-type constitutive equations of magnetoelastic materials. These models have individual advantages in applicable materials, suitability of numeric calculations, easiness of parameter identification, etc. From the comparison of the induced stress magnetization effects, it is proved that the constitutive equations maintain the original magnetization characteristics and can unifiedly describe the various magnetoelastic behaviors. In particular, it is confirmed that the constitutive equations with the extended Preisach model can express the stress magnetization curve of nickel more accurately than the one with the extended Jiles–Atherton model.

In this paper a thermodynamic model with internal variables is presented and applied to ferromagnetic hysteresis. The out-of-equilibrium Gibbs free energy of a magnetic system is expressed as a function of the internal state of the Preisach model. Expressions for the system entropy and the entropy production are derived. By this approach it is possible to reproduce the characteristic features of the experimentally observed temperature changes (of the order of 10 - 4 K around room temperature) induced by the magnetic field along the hysteresis loop performed in iron under adiabatic condition.

A review of recent advances in the area of hysteretic nonlinearities driven by di.usion processes is presented. The analysis of these systems is based on the Preisach formalism for the description of hysteresis to represent complex nonlinearities as a weighted superposition of rectangular loops. The mathematical theory of di.usion processes on graphs is then applied to solve problems for stochastically driven hysteresis loops. Closed form expressions for the expected value and spectral density of the output are obtained, and sample computations for these quantities are presented. Because of the universality of the Preisach model, this approach can be used to investigate stochastic aspects in hysteretic systems of various physical origins.

In this paper a new model of hysteresis is described. This new model allows to describe a wider class of rate independent hystereses than the previous Classic and nonlinear Preisach models. The broader area of applicability arises from the relaxation of the minor loops equal chord requirement by introducing a less stringent property SVEC(same-vertexes-equal-chords). The new model allows one to fit n -order transition curves, whereas the former models allow only for fitting of first and second-order transition curves. Due to this fact this new model improves upon existing results. The model structure has been developed to be easily implemented in inverse hysteresis control schemes, widely used for hysteretic systems regulation.

In this article, the polarisation kinetics of an electrically connected ferroelectric bimorph structure is described with an electric model by means of equivalent circuit analysis. This model results in a system of ordinary differential equations (ODEs) that can be solved numerically. A bimorph model structure consisting of wire-connected layers of barium–titanate–stannate ceramics was poled. The conductivities of the layers can be estimated by comparing of the measured electric field in the layers and the results of the poling model. In order to consider hysteretic effects, the Preisach model of hysteresis is included into the poling model. Within the ODEs, the slope of the hysteresis loop is needed. An algorithm for estimating it via the Preisach model was developed. This approach is based upon linear interpolation between adjacent grid points of the discretised electric field within the Preisach model. An example shows the capabilities of this method for considering poling, switching effects and depolarisation.

We present a new identification procedure for a hysteresis model based on nonlinear circuit cells. The response of elementary cells is equal to a generalized play operator. The procedure identifies exactly the limit symmetric hysteresis loop and can minimize the reconstruction error on minor loops. We present test cases for three different soft magnetic materials with peculiar behavior and we discuss the results.

The Preisach operator and its variants have been successfully used in the modeling of hysteresis observed in ferromagnetic, magnetostrictive, and piezoelectric materials. However, in designing with these "smart" materials, one has to determine a density function for the Preisach operator by using the input-output behavior of the material at hand. In this paper, we describe a method for numerically determining an approximation of the density function when there is not enough experimental data to uniquely solve for the actual density function by Mayergoyz's method. We present theoretical justification for our method by establishing links to regularization methods for ill-posed problems. We also present numerical results where we estimate an approximate density function from data published in the literature for a magnetostrictive actuator and two electroactive polymers.

The control accuracy of smart actuators, such as a shape memory alloy (SMA) or piezoceramic actuator, is limited due to their inherent hysteresis nonlinearities with a local memory, resulting from the influence of a previous input on subsequent behavior. In addition, the existence of minor loops in the major loop because of a local memory also makes the mathematical modeling and design of a controller difficult for SMA actuators. Therefore, to enhance the controllability of a smart actuator, the Preisach hysteresis model has emerged as an appropriate behavioral model, yet the modeling is difficult and the model equation complex. Accordingly, to resolve these difficulties, the current paper proposes a simple method based on applying the proportional relationship between the major loop and the FOD curves of an SMA actuator to the Preisach model. As such, using only data for the major hysteresis loop, the proposed method enables the FOD curves to be easily approximated and the output length rapidly computed. The efficacy of the proposed Preisach modeling method is confirmed based on comparative experiments with the classical Preisach model.

The samples Sr1−xCaxRuO3 (x = 0.0, 0.2, 0.6) have been synthesized by a solid state reaction, and characterized by the zero field cooled (ZFC), field cooled (FC) magnetic moments and the major hysteresis loops. The data have been analyzed within the framework of a generalized Preisach model, which includes thermal fluctuations, critical phenomenon, and temperature dependent distribution of free energy barriers. The model provides an excellent description of the experimental data, and the simulating results are in good agreement with the experiment results. All the ZFC/FC curves at different applied fields and all the major hysteresis loops at different temperatures can be replicated by the model with one set of parameters. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Hysteretic behavior of polarized piezoelectric materials is of importance in the context of high power electro-mechanical transduction. The main goal of this article is to combine the Tiersten theory of electroelasticity and a Preisach model of hysteresis to model a simple force loaded piezoelectric actuator. The proposed theory of piezo-ferro-elasticity extends the derivation of Tiersten and Huang to the case of an arbitrary polarization direction in the ferroelectric domain. The general model is subsequently reduced to a mono-dimensional stack actuator under low operating voltage; therefore, the modeling focuses on minor loop modeling around the initial state of polarization. The model of hysteresis between polarization and electric field proposed here takes into account the nonlocal (macroscopic) memory of a piezoelectric ceramic by the use of a Preisach model. The Preisach model of hysteresis and the set of new ferro-electro-elastic constants that account for the irreversible relation between electric field and polarization are identified through experiments. The nonlinear model successfully reproduces the nonlinear dependence of generated displacements and forces as a function of applied electric field. Possible applications of this work involve nonlinear actuator behavior in the active control of vibration.

In this paper we use a Reduced Vector Preisach Model for a preliminary analysis of rotating hysteresis in laminated Si–Fe steels. After the description of the main facts about the vectorial hysteresis modeling and the formulation of the cross coupling Preisach functionals, we present here a numerical technique for the identification of the model using the hard and easy axis measurements. An applicative example for non oriented grain steels is presented.

The product model of magnetic hysteresis was proposed as a modification of the Preisach model in order to eliminate some shortages of the traditional model. The main novelty of the product model was the emphasis on the differential susceptibility of magnetization curves, namely the introduction of an output-dependent limiting multiplier function. With this the magnetization curve can be described with an indirect mathematical function, whose argument contains the terms of the reversible and the hysteretic irreversible contribution of the magnetization. Experimental data suggest that the Brillouin function is a proper envelope of the indirect function. Fitting procedures and examples of evaluation of experimental data are presented.

The present work proposes a simple magnetic system as a candidate for a Standard Problem for Preisach-based models. The system consists in a regular square array of magnetic particles totally oriented along the direction of application of an external magnetic field. The behavior of such system was numerically simulated for different values of the interaction between particles and of the standard deviation of the critical fields of the particles. The characteristic parameters of the Preisach moving model were worked out during simulations, i.e., the mean value and the standard deviation of the interaction field. For this system, results reveal that the mean interaction field depends linearly on the system magnetization, as the Preisach moving model predicts. Nevertheless, the standard deviation cannot be considered as independent of the magnetization. In fact, the standard deviation shows a maximum at demagnetization and two minima at magnetization saturation. Furthermore, not all the demagnetization states are equivalent. The plot standard deviation vs. magnetization is a multi-valuated curve when the system undergoes an AC demagnetization procedure. In this way, the standard deviation increases as the system goes from coercivity to the AC demagnetized state.