Preisach Model Research Articles

Identification of the scalar Preisach model with a single branch of descending hysteresis loop and numerical interpolation for the electrical steel sheet lamination with soft magnetic properties

The developed scalar Preisach model predicts the hysteresis behavior of the soft magnetic, electrical steel sheet. The experimental hysteresis loops of the electrical steel lamination prepare the Everett function required to predict the hysteresis behavior of the electrical steel lamination. We obtain the Everett function in two ways, from the series of minor loops and a single descending branch of a hysteresis loop. The Everett function has a closed algebraic form in the method using the minor loops. A genetic algorithm carries out the subsequent fitting based on the closed algebraic equation and optimization; however, the calculated flux values have highly deviated from the measured values. In another way, the Everett function consists of numerically driven Fs and B factorable functions. The values extracted from a limiting hysteresis loop determine the function Fs and B. The predicted values are correct, and the proposed method for determining the Everett function is only valid for soft magnetic materials representing symmetric and non-exchange-bias hysteresis behavior. While the method has application limitations to general magnetic hysteresis, it demonstrates the validity of using a function derived from experimentally measured hysteresis loops rather than a closed-algebraic equation to determine the Everett function. With the Everett surface the Preisach distribution function (PDF) is numerically derived and represents the difference in domain structure between two specimens.

Piecewise Linear Modeling for Inrush Safety Regions Detection and Its Validation Through a Preisach Model and Experimental Data

An alternative modeling approach to detect the occurrence of Inrush currents in power transformers, is discussed. The inrush current phenomenon is affected by the core <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">residual</i> magnetizazion <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J_r</i> and voltage source <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">initial phase</i> , θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> , through which a region in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J_r</i> – θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> plane where inrush currents doesn’t occur (named Inrush Safety Region - ISR) is defined. The approach is founded on the awareness that a fairly accurate description of the inrush process does not require a detailed description of core magnetization process, leading to the employment of a Piecewise linear magnetization model, able to detect in a straightforward way the ISR. The main advantage of the approach is to set up a fast algorithm for ISR detection, suitable for a real-time control. An accurate model of the transformer, based on a Preisach model magnetization algorithm has been exploited, along with a suitable set of experimental results allow to confirm the validity of the proposed identification approach.

Adaptive Pseudoinverse Control for Constrained Hysteretic Nonlinear Systems and its Application on Dielectric Elastomer Actuator

Flexible smart material actuators, such as dielectric elastomer actuators (DEA) and ionic polymer metal composites, have shown greatly potential applications in the field of soft biomimetic robots and rehabilitation robots due to their human-like muscle softness, large stretch, and high energy density characteristics. In this article, a fuzzy logic system (FLS) and barrier Lyapunov function (BLF) based adaptive pseudoinverse control scheme is proposed for a class of state-constrained hysteretic nonlinear systems, where all the states are always strictly limited in each constrained set. The main features of this article are: 1) the hysteresis nonlinearity in the actuators is considered and mitigated by the proposed pseudoinverse control algorithms, which implies that the direct hysteresis inverse model is not required, instead a searching mechanism of the actual control signal from the temporary control signal; 2) the all-state-constrained control problem of the Preisach hysteresis model is overcome when the control signal is coupled in the double integral functions with the aid of an FLS, BLFs, and the proposed hysteresis pseudoinverse algorithms; and 3) the DEA-based motion control platform is constructed, and the experiments are conducted to validate the effectiveness of our proposed control scheme.

Hysteresis and Loss Characteristics of Soft Magnetic Materials Based on Nonlinear Preisach Model

Hysteresis and Loss Characteristics of Soft Magnetic Materials Based on Nonlinear Preisach Model

Harmonic and DC Bias Hysteresis Characteristics Simulation Based on an Improved Preisach Model.

Transformers, reactors and other electrical equipment often work under harmonics and DC-bias working conditions. It is necessary to quickly and accurately simulate the hysteresis characteristics of soft magnetic materials under various excitation conditions in order to achieve accurate calculations of core loss and the optimal design of electrical equipment. Based on Preisach hysteresis model, a parameter identification method for asymmetric hysteresis loop simulation is designed and applied to the simulation of hysteresis characteristics under bias conditions of oriented silicon steel sheets. In this paper, the limiting hysteresis loops of oriented silicon steel sheets are obtained through experiments under different working conditions. The first-order reversal curves(FORCs) with asymmetric characteristics is generated numerically, and then the Everett function is established under different DC bias conditions. The hysteresis characteristics of the oriented silicon steel sheets under harmonics and DC bias are simulated by improving FORCs identification method of the Preisach model. By comparing the results of simulation and experiment, the effectiveness of the proposed method is verified, so as to provide an important reference for material production and application.

Precision Motion Control of a Piezoelectric Actuator via a Modified Preisach Hysteresis Model and Two-Degree-of-Freedom H-Infinity Robust Control.

The nonlinear hysteresis phenomenon can occur in piezoelectric-driven nanopositioning systems and can lead to reduced positioning accuracy or result in a serious deterioration of motion control. The Preisach method is widely used for hysteresis modeling; however, for the modeling of rate-dependent hysteresis, where the output displacement of the piezoelectric actuator depends on the amplitude and frequency of the input reference signal, the desired accuracy cannot be achieved with the classical Preisach method. In this paper, the Preisach model is improved using least-squares support vector machines (LSSVMs) to deal with the rate-dependent properties. The control part is then designed and consists of an inverse Preisach model to compensate for the hysteresis nonlinearity and a two-degree-of-freedom (2-DOF) H-infinity feedback controller to enhance the overall tracking performance with robustness. The main idea of the proposed 2-DOF H-infinity feedback controller is to find two optimal controllers that properly shape the closed-loop sensitivity functions by imposing some templates in terms of weighting functions in order to achieve the desired tracking performance with robustness. The achieved results with the suggested control strategy show that both hysteresis modeling accuracy and tracking performance are significantly improved with average root-mean-square error (RMSE) values of 0.0107 μm and 0.0212 μm, respectively. In addition, the suggested methodology can achieve better performance than comparative methods in terms of generalization and precision.

Analysis and Compensation of Hysteresis Effect on Electromagnetic Force in Axial Magnetic Bearings

Magnetic bearings (MBs) enable the rotor to run at high speed without lubrication due to no mechanical contact. However, the inherent hysteresis of ferromagnetic materials affects the support characteristics, reducing the design performance and stability margin of MBs, especially for axial MBs using materials with high coercive force. To analyze and compensate for the hysteresis effect on the electromagnetic force in axial MBs, an efficient method is proposed in this paper. Firstly, the hysteresis properties of the ferromagnetic materials are simulated by the Preisach model, and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> relationships under any external magnetic field can be determined. Taking into account the non-ideal factors such as hysteresis and saturation effects, the nonlinear magnetic circuit model of the axial MBs is established. The magnetic flux density working point under different control currents and eccentric displacements can be determined through iterative calculation, and then the air gap flux density distribution and electromagnetic force of the axial MBs are calculated. On this basis, the adverse effects of hysteresis on the bearing capacity and system stability of axial MBs are analyzed. A compensation algorithm is designed based on the inverse model to reduce the hysteresis effect. The inverse model is approximated modeled by the Lissajous curve. Finally, the proposed analysis and control methods are verified by the finite element method (FEM) or experiments. The results show that the proposed analysis method is capable of accomplishing good accuracy and requires less computation time than FEM, it can be applied to arbitrary current variation processes. In addition, the phase lag of the system is effectively improved with the compensation algorithm.

Review of Hysteresis Models for Magnetic Materials

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.

Everett Map Construction for Modeling Static Hysteresis: Delaunay-Based Interpolant Versus B-Spline Surface

The Everett map is a component used by the Preisach model that stores hysteresis behavior. In magnetics it often contains the characterized magnetic properties of a soft-magnetic material. Fundamentally, the Everett map is created from scattered data points, obtained from a set of magnetic measurements, which must be interpolated to obtain a continuous map. The commonly adopted method to perform the interpolation is based on a Delaunay triangulation computation and subsequent polynomial or B-spline surface fit. However, this approach introduces artifacts in the modeled hysteresis results. Therefore, this work presents an alternative method to construct an artifact free Everett map, by reconstructing a set of measured hysteresis loops with a pre-processing algorithm, and representing the data with a scattered B-spline surface. When applied in the Preisach model, a set of test hysteresis loops was reproduced with high accuracy and without artifacts, compared to the commonly used Delaunay based interpolant.

A Computationally Efficient Compact Model for Ferroelectric Switching With Asymmetric Nonperiodic Input Signals

In this paper, we develop a Verilog-A implementable compact model for the dynamic switching of ferroelectric FinFETs (Fe-FinFETs) for asymmetric non-periodic input signals. We use the multi-domain Preisach Model to capture the saturated P-E loop of the ferroelectric capacitors. In addition to the saturation loop, we model the history dependent minor loop paths in the P-E by tracing input signals’ turning points. To capture the input signals’ turning points, we propose an RC circuit based approach in this work. We calibrate our proposed model with the experimental data, and it accurately captures the history effect and minor loop paths of the ferroelectric capacitor. Furthermore, the elimination of storage of each turning point makes the proposed model computationally efficient compared with the previous implementations. We also demonstrate the unique electrical characteristics of Fe-FinFETs by integrating the developed compact model of Fe-Cap with the BSIM-CMG model of the 7nm FinFET.

Hysteresis Behavior Modeling of Magnetorheological Elastomers under Impact Loading Using a Multilayer Exponential-Based Preisach Model Enhanced with Particle Swarm Optimization.

Magnetorheological elastomers (MREs) are a type of smart material that can change their mechanical properties in response to external magnetic fields. These unique properties make them ideal for various applications, including vibration control, noise reduction, and shock absorption. This paper presents an approach for modeling the impact behavior of MREs. The proposed model uses a combination of exponential functions arranged in a multi-layer Preisach model to capture the nonlinear behavior of MREs under impact loads. The model is trained using particle swarm optimization (PSO) and validated using experimental data from drop impact tests conducted on MRE samples under various magnetic field strengths. The results demonstrate that the proposed model can accurately predict the impact behavior of MREs, making it a useful tool for designing MRE-based devices that require precise control of their impact response. The model's response closely matches the experimental data with a maximum prediction error of 10% or less. Furthermore, the interpolated model's response is in agreement with the experimental data with a maximum percentage error of less than 8.5%.

A Numerical Comparison between Preisach, J-A and D-D-D Hysteresis Models in Computational Electromagnetics

The incorporation of hysteresis models in computational electromagnetic software is of paramount importance for the accurate prediction of the ferromagnetic devices’ performance. The Preisach and Jiles-Atherton (J-A) models are frequently used for this purpose. The former is more accurate and can represent a broad range of magnetic materials, but it is computationally expensive. The latter is more efficient but can accurately model only soft ferromagnetic materials. In this paper, a recently proposed hysteresis model, referred to as the D’Aloia-Di Francesco-De Santis (D-D-D) model, is shown to have the best trade-off between accuracy and computational burden. For the first time, a numerical comparison between the Preisach, J-A and D-D-D models is provided for a large class of hysteresis loops including soft, semi-hard and hard ferromagnetic materials.

Fixed-time adaptive fuzzy control scheme with prescribed tracking accuracy for uncertain nonlinear hysteretic systems

When the Preisach operator, a commonly used hysteresis model, is coupled with uncertain unparametrizable nonlinear dynamics of systems, its tracking control problem in particular with the demands for prescribed tracking accuracy and finite convergence time is challenging, and has not yet been solved in the existing literature. In this study, we focus on the problem, and develop a fixed-time adaptive fuzzy control scheme as a solution to it, based upon a novel decomposition of the Preisach model, the design of a robust control framework, and the integration of a direct adaptive fuzzy control approach. With our scheme, it can be rigorously proved that the tracking error goes to a predefined interval around zero in a bounded convergence time, and all signals in the closed-loop system are bounded. Besides theoretical analysis, the obtained results are also confirmed by experimental tests based on a real-life piezoactuated positioner.

Neural network model for hysteretic characteristic of shape memory alloy

Shape memory alloy has obvious hysteretic characteristics, which is crucial for the utilization of shape memory alloy, so a rational model is needed to describe them. In the current paper, a model for shape memory alloy based on the neural network is established, in which the activation function is modified so that it can naturally describe the hysteretic curve of shape memory alloy. The proposed neural network model is used to simulate temperature-induced hysteresis and stress-induced hysteresis, and the results show that the proposed model has a good effect and has certain adaptability. The reason why the proposed neural network model can describe hysteresis is qualitatively explained, and it is further pointed out that the model can be regarded as a generalized model of the Preisach model. The model is further extended to accommodate hysteretic curves under different conditions. The proposed neural network model has a simple form and high accuracy, especially in comparison with traditional models, and can be used for the modelling of shape memory alloys or other materials with hysteretic characteristics.

Review of Play and Preisach Models for Hysteresis in Magnetic Materials

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.

Simulation for pulse discharge performance of antiferroelectric capacitors

The discharge performance of antiferroelectric (AFE) capacitors is complicated and difficult to simulate due to the nonlinear polarization behavior of AFE. In this work, a nonlinear model for pulsed discharge AFEs was proposed based on a combination of the Preisach model and Kirchhoff’s law. The model was driven by the data from first-order reversal curves and direct-current-bias (DC-bias) dielectric test measurements. Thus, the discharge behavior of the AFE can be studied without actual discharge experiments. Specifically, AFE discharge waveforms were calculated and evaluated for different size parameters and external circuit parameters that were conducive to compare the properties of different AFE materials. Moreover, the size effect of the capacitor on the discharge performance was discussed, which should draw the attention of researchers to prevent exaggerated conclusions. As a consequence, this method would fill the gap of AFE discharge simulation.

Comparison between different models of magnetic hysteresis in the solution of the TEAM 32 problem

AbstractThe numerical modeling of magnetic materials in simulators is a difficult task, above all in real devices with specific excitation. The aim of this work is to compare the accuracy of scalar and vector Preisach models in a well know test benchmark: the TEAM 32 problem. The availability of measured data for this benchmark test and the simple geometry allow us to build hysteresis models and to test them in a 2D finite element analysis (FEA) scheme. The specific numerical formulation of each hysteresis model implemented is described, including the technique for the numerical identification of parameters starting from measured data. The comparison among the models is done in terms of accuracy, but also in terms of easy implementation in the FEA scheme and of computational cost.

Deep neural networks for the efficient simulation of macro-scale hysteresis processes with generic excitation waveforms

An effective and performing hysteresis model, based on a deep neural network, with the capability to reproduce the evolution of magnetization processes under arbitrary waveforms of excitation is here presented. The proposed model consists of a standalone multi-layer feed-forward neural network, with reserved input neurons for the past values of both the input (H) and output (M), aiming at the reproduction of the storage mechanism typical of hysteretic systems. The training set has been opportunely prepared starting from a set of simulations, performed by the Preisach hysteresis model. The optimized training procedure, based on multi-stage check of the model performance, will be comprehensively discussed. The comparative analysis between the neural network-based model, implemented at low level of abstraction, and the Preisach model covers additional hysteresis processes, different from those involved in the training. The mild/moderate memory requirement and the significant computational speed make the proposed approach suitable for a future coupling with finite-element analysis.

Using Preisach Theory to Evaluate Chemical Remanent Magnetization and Its Behavior During Thellier‐Thellier‐Coe Paleointensity Experiments

AbstractThe behavior of grain‐growth chemical remanent magnetizations (gCRM) are investigated for different coercivity and magnetostatic‐interaction‐field distributions and acquisition conditions using a thermally activated Preisach model for assemblages of interacting single‐domain grains. A new growth‐rate dependent equation was derived, from which it was found that gCRM intensity is over 10% more sensitive to growth rate than previously modeled. We compare the gCRM results to the behavior of thermoremanences (TRM). gCRMs are two times more sensitive to changes in coercivity distribution, whereas TRMs are four times more sensitive to changes in magnetostatic interactions. The Thellier‐Thellier‐Coe paleointensity protocol was simulated in Preisach space, and gCRMs were found to produce concave‐up Arai plots with pTRM checks which plot to the left of the Arai plot and positive partial‐TRM tail checks that increase with magnetostatic interactions. This often leads to the failure of selection criteria, but high‐temperature segments can pass the criteria for weakly interacting gCRMs; these estimates can underestimate the field by up to 66%.

A Simple Model of the Energy Harvester within a Linear and Hysteresis Approach.

In this article, a model of an energy harvester, the mechanical part of which is an inverted pendulum, is proposed. We investigated the stability of a linearized system. It was proven that the stabilizing control of the pendulum, based on the feedback principle, enables the stabilization of the system. We have identified the zones of stability and the amplitude-frequency characteristics. In the second part of this article, a generalization of the dynamic system for the case of the hysteresis friction in the mechanical joint is considered. The role of nonlinear effects within the design Preisach model and the phenomenological Bouc-Wen model is shown.