Classical Preisach Model Research Articles

Modeling hysteresis in piezoelectric actuators using NARMAX models

This paper presents a non-linear moving average model with exogenous inputs (NMAX) and a non-linear auto-regressive moving average model with exogenous inputs (NARMAX) respectively to model static and dynamic hysteresis inherent in piezoelectric actuators. The modeling approach is based on the expanded input space that transforms the multi-valued mapping of hysteresis into a one-to-one mapping. In the expanded input space, a simple hysteretic operator is proposed to be used as one of the coordinates to specify the moving feature of hysteresis. Both the modified Akaike's information criterion (MAIC) and the recursive least squares (RLS) algorithm are employed to estimate the appropriate orders and coefficients of the models. The advantage of the proposed approach is in the systematic design procedure which can on-line update the model parameters so as to accommodate to the change of operation environment compared with the classical Preisach model. Moreover, the obtained model is non-linear in variables but linear in parameters so that it can avoid the problem of sticking in local minima which the neural network based models usually have. The results of the experiments have shown that the proposed models can accurately describe static and dynamic behavior of hysteresis in piezoelectric actuators.

Leveraging the Equivalence of Hysteresis Models From Different Fields for Analysis and Numerical Simulation of Jointed Structures

An important problem that spans across many types of systems (e.g., mechanical and biological) is how to model the dynamics of joints or interfaces in built-up structures in such a way that the complex dynamic and energy-dissipative behavior that depends on microscale phenomena at the joint/interface is accurately captured, yet in a framework that is amenable to efficient computational analyses of the larger macroscale system of which the joint or interface is a (spatially) small part. Simulating joint behavior in finite element analysis by meshing the joint regions finely enough to capture relevant micromechanics is impractical for large-scale structural systems. A more practical approach is to devise constitutive models for the overall behavior of individual joints that accurately capture their nonlinear and energy-dissipative behavior and to locally incorporate the constitutive response into the otherwise often-linear structural model. Recent studies have successfully captured and simulated mechanical joint dynamics using computationally simple phenomenological models of combined elasticity and slip with associated friction and energy dissipation, known as Iwan models. In the present article, the author reviews the relationship, and in some cases equivalence, of one type of Iwan model to several other models of hysteretic behavior that have been used to simulate a wide range of physical phenomena. Specifically, it is shown that the “parallel-series” Iwan model has been referred to in other fields by different names, including “Maxwell resistive capacitor,” “Ishlinskii,” and “ordinary stop hysteron.” Given this, the author establishes the relationship of this Iwan model to several other hysteresis models, most significantly the classical Preisach model. Having established these relationships, it is then possible to extend analytical tools developed for a specific hysteresis model to all of the models with which it is related. Such analytical tools include experimental identification, inversion, and analysis of vibratory energy flow and dissipation. Numerical case studies of simple systems that include an Iwan-modeled joint illustrate these points.

Plane Wave Model for the Electromagnetic Behavior of SiFe Alloys

We present a model that evaluates in the frequency domain the magnetic behavior of laminated SiFe alloys caused by a magnetic field imposed at the material edge. The model is based on plane wave theory describing how an electromagnetic wave penetrates a material. As the nonlinear material with hysteresis can cause harmonic frequency components of the field and induction inside the material, the model takes into account several harmonics simultaneously by applying the harmonic balance principle. The plane wave model is solved iteratively with a classical Preisach model as constitutive law. We compare the model with a time domain finite-element model and with measurements on a ring core and find a good correspondence. The CPU time is low if only a few harmonics are considered and if the nonlinearity of the material is rather mild.

Properties of a class of vector hysteron models

In this paper we present a vector hysteron model, which is a generalization in three dimensions of the classical scalar Preisach model and an extension to the radial vector model previously published. We show that the vector model satisfies the second principle of thermodynamics. In addition the properties of the vector deletion and congruency are discussed. An example applied to a Si–Fe commercial steel is presented.

A first order reversal curve investigation of pressure hysteresis in multiferroics spin transition compound

Spin crossover multiferroic [Fe(PM-BiA)2(NCS)2] is investigated for the first time with the first order reversal curve (FORC) diagram method for its hysteretic pressure behavior. The experimental setup allows the measurements of the high spin fraction as the function of temperature, light intensity, and pressure. The experimental FORC diagrams obtained in compression and releasing modes show significant differences which are in disagreement with the classical Preisach model. Also, stronger kinetic effects are evidenced in the compression mode and possible explanations of this effect considering the viscoelastic behavior are provided.

Hysteresis compensation of smart actuators under variable stress conditions

A new model able to describe magnetostriction for slowly varying mechanical load is presented. The model and its pseudo-compensator exploit the formalism of the classical Preisach model and is therefore easy to implement and well behaved. Experimental results showing the encouraging performances of the approach are provided.

Hysteresis model of magnetostrictive actuators and its numerical realization

This paper presents two numerical realization of Preisach model by Density Function Method (DFM) and F Function Method (FFM) for a giant magnetostrictive actuator (GMA). Experiment and simulation showed that FFM is better than DFM for predicting precision of hysteresis loops. Lagrange bilinear interpolation algorithm is used in Preisach numerical realization to enhance prediction performance. A set of hysteresis loops and higher order reversal curves are predicted and experimentally verified. The good agreement between the measured and predicted curves shows that the classical Preisach model is effective for modelling the quasi-static hysteresis of the GMA.

Element-Free Galerkin Modeling of Electromagnetic Phenomena in Ferromagnetic Deformable Bodies

In this paper, the element-free Galerkin method is employed for evaluating eddy current distribution in ferromagnetic media, whose cross-section is subjected to an imposed time-dependent homothetic transformation and to a time-varying magnetic flux. A step-by-step procedure is used for handling the transient evolution. The extension to nonlinear and hysteretic media is realized adopting the fixed point scheme and the classical Preisach model

Internal model control for shape memory alloy actuators using fuzzy based Preisach model

This paper investigates a possible application of Preisach model to control shape memory alloy (SMA) actuators using an internal model control strategy. The developed strategy consists in including the Preisach hysteresis model of SMA actuator and the inverse Preisach model within the control structure. In this work, an extrema input hystory and a fuzzy inference is utilized to replace the classical Preisach model. This allows to reduce a large amount of experimental parameters and computation time of the classical Preisach model. To demonstrate the effectiveness of the proposed controller in improving control performance and hysteresis compensation of SMA actuators, experimental results from real time control are presented.

Modeling and compensation of piezoceramic actuator hysteresis for helicopter vibration control

Hysteresis in piezoceramic materials causes considerable complications in the use of piezo actuators in applications, such as vibration control. In this study, the classical Preisach model is used to characterize the hysteresis in a piezostack actuator used to move a trailing-edge flap for helicopter vibration control. The hysteresis in the actuator is primarily due to material nonlinearity and to a lesser extent due to losses in the amplification mechanism. Most helicopter vibration control studies ignore the effect of the hysteresis on the actuator performance. The desired motion of the flap for maximum reduction in vibration is determined using an aeroelastic analysis of the helicopter. Numerical results indicate that complete compensation of actuator hysteresis can result in up to 90% reduction in helicopter vibrations. The performance of the vibration control system deteriorates considerably when the actuator is represented by a linear model or when the compensator is based only on the primary material hysteresis of the actuator. Complete compensation of both material and mechanical hysteresis in the actuator is therefore critical to the performance of the trailing-edge flap vibration control system in a helicopter.

Effect of Piezoelectric Hysteresis on Helicopter Vibration Control Using Trailing-Edge Flaps

This study investigates the effect of piezoelectric actuator hysteresis on helicopter vibration control using trailingedge flaps. An aeroelastic analysis is used represent the helicopter with trailing-edge flaps. A compressible unsteady aerodynamic model is used to predict the incremental airloads due to trailing-edge flap motion. The material and mechanical hysteresis in the piezoelectric actuator is modeled using the classical Preisach model. Experimental data from the literature are used to estimate the weighting function through geometric interpretation and numerical implementation. Results are obtained from vibration control studies performed using a trailing-edge flap with 1) ideal linear actuator and 2) real actuator with hysteresis modeled. Multicyclic control input gives 90 and 81% reduction in hub vibration at high-speed flight $(\mu = 0:30)$ for the ideal and real actuator, respectively. In low-speed flight $(\mu = 0:15)$, the hub vibration is reduced by 99 and 86% for ideal and real actuator, respectively. Results indicate that the presence of actuator hysteresis nonlinearity leads to deterioration in controller performance and lower vibration reductions in both high- and low-speed forward flight.

Element-free galerkin method in eddy-current problems with ferromagnetic media

This paper focuses on the application of the element-free Galerkin method to the solution of eddy-current problems in ferromagnetic media. The method is first validated by comparison with an analytical linear solution, discussing the role of the numerical parameters that affect the solution accuracy. Then, the application is extended to nonlinear and hysteretic media, adopting the fixed point iterative scheme and the classical Preisach model. The proposed method is also tailored for nonhomogenous structures. The merits and drawbacks with respect to a finite-element approach are discussed for all the considered problems.

Magnetic energy and radial vector model of hysteresis

In this paper we discuss some properties of the radial vector model (RVM) proposed as a three-dimensional extension of the classical scalar Preisach model (CSPM). In particular, we prove that the irreversible model of magnetization of the RVM is consistent with the conservation of magnetic energy and with the second law of thermodynamics. The model continues to have these properties even when a reversible component of magnetization is added to the magnetization.

Dynamic vector hysteresis modeling

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.

Inclusion of a stress‐dependent Preisach model in 2D FE calculations

PurposeMechanical stress can heavily affect the magnetic behaviour law in ferromagnetic materials. This paper, aims to take into account the effect of mechanical stress into a hystreresis model. This model is implemented in a finite element analysis code and tested in the case of a simple system.Design/methodology/approachA simple extension of the classical Preisach model is proposed, in which a function linked to the Preisach density is parameterized using the mechanical stress as a supplementary parameter. The methodology is based on experimental measurements for identifying the required function. As a first approach, a linear interpolation is used between the measurements in order to have a continuous evolution of the magneto‐mechanical behaviour. This model has been tested in the case of a steel sheet in which width is not constant in order to obtain a non‐uniform distribution of stress and magnetic flux density.FindingsThe model can predict the magneto‐mechanical behaviour with a good accuracy in the case of tensile stress. Implementation of the model in finite element analysis has shown that the model can predict the behaviour of steel sheet subject to a non‐uniform stress distribution.Originality/valueThis paper shows that a classical hysteresis model can be extended to take into account the magneto‐mechanical behaviour. This is useful for the design of electrical machines which are subject to non‐negligible mechanical stress.

Characterization of static hysteresis models using first-order reversal curves diagram method

First-Order Reversal Curves (FORC) diagram method is known as a non-parametrical identification method for the Classical Preisach Model. However, the FORC diagram is used for material characterization and can be simulated by any hysteresis model. In this paper we analyze the possibility to use FORC diagrams for the identification of the hysteresis models parameters and the limits of this approach.

A neuro-fuzzy-based Preisach approach on hysteresis modeling

Most of the present identification techniques of the Preisach model rely on a fairly large amount of experimental data. This paper proposes a method that utilizes the available data in the major loop and omits the need of measuring the first-order reversal curves. The method models hysteresis by applying the classical Preisach model whose identification procedure is performed by the utility of neuro-fuzzy approximators. The method is applied to the prediction of cyclic minor loops of a soft magnetic composite. The simulation and measurement results show the good accuracy of the method and validate the proposed approach.

Hysteresis modeling based on symmetric minor loops

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.

Tracking Control of a Piezoceramic Actuator With Hysteresis Compensation Using Inverse Preisach Model

This paper presents the classical Preisach hysteresis modeling and tracking control of a curved pre-stressed piezoceramic patch actuator system with severe hysteresis. The actuator is also flexible with very small inherent damping. It has potential applications in active antennas. A series of tests are conducted to study the hysteresis properties of the piezoceramic actuator system. The numerical expressions of the classical Preisach model for different input variations are presented. The classical Preisach model is applied to simulate the static hysteresis behavior of the system. Higher order hysteresis reversal curves predicted by the classical Preisach model are verified experimentally. The good agreement found between the measured and predicted curves showed that the classical Preisach model is an effective mean for modeling the hysteresis of the piezoceramic actuator system. Subsequently, the inverse classical Preisach model is established and applied to cancel the hysteresis the piezoceramic actuator system for the real-time microposition tracking control. In order to improve the control accuracy and to increase damping of the actuator system, a cascaded PD/lead-lag feedback controller is designed with consideration of the dynamics of the actuator. In the experiments, two cases are considered, control with major loop hysteresis compensation, and control with minor loop hysteresis compensation. Experimental results show that RMS tracking errors are reduced by 50% to 70% if the hysteresis compensation is added in the feedforward path in both cases. Therefore, hysteresis compensation with the feedback controller greatly improves the tracking control accuracy of the piezoceramic actuator.

Fast Preisach modeling method for shape memory alloy actuators using major hysteresisloops

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