Phenomenological Hysteresis Model Research Articles

Reluctance Network Model of IPM Motor Representing Dynamic Hysteresis Characteristics for High-Accuracy Iron Loss Calculation Considering Carrier Harmonics

It is essential to establish a simple and practical method for quantitatively estimating the iron loss considering the dynamic hysteresis behavior to further improve the efficiency of electric machines. In a previous study, a novel simple magnetic circuit model representing the dynamic hysteresis characteristics was presented by incorporating a play model, one of the phenomenological dc hysteresis models, and a Cauer circuit, which can consider the skin effect. It was demonstrated that this magnetic circuit model could accurately calculate the hysteresis loops and iron loss even under PMW excitation for magnetic reactors made of several types of core materials in a short time. However, this method can only be used for an object with a simple shape, such as a ring core. Hence, this paper describes that the previously proposed magnetic circuit model is extended to a reluctance network analysis (RNA) to expand the application range. Furthermore, the proposed method was experimentally validated using an interior permanent magnet (IPM) synchronous motor driven by a PWM converter as the examination target.

An analytical formula to identify the parameters of the energy-based hysteresis model

Energy-based models (also called Vector Play models) are a class of phenomenological models of magnetic hysteresis. In this work an original identification method is presented. The main advantage of this method is its speed and its robustness. Conversely to optimization-based methods, which are prone to convergence problems, the new method is based on analytical formulas. The method is tested experimentally with three different materials (a ferrite and two non oriented steels), and provide an accuracy comparable to classical identification methods, with a much lower computational cost.

A dynamic hysteresis model based on Landau phenomenological theory of fatigue phenomenon in ferroelectrics

In the current paper, the coupled fatigue hysteretic behaviors in ferroelectric ceramics are modeled by a blending a phenomenological hysteresis model with point defects. The time-dependent phenomenological model is employed to capture the hysteresis loops associated with phase transitions. The fatigue hysteresis is modeled by combining the single-crystal model with time functions. The mechanism of fatigue in ferroelectric ceramics is interpreted as an accumulation of residual polarization in the proposed model. Numerical results of static and dynamic hysteretic behaviors are presented and compared to their experimental counterparts. The capability of the proposed model for capturing the fatigue phenomenon is validated.

A novel learning adaptive hysteresis inverse compensator for pneumatic artificial muscles

Because of friction and elastic deformation, a pneumatic artificial muscle (PAM) has strong asymmetric hysteresis which negatively affects the driving performance. The hysteresis is generally described by a phenomenological model. However, the phenomenological hysteresis model always only depicts the hysteresis under certain conditions, so the compensator based on it has poor universality for different external conditions. In this article, we proposed a guided reinforcement learning (GRL) algorithm to online adjust the output of a Kriging-median inverse hysteresis compensator (KMIC), so that improve the compensation performance of the compensator for PAMs under different size, external load, and input signal frequency conditions. We name the novel compensator as a guided reinforcement learning Kriging- median inverse compensator (GRL-KMIC). Both simulation and experiment platform are set up to verify the effectiveness of the proposed compensator. The results show that the GRL algorithm improves the universality of KMIC obviously, so GRL-KMIC always keeps better compensation control performance than KMIC for different external conditions.

A novel hysteresis modelling method with improved generalization capability for pneumatic artificial muscles

A pneumatic artificial muscle (PAM) consists mainly of an inner elastomeric bladder surrounded by a braided shell. Due to the special geometric structure, PAMs are subject to the typical drawbacks of a highly-asymmetric hysteresis-based nonlinear system. This paper presents a D-extended un-parallel Prandtl–Ishlinskii model (D-EUPI) model for modelling the asymmetric hysteresis of PAMs, which is a deep learning-based model combining a modified EUPI model and a convolution neural network (CNN). Compared with the existing phenomenological hysteresis models, the proposed model has good generalization capability, meaning that not only can it be suitable for trained data, but also can accurately predict the PAM displacement corresponding to input pressure independent of trained data. We investigate the influences of input frequency and amplitude on the inherent hysteresis characteristics of PAMs via experiments. The experiments reveal that the asymmetric hysteresis of the PAM is quasi-rate independent but dependent on its input amplitude for the low frequency range in this study. Furthermore, the D-EUPI model is trained and tested based on the experimental data. The results show that the D-EUPI model is effective in predicting the hysteresis of PAMs over a wide range of input amplitudes. And the D-EUPI model has better performance in modelling complex multi-loop hysteresis by comparison with the EUPI model and the CNN model.

Reluctance Network Model of Three-Phase-Laminated-Core Variable Inductor Considering Magnetic Hysteresis Behavior

The quantitative analysis of the iron loss taking magnetic hysteresis behavior into account is essential for the development of high-efficiency electric machines. In a previous paper, a novel magnetic circuit model incorporating a play model, which is one of the phenomenological models of magnetic hysteresis, was proposed. It was clear that the proposed model can calculate the hysteresis loop of a ring core with high speed and high accuracy. However, this method was applied only for the objects with simple shapes. Thus, it is necessary to extend the applicable range for the objects with more complicated shapes. This paper presents a novel reluctance network analysis (RNA) model incorporating the play model and indicates the validity of the proposed RNA model by using a three-phase-laminated-core variable inductor as an object of discussion.

Dynamics of a Damping Device Based on Ishlinsky Material

In present paper we consider the damping properties of the oscillating system with hysteretic nature. The mathematical model of considered system is based on the operator approach for the hysteretic nonlinearity on the example of Ishlinsky material. Such a converter is a continual analogue of the set of stops connected in parallel. In the frame of the paper we compare the various approaches to modeling of damping systems. Namely, together with the hysteretic damper we consider the so-called nonlinear viscous damper which is a generalization of a standard linear damper with dependence on the velocity. The mathematical model of the considered system is formulated in terms of second order ordinary differential equation with hysteretic nonlinearity (namely, the operator-type nonlinearity). In comparison with the phenomenological models of hysteresis (such as Bouc-Wen model) that are often used in the modeling, the Ishlinsky model allows to " feel" the hysteretic nature of the material on the physical level. The major result of the presented paper is the comparison both the hysteretic and viscous (including the linear and nonlinear cases) dampers. Such a comparison is made in terms of transmission functions that reflect the "efficiency" of suppression of the external perturbations by the force transmission from an external source to the load. The results of numerical simulations showed the high efficiency of hysteretic damper both in and outside the resonance region (at the same time it is well known that the linear viscous damper has a weak efficiency outside the resonance region). The disadvantage of the hysteretic damper lies in the fact that its ability to dump the relative motion of the system under external forces is insignificantly reduced outside the resonance region.

High-Precision Tracking Control of a Soft Dielectric Elastomer Actuator With Inverse Viscoelastic Hysteresis Compensation

In this paper, we present a new control approach for high-precision tracking control of a soft dielectric elastomer actuator (DEA) with inverse viscoelastic hysteresis compensation. To this end, we first investigate the viscoelastic response of the DEA and divide it into transition region and stable region. Then, the viscoelastic response is characterized by creep and hysteresis effects according to the different features of the two regions. Finally, a two-level tracking control approach is developed as follows: a direct inverse hysteresis compensation controller with a phenomenological hysteresis model is designed for the viscoelastic hysteresis description and compensation, and a conventional proportional-integral feedback controller is combined to compensate for the model uncertainty and creep effect. To verify the effectiveness of the developed tracking control approach, several experiments are conducted with various reference sinusoidal trajectories. Experimental results show that: when the frequency of the trajectory is within the range of 0.1 to 1 Hz, the maximum tracking error and the root-mean-square error decrease from 40.63% to 3.95% and 28.38% to 1.86%, respectively. This paper is the first attempt to achieve high-precision tracking control of soft DEAs by combining a phenomenological-model feedforward compensator and a feedback control law for the viscoelastic compensation, which may accelerate the practical applications of DEAs to soft robots.

Relationships between grain size in self-developed soft magnetic composites and the Grucad hysteresis model

Abstract Soft magnetic composites (SMCs) have been in the spotlight of magnetic community due to their unique properties which can easily be tailored up to a specific application. The present paper is focused on the possibility to develop SMC cores produced from iron powder mixed with suspense polyvinyl chloride. Important processing parameters like grain size are correlated with the parameters of a simple phenomenological hysteresis model developed by the Grucad research group.

Dynamic analysis of beam-soil interaction systems with material and geometrical nonlinearities

In this paper a Hybrid Domain Boundary Element Method is developed for the geometrically nonlinear dynamic analysis of inelastic Euler-Bernoulli beams of arbitrary doubly symmetric simply or multiply connected constant cross-section, resting on viscous inelastic Winkler foundation. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse dynamic loading and bending moments in both directions as well as to axial loading, while its edges are subjected to the most general boundary conditions. A displacement based formulation is developed and inelastic redistribution is modelled through a distributed plasticity (fibre) approach. A uniaxial hysteretic law is considered for the evolution of the plastic part of the normal stress following the phenomenological hysteresis model, while hysteretic force-displacement model is also employed in order to describe the inelastic behaviour of the Winkler springs. Numerical integration over the beam cross sections is performed in order to resolve the hysteric parts of the stress resultants. Application of the boundary element technique yields a system of nonlinear Differential-Algebraic Equations, which are written in state-space form and solved by an incremental–iterative solution strategy. Numerical examples are worked out confirming the accuracy and the computational efficiency of the proposed beam formulation, as well as the significant influence of material and geometrical nonlinearities in the response of beam-soil interaction systems.

Comparison of macroscopic descriptions of magnetization curves

The paper considers a qualitatively different behaviour of two phenomenological hysteresis models. The first one is the widespread Jiles-Atherton description, which is based on the ”effective field” concept. The other model is the proposal by the Brazilian research team GRUCAD. First order reversal curves simulated with the latter formalism do not exhibit negative slopes. This feature is in accordance with the experiment.

Experimental characterization and modeling of rate-dependent asymmetric hysteresis of magnetostrictive actuators

The hysteresis nonlinearities of a magnetostrictive actuator were characterized under different amplitudes of simple and complex harmonic excitations over a wide range of frequencies (10–200 Hz) and magnetic bias levels (35–75 kA m−1). The measured data revealed asymmetric output–input characteristics and strong dependence on the magnetic bias, amplitude and frequency of the input. Output saturation was also observed under moderate to high amplitude excitations. A phenomenological hysteresis model is proposed in this study to model the hysteresis nonlinearities of a magnetostrictive actuator. A rate-dependent Prandtl–Ishlinskii model integrating a memoryless function of deadband operator was subsequently formulated to describe both the rate dependence and the asymmetric hysteresis loops of the magnetostrictive actuator in addition to the output saturation. Comparisons of the integrated Prandtl–Ishlinskii model responses with the measured data suggested that the model can effectively describe the nonlinear hysteresis properties of the magnetostrictive actuator over a broad range of excitation amplitudes and frequencies. The inverse of the proposed rate-dependent Prandtl–Ishlinskii model can be obtained analytically. Then, the inverse model can be applied as feedforward compensator for compensation of asymmetric rate-dependent hysteresis nonlinearities without using feedback control techniques.

Precise position control of shape memory alloy actuator using inverse hysteresis model and model reference adaptive control system

Position control of Shape Memory Alloy (SMA) actuators has been a challenging topic during the last years due to their nonlinearities in the governing physical equations as well as their hysteresis behaviors. Using the inverse of phenomenological hysteresis model in order to compensate the input–output hysteresis behavior of these actuators shows the effectiveness of this approach. In this paper, in order to control the tip deflection of a large deformation flexible beam actuated by an SMA actuator wire, a feedforward–feedback controller is proposed. The feedforward part of the proposed control system, maps the beam deflection into SMA temperature, is based on the inverse of the generalized Prandtl–Ishlinskii model. An adaptive model reference temperature control system is cascaded to the inverse hysteresis model in order to estimate the SMA electrical current for tracking the reference signal. In addition, a closed-loop proportional–integral controller with position feedback is added to the feedforward controller to increase the accuracy as well as eliminate the steady state error in position control process. Experimental results indicate that the proposed controller has great accuracy in tracking some square wave signals. It is also experimentally shown that the suggested controller has precise tracking performance in presence of environmental disturbances.

A COMPARATIVE STUDY OF PHENOMENOLOGICAL MODELS OF MR BRAKE BASED ON NEURAL NETWORKS APPROACH

In this paper a full-scale commercially available magnetorheological (MR) brake installed in a semi-active suspension (SAS) system is modeled and simulated. Two well-known phenomenological hysteresis models are explored: Bouc–Wen and Dahl ones. In particular, influence of their parameters on the response is evaluated and assessed. The next step is to introduce the artificial neural networks and discuss their application in the field of systems identification. Subsequently, two feedforward neural networks are created and trained to estimate parameters characterizing each of the MR damper models described. The semi-active suspension (SAS) system equipped with a MR brake is described and the detailed procedure for acquisition of the reference data used in the models validation stage is elaborated. The models outputs obtained by simulating them with the values of coefficients as identified by the networks are compared to each other as well as to the reference experimental data. Thanks to that, the comparative analysis between the suggested vibration suppression models and the full-scale MR brake is done and it is concluded which of the discussed models has a better performance. The usability of neural networks in the field of parameters estimation of the mathematical models of the real world phenomena is described as well. The novelty of the presented methodology is the application of artificial intelligence methods to estimate model parameters of a MR brake utilized in a SAS system. The results of this approach have a strong potential to be successfully implemented in the area of model-based control of semi-active vibration suppression systems.

Position control of shape memory alloy actuator based on the generalized Prandtl–Ishlinskii inverse model

Hysteresis and significant nonlinearities in the behavior of Shape Memory Alloy (SMA) actuators encumber effective utilization of these actuator. Due to these effects, the position control of SMA actuators has been a great challenge in recent years. Literature review of the research conducted in this area shows that using the inverse of the phenomenological hysteresis models can compensate the hysteresis of these actuators effectively. But, inverting some of these models, such as Preisach model, is numerically a complex task. However, the generalized Prandtl–Ishlinskii model is analytically invertible, and therefore can be implemented conveniently as a feedforward controller for compensating hysteresis nonlinearities effects in SMA actuators. In this paper a feedforward–feedback controller is used to control the tip deflection of a large deflected flexible beam actuated by an SMA actuator wire. The feedforward part of the control system is based on the generalized Prandtl–Ishlinskii inverse model while a conventional proportional–integral feedback controller is added to the feedforward controller to increase the accuracy together with eliminating the steady state error in position control process. Experimental results show that the proposed controller performs well in terms of achieving small overshoot and undershoot for square wave tracking as well as small tracking errors for sinusoidal trajectory. It has also great capability for tracking hysteresis minor loops.

Experimental comparison of some phenomenological hysteresis models in characterizing hysteresis behavior of shape memory alloy actuators

Among the phenomenological hysteresis models, the Preisach model, Krasnosel’skii–Pokrovskii model, and Prandtl–Ishlinskii model have found extensive applications for modeling hysteresis in shape memory alloys and other smart actuators. Since the mathematical complexity of the identification and inversion problem depends directly on the type of phenomenological hysteresis modeling method, choosing a proper phenomenological model among the mentioned models for modeling the hysteretic behavior of shape memory alloy actuators is a task of crucial importance. Moreover, the accuracy of the hysteresis modeling method in characterizing shape memory alloy hysteretic behavior consequently affects the whole compensator design task. In this article, the accuracy of the mentioned phenomenological models in characterizing and predicting the hysteretic behavior of shape memory alloy actuators is experimentally compared. It will be shown that although, unlike the Preisach and Krasnosel’skii–Pokrovskii models, the identification process of the Prandtl–Ishlinskii model is a time-consuming process, it leads to the best results when the outputs of these models are compared with the experimental data. Since the Prandtl–Ishlinskii model is also analytically invertible and can be easily implemented as a feed-forward controller for compensating the hysteretic nonlinearity behavior of shape memory alloy actuators, it seems to be the best model for modeling and compensating the hysteretic behavior of shape memory alloy actuators.

Dynamic and Anisotropic Vector Hysteresis Model Based on Isotropic Vector Play Model for Nonoriented Silicon Steel Sheet

A phenomenological vector hysteresis model is developed to represent dynamic and weakly anisotropic vector hysteretic properties of nonoriented silicon steel sheets. The anisotropic vector hysteresis is represented by the multiplication of an anisotropy matrix and an isotropic vector play model. An eddy-current field vector given by classical eddy-current theory and an anomaly factor is added to the vector hysteresis model. The anomaly factor is determined to model the decrease in anomalous eddy-current loss under conditions of large rotational magnetic flux. The alternating and rotational properties simulated by the proposed model reconstruct the measured magnetic properties of nonoriented silicon steel sheets.

Use of Jiles–Atherton and Preisach Hysteresis Models for Inverse Feed-Forward Control

Hysteresis effects hinder the accurate control of electromagnetic actuators and require auxiliary sensors for properly determining the hysteretic system state. The physics-based Jiles-Atherton and the phenomenological Preisach hysteresis models provide powerful means to describe the magnetic hysteresis and its inverse. In this paper, we consider both hysteresis models in the scalar form from the control points of view, with a primary objective of the sensorless inverse feed-forward control. The identification complexity, the runtime, and the space efficiency of the control-oriented implementation are analyzed and compared for both modeling approaches. Their control performance for an inverse hysteresis compensation is experimentally evaluated on a specific force-controlled electromagnet system.

Analysis of Noise Spectral Density for Phenomenological Models of Hysteresis

A statistical technique based on Monte Carlo simulations is developed to compute the spectral densities of the output variable in phenomenological models of hysteresis. The input signal is described by an Ornstein-Uhlenbeck process and the magnetization is computed by using various hysteresis models: the Energetic, Jiles-Atherton, and Preisach models. General qualitative features of these spectral densities are examined and their dependence on various parameters is discussed. For values of the diffusion coefficient near and smaller than the coercive field, the output spectra deviate significantly from the Lorentzian shape, which is characteristic of the input process. The intrinsic differences between the transcendental, differential, and integral modeling of hysteresis yield significantly different spectra at low frequency region, which reflect the long-time correlation behavior.

Analysis of magnetic aftereffect by using Monte Carlo methods

Magnetic aftereffect phenomena are simulated in the framework of phenomenological models of hysteresis by using the Monte Carlo technique. It is shown that a log t-type dependence of the average value of the output variable (usually the magnetization) can be qualitatively predicted by using simplified models of hysteresis with local memory, such as the Jiles–Atherton, Hodgdon, or the Energetic model. These models are computationally much more efficient than the more elaborate models of hysteresis with global memory like the Preisach model. Numerical results related to the decay of the output variable as of function of time are presented. The viscosity coefficient as well as the temperature dependence of the viscosity coefficient is analyzed in detail.