Preisach Hysteresis Research Articles

High-Speed Preisach Hysteresis Model Identification Method of Piezoelectric Actuators Based on Mapping Graph

High-Speed Preisach Hysteresis Model Identification Method of Piezoelectric Actuators Based on Mapping Graph

Algorithms to reduce the computational cost of vector Preisach model in view of Finite Element analysis

The purpose of this work is to devise algorithms to reduce the memory consumption of the vector Preisach model in view of its usage in Finite Element analysis. Four algorithms, which all implement a vector Preisach hysteresis model, are presented and critically compared theoretically and by numerical experiments taken on with two materials and three signals. Several strategies are presented to reduce both the memory occupation and the computational cost of several orders of magnitude.

Improved Preisach Model for the Vector Hysteresis Property of Soft Magnetic Composite Materials Based on the Hybrid Technique of SA-NMS

The two-dimensional hysteresis property of the soft magnetic composite (SMC) material under circular rotational excitation was measured by the experimental platform. The first-order reversal curves and the corresponding scalar Everett functions can be numerically generated by the measured major hysteresis loops along the orthogonal easy axis and hard axis. Different from the classical model, an improved vector Preisach hysteresis model that considers the anisotropic property of the SMC materials under vector magnetic excitation was put forward by introducing two parameters w and z. The two parameters were used to identify the vector Everett functions and adjust the shape of hysteresis curves under different magnitudes of the magnetic flux density. Furthermore, an efficient hybrid algorithm that combines simulated annealing with Nelder-Mead simplex technique was proposed for the accurate extraction of optimal parameters. The simulated results based on the improved model agree well with the measured ones; thus, the effectiveness and accuracy of the proposed method were verified.

Design, characterization, modeling, and comparison of helically wrapped super-coiled polymer artificial muscles

Super-coiled polymer (SCP) artificial muscles demonstrate a number of desirable properties, like high power density, inherent compliance, light weight, and lowcost. However, the realization of their full potential in achieving appreciable robot motion is hindered by their limited strain or force generation capabilities. Fabricated with multi-thread nylon filament, non-mandrel-coiled SCP actuators can only generate up to 10–20% strain, and mandrel-coiled SCP actuators are often fragile and fail to produce large force consistently. This paper presents the design, characterization, and modeling of helically-wrapped SCP (HW-SCP) actuators. HW-SCP actuators exhibit the advantages of mandrel-coiled and non-mandrel-coiled SCP actuators simultaneously—they can produce 15–55% strain, and consistently lift more than 90 g of weight. The design parameters of HW-SCP actuators can be conveniently adjusted to tune the actuator's performance. Furthermore, this work presents the first comprehensive comparative study of non-mandrel-coiled, mandrel-coiled, and HW-SCP actuators based on conductive multi-thread nylon filament. The correlations between strain and constant voltage were accurately captured by Preisach hysteresis models. The correlations between force and constant voltage were modeled by three low-order polynomial models. This work contributes to the development of high-performance artificial muscles and may facilitate optimal selection of SCP actuators under scenario-specific future studies.

Dynamics of SIR model with vaccination and heterogeneous behavioral response of individuals modeled by the Preisach operator.

We study global dynamics of an SIR model with vaccination, where we assume that individuals respond differently to dynamics of the epidemic. Their heterogeneous response is modeled by the Preisach hysteresis operator. We present a condition for the global stability of the infection-free equilibrium state. If this condition does not hold true, the model has a connected set of endemic equilibrium states characterized by different proportion of infected and immune individuals. In this case, we show that every trajectory converges either to an endemic equilibrium or to a periodic orbit. Under additional natural assumptions, the periodic attractor is excluded, and we guarantee the convergence of each trajectory to an endemic equilibrium state. The global stability analysis uses a family of Lyapunov functions corresponding to the family of branches of the hysteresis operator.

Modelling preferential flow through unsaturated porous media with the Preisach model and an extended Richards Equation to capture hysteresis and relaxation behaviour

The unsaturated flow of water in soil through unstable wetting fronts has been documented in literature. These instabilities can lead to the development of finger-flow profiles, whose paths can be “remembered” by a solid matrix of soil during future infiltration even after periods of desaturation. This process has been modelled for a 1D column of soil by the Richards equation, a non-equilibrium relaxation ODE, and Preisach hysteresis, all of which are required for finger flow. In this paper a comparison is made to similar work that use Parlange’s model of hysteresis and show that similar results are achieved by instead including the Preisach model. In addition, the model allows for the strength of hysteresis to be changed by a single parameter thus allowing the potential of parameter fitting of data in the future.

Compliant, Large-Strain, and Self-Sensing Twisted String Actuators.

Twisted string actuators (TSAs) convert rotational motion from twisting into linear motion. They are known for high energy efficiency, and large linear strain and stress outputs. Although they have been successfully applied as the moving mechanism for different robot applications, their potential in soft robotics is mainly challenged by two aspects: First, the conventional strings of TSAs are stiff and strong but not compliant. Second, precise control of TSAs predominantly relies on external position or force sensors. Because of these, TSA-driven robots are often rigid and bulky. In this study, we propose the design, modeling, and robotic application of TSAs that are compliant, can produce large strain, and are capable of self-sensing during twisting-induced actuation. The design is realized by replacing conventional stiff strings with compliant, thermally activated, and conductive supercoiled polymer strings. Experiments show that the developed TSAs have normalized stiffness of <50 N, strain >30%, and position self-sensing capability during twisting. The quasi-static actuation and self-sensing properties are accurately captured by the Preisach hysteresis operators. In particular, both the twisting-induced actuation and thermally induced actuation are considered. Finally, the proposed TSAs are successfully demonstrated in a low-cost three-dimensionally printed compliant robotic gripper.

A Dynamic Hysteresis Model for Loss Estimation of GO Silicon Steel Under DC-Biased Magnetization

A new algorithm for numerical identification of the static Preisach hysteresis model is proposed for more accurate estimation of dc-biasing hysteresis curves and hysteresis loss of the grain-oriented silicon steel sheet. Based on the experimental asymmetric major hysteresis loop under dc-biased magnetization, two sets of first-order reversal curves corresponding to ascending and descending branches, respectively, are numerically generated for construction of the Everett function. According to the equivalent field separation technique, a dynamic hysteresis model is established by parameter extraction of excess loss, and then used for simulation of dc-biasing dynamic hysteretic behaviors. The consistency between the simulated results and the measured ones demonstrates the effectiveness of the proposed method. The effect of dc bias on iron loss is analyzed as well.

Recursive Algorithm for the Control of Output Remnant of Preisach Hysteresis Operator

We study in this paper the control of hysteresis-based actuator systems where its remanence behavior (e.g., the remaining memory when the actuation signal is set to zero) must follow a desired reference point. We present a recursive algorithm for the output regulation of the hysteresis remnant behavior described by Preisach operators. Under some mild conditions, we prove that our proposed algorithm guarantees that the output remnant converges to a desired value. Simulation result shows the efficacy of our proposed algorithm.

Modeling of a Bending Supercoiled Polymer (SCP) Artificial Muscle

As a recently developed artificial muscle, supercoiled polymer (SCP) actuators exhibit many desirable properties such as inherent compliance, large linear tensile actuation, and high energy and power densities. By embedding linear SCP actuators into flexible beams and activating them, bending SCP actuators can be created with outstanding deflection performances. However, their full potential as bending robotic muscles is challenged by their hysteresis nonlinearity and the complex coupling between the beam and the linear SCP actuator. In this study, we propose a nonlinear model that can accurately capture and estimate the steady-state displacement of the bending SCP actuator. The proposed model is constructed by coupling a Preisach hysteresis model and nonlinear beam equations. Numerical solution is obtained using a bisection technique-based algorithm and Runge-Kutta method. For comparison purposes, a linear model is also considered. Both simulation and experimental investigations are conducted. The effectiveness of the proposed modeling approach is confirmed.

Comparison of Preisach and Congruency-Based Static Hysteresis Models Applied to Non-Oriented Steels

Two hysteresis models are investigated for modeling static hysteresis phenomenon in nonoriented magnetic steels. First, the static Preisach model is studied, and two types of experimental data, i.e., first-order reversal curves (FORCs) and concentric hysteresis loops, are employed to identify the weight function. Due to negative values in the obtained experimental weight functions, the resulting Preisach models show nonphysical behavior. To eliminate this nonphysical behavior, an optimization procedure is applied to remove these negative values. The nonphysical behavior is resolved in the modified Preisach model; however, the model still has poor accuracy for asymmetric loops. Alternatively, a new congruency-based static hysteresis model is proposed. In this model, third- or higher-order reversal curves are approximated using measured FORCs and second-order reversal curves (SORCs) by means of a congruency regularity. According to this regularity, any third- or higher-order reversal curve is congruent to SORCs with the same reversal point. A 3-D piecewise interpolation function is employed to interpolate the measured major loop, FORCs, and SORCs. The proposed model results are compared with quasi-static measurements. The comparison reveals that the model is capable of approximating the magnetization curves for the measurements containing complex-shaped $B$ waveforms with a relative energy error of less than 4%.

Model predictive control with fatigue-damage minimization through the dissipativity property of hysteresis operators

In this paper, we propose an approximation method for the well-known fatigue-damage estimation of rainflow counting (RFC) using the dissipativity property of hysteresis operators that can be embedded in model predictive control (MPC) frameworks. Firstly, we revisit results that establish the equivalence between RFC to an energy dissipation property of an infinite-dimensional operator of the Preisach hysteresis model. Subsequently, we approximate the Preisach model using a finite-dimensional differential Duhem hysteresis model and propose an extended MPC scheme that takes into account the dissipated energy of Duhem hysteresis model as a damage proxy in the optimization problem formulation. Lastly, we present an example of control design for damage minimization in the shaft of a wind turbine where we illustrate the proposed strategy.

Difficulties Caused by Magnetic After-effect during Identification of the Preisach Hysteresis Model Weighting Function

Difficulties Caused by Magnetic After-effect during Identification of the Preisach Hysteresis Model Weighting Function

Mathematical analysis and numerical solution of models with dynamic Preisach hysteresis

Hysteresis is a phenomenon that is observed in a great variety of physical systems, which leads to a nonlinear and multivalued behavior, making their modeling and control difficult. Even though the analysis and mathematical properties of several rate-independent and rate-dependent hysteresis models are known, this is not the case for the Bertotti’s rate-dependent extension of the classical Preisach model; the so-called dynamic Preisach model for which current approaches lack a proper functional analytic framework which is essential to formulate optimization problems and develop stable numerics, both being crucial in practice. This paper deals with the description and mathematical analysis of the dynamic Preisach hysteresis model. Toward that end, we complete a widely accepted definition of the dynamic model commonly used to describe the constitutive relation between the magnetic field H and the magnetic induction B, in which, the values of B not only depends on the present values of H but also on the past history and its velocity. We first analyze mathematically some important properties of the model and compare them with known results for the static Preisach model. Then, we consider a parabolic problem with dynamic hysteresis motivated by electromagnetic field equations. Under suitable assumptions, we prove the existence of a solution of a weak formulation of the problem and solve it numerically. Finally, we report a numerical test in order to assess the order of convergence and to illustrate the behavior of the numerical solution for different configurations of the dynamic Preisach model.

Hysteresis Identification of Bidirectional Magneto-Rheological Actuators Employing Preisach Model

As known, the aim of this paper is to present the field hysteresis behavior of a BMR actuator via identifying the hysteresis model. In order to realize this purpose, firstly, a BMR actuator is manufactured. The feature of this actuator has two disks which are rotated in opposite direction at the same speed and two coils are placed directly on each side of the housing. The two input signals consisting of velocity and current are applied to the BMR actuator to investigate the characteristic of this actuator. Secondly, a proper Preisach hysteresis model is built with two inputs and one output to estimate the torque of the actuator. Finally, the accuracy and the effectiveness of the model are demonstrated by the errors comparison between the constructed hysteretic curves and the experimental ones

Implementation and Identification of Preisach Parameters: Comparison Between Genetic Algorithm, Particle Swarm Optimization, and Levenberg–Marquardt Algorithm

Electromagnetic simulations of devices with soft materials and the study of the influence of cutting edge deformations/stresses on the degradation of magnetic performances require the identification of hysteresis parameters. Hence, computationally efficient implementation and identification of the hysteresis model is needed to obtain a solution with high accuracy within a reasonable time. Many studies on hysteresis identification have been reported, but few compare different methods to identify the optimal one. In the present study, we focus on the Preisach hysteresis model combined with the Lorentz modified distribution function to describe the magnetic behavior of a fully processed nonoriented Fe–3wt% Si steel sheet under static excitation. Three different identification techniques are implemented and evaluated: particle swarm optimization (PSO), genetic algorithms (GAs), and nonlinear least-squares approximation based on the Levenberg–Marquardt (LM) method. We evaluate each approach with regard to the accuracy, central processing unit computation time, and repeatability of the results. All the techniques perform well in this high-nonlinearity problem. The root-mean-square error is < 3%. However, the implementation of the GA is more complex than the PSO and LM methods. The optimized parameters are obtained in a few minutes in the case of the LM method, but a few hours are required for both the other techniques. Therefore, the LM method is the most suitable technique for the identification of Preisach hysteresis.

Improved estimation of iron losses for non-sinusoidal voltages

PurposeThe electrical machines connected to modern electric power grids are non-sinusoidal excited, and their augmented losses, including iron losses, limit their working characteristics. This paper aims to propose a prediction method for iron losses in non-oriented grains (NO) FeSi sheets under non-sinusoidal voltage, involving an inverse classical Preisach hysteresis model and the time-integration of each loss component.Design/methodology/approachThe magnetic history management in inverse Preisach model is optimized and a numerical Everett function is identified from measured symmetrical hysteresis cycles. The experimental data for sinusoidal waveforms obtained by a single sheet tester were also used to identify the parameters involved in Bertotti’ losses separation method. The non-sinusoidal magnetic induction waveform, corresponding to a measured voltage in an industrial electrical grid, was the input for Preisach model, the output magnetic field being accurately computed. The hysteresis, classical and excess losses are calculated by time-integration and the total losses are compared with those obtained for sinusoidal excitation.FindingsThe proposed method allows to estimate the iron losses for non-sinusoidal magnetic induction, using carefully identified parameters of FeSi NO sheets, using experimental data from sinusoidal regimes.Originality/valueThe method accuracy is assured by using a numerical Everett function, a variable Preisach grid step (adapted for the high non-linearity of FeSi sheets) and high-order fitting polynomials for the microscopic parameters involved in the excess loss estimation. The procedure allows a better design of magnetic cores and an improved estimation of the electric machine derating for non-sinusoidal voltages.

Magnetic Position Estimation in Ferromagnetic Systems Involving Significant Hysteresis

The proximity of a magnetic sensor to a magnet has been utilized for position measurement in many applications involving small ranges of motion. However, such position measurement becomes challenging when the application involves a ferromagnetic environment and larger ranges of motion. The movement of a magnet magnetizes and demagnetizes the ferromagnetic surroundings and creates significant hysteresis in the magnetic field versus position relationship. This relationship can no longer be represented by an algebraic mathematical function and needs to take the history of previous motions into consideration for calculation of position from magnetic field measurement. This paper presents a position estimation system that utilizes various models to represent the hysteresis behavior, including an interacting multiple model approach, a Preisach model, and a modified Preisach model. The developed position estimation system is evaluated on a large hydraulic actuator used in mobile construction vehicle applications. Experimental results show that an unscented Kalman filter using the modified Preisach hysteresis model can provide a position estimate with an accuracy better than 2% of stroke, in spite of significant hysteresis.

Variable-flux outer-rotor permanent magnet synchronous motor for in-wheel direct-drive applications

In-wheel direct-drive is the most efficient driving mode for electric vehicles, and it is the trend for applications in the future. In this paper, a novel variable-flux outer-rotor permanent magnet synchronous motor with a hybrid magnetic structure design is developed. Due to the hybrid magnetic pole with Nd-Fe-B and Al-Ni-Co permanent magnet(PM), the air-gap flux can be adjusted by changing the magnetization states of Al-Ni-Co PM, which is beneficial to realize a wide range of speeds and loads from the electromagnetic structure design. Firstly, basic structure features of the motor and the flux-adjusting principle are introduced. The design and calculation method of the PM dimensions is derived based on magnetic circuit analysis. Then the Preisach hysteresis model of Al-Ni-Co PM is described and is adopted to analyze the motor performance with the coupling of the time step finite element method(FEM), and the magnetization are investigated. Finally, the operational performance of the proposed motor is obtained by simulation, which verifies the design.

An Easy-to-Implement Hysteresis Model Identification Method Based on Support Vector Regression

The classical Preisach hysteresis model and its modifications are time consuming to implement due to the determination of the weight function. Another defect of the Preisach-based model is that it could only be an approximation in the absence of the congruency property. For such reasons, this paper proposes a hysteresis model identification method based on support vector regression which could be a promising alternative in practical applications. Support vector machine is attractive in regression analysis due to its strong generalization capability. A four-stage identification procedure is implemented and key techniques are introduced in detail. The penalty parameter and the kernel parameter are optimized using grid search and cross-validation method. The influences of data scaling and parameter optimization are analyzed. An identified hysteresis model of aluminum nickel cobalt alloy is evaluated and verified with the criteria of mean squared error and identified time.