Preisach Hysteresis Research Articles

Simulation of Preisach hysteresis model based on the first-order reversal curves

Simulation of Preisach hysteresis model based on the first-order reversal curves

Dynamic extension of vector Preisach model

The objective of the present paper is to generalize the vector Preisach hysteresis model to take dynamic effects into account. A comprehensive analysis of the vector behavior has been performed by a single sheet tester with a specimen of round shape. The locus of the magnetic flux density vector has been controlled by a digital measurement set up at different frequency. An inverse vector Preisach hysteresis model has been built up by viscous-type scalar models and an identification procedure has been developed to follow the measured data. Finally, the model has been inserted into a finite element procedure through the fixed point technique to simulate electrical engineering problems.

Difficulty in identification of Preisach hysteresis model weighting function using first order reversal curves method in soft magnetic materials

The Preisach model can be used for detailed analysis of devices based on ferromagnetic materials, if its parameter, its weighting function, is well-known. Usually the weighting function is approximated by analytical formula. The second approach is to determine it directly from experimental data. Most widely used method to obtain the weighting function is the first order reversal curve method that is based on two partial derivatives of measured magnetization using a special excitation pattern beginning from deep material saturation. Since the derivative enhances the experimental error, a precision experiment is necessary. Furthermore, it is not easy to achieve the deep saturation with the required signal pattern. Therefore sophisticated data processing followed, in order to reduce experimental errors before performing the numerical derivative. The paper concerns measurements errors caused by insufficient saturation and also problems of negative values of the weighting function, partially due to the noise. Irrespective of measurement errors, the agreement between model and experiment is good and fully acceptable in technical praxis.

Temperature characteristics modeling of Preisach theory

This paper proposes a modeling method of the temperature characteristics of Preisach theory. On the basis of the classical Preisach hysteresis model, the Curie temperature, the critical exponent and the ambient temperature are introduced after which the effect of temperature on the magnetic properties of ferromagnetic materials can be accurately reflected. A simulation analysis and a temperature characteristic experiment with silicon steel was carried out. The results are basically the same which proves the validity and the accuracy of the method.

Robust homoclinic orbits in planar systems with Preisach hysteresis operator

We construct examples of robust homoclinic orbits for systems of ordinary differential equations coupled with the Preisach hysteresis operator. Existence of such orbits is demonstrated for the first time. We discuss a generic mechanism that creates robust homoclinic orbits and a method for finding them. An example of a homoclinic orbit in a population dynamics model with hysteretic response of the prey to variations of the predator is studied numerically.

A compressive sensing-based approach for Preisach hysteresis model identification**This work was supported by the National Science Foundation (CMMI 1301243).

The Preisach hysteresis model has been adopted extensively in magnetic and smart material-based systems. Fidelity of the model hinges on accurate identification of the Preisach density function. Existing work on the identification of the density function usually involves applying an input that provides sufficient excitation and measuring a large set of output data. In this paper, we propose a novel compressive sensing-based approach for Preisach model identification that requires fewer measurements. The proposed approach adopts the discrete cosine transform of the output data to obtain a sparse vector, where the order of all the output data is assumed to be known. The model parameters can be efficiently reconstructed using the proposed scheme. For comparison purposes, a constrained least-squares scheme using the same number of measurements is also considered. The root-mean-square error is adopted to examine the model identification performance. The proposed identification approach is shown to have better performance than the least-squares scheme through both simulation and experiments involving a vanadium dioxide ()-integrated microactuator.

A new hysteresis identification model using a diagonal-weighted Preisach model and recursive approach with application to piezostack actuators

This article presents a new hysteresis model of a piezostack actuator which is designed from the modification of the conventional Preisach hysteresis model. The proposed model which is called diagonal-weighted Preisach model is featured by weights of fundamental elements constituting triangles just along their own diagonal. With such an approach, there is no discontinuous jump at two consecutive elements in the Preisach triangle. Consequently, there is no need to adopt any further interpolation tool. In this work, a recursive approach with a simple computation associated with the proposed model is also developed. It is noted that in order to implement the proposed model, weights of fundamental elements must be obtained in prior. In order to demonstrate some characteristics of the proposed model, the prediction accuracy of the hysteresis is investigated based on the discretized number and compared with the conventional Preisach model. In addition, the proposed model is experimentally realized for the piezostack actuator and the identified displacement from the proposed model is compared with the actual one to validate the effectiveness.

Theoretical Insights on Contraction-Type Iterative Learning Control for Biorobotic Systems with Preisach Hysteresis

This article offers new insights on the learning control approach developed by [Hu et al. IEEE/ASME Trans. Mechatronics, 19(1): 191–200, 2014]. Theoretical insights are further proposed to unveil why the contraction-type iterative learning control (ILC) schemes are suitable and effective in compensating for hysteresis, widely existing in biorobotic locomotion. Under such circumstances, iteration-based second-order dynamics is adopted to describe the biorobotic systems acted upon by one unknown Preisach hysteresis term. The memory clearing operator is mathematically proven to enable feasibility of contraction-type ILC methods, regardless of whether the initial state is accurately set or not. The simulation examples confirm that the developed iteration-based controller combined with a preceded operator effectively reduce tracking errors caused by the hysteresis nonlinearity. Furthermore, the new insights on theoretical feasibility are definitively corroborated in accordance with the previously published experimental results.

Convergence of Direct Recursive Algorithm for Identification of Preisach Hysteresis Model with Stochastic Input

We consider a recursive iterative algorithm for identification of parameters of the Preisach model, one of the most commonly used models of hysteretic input-output relationships. This online algorithm uses a simple rule for updating the values of the piecewise constant density function in the switching region at each time step. The so-called persistent excitation condition has been shown to play an important role for convergence of recursive iteration schemes when input-output data are generated by a deterministic input (such as, for example, a periodically repeated sequence of test inputs prescribed by the classical Mayergoyz identification algorithm). In this work, we assume that the input randomly fluctuates and these fluctuations can be described by a stochastic Markov process. Assuming that accurate measurements of the input and output are available, we prove the exponential convergence of the recursive identification algorithm, estimate explicitly the convergence rate, and explore which properties of the stochastic input and the algorithm affect the guaranteed convergence rate. An analogue of the persistent excitation condition suitable for analysis of stochastic Markov inputs is established. Numerical examples that test the convergence of the algorithm in the case of a time-dependent density function and in the presence of measurement noise are presented.

Computationally Efficient Formulation of Relay Operator for Preisach Hysteresis Modeling

An algebraic expression for the Preisach hysteron, which is a non-ideal (delayed) relay operator, is formulated for a computationally efficient real-time implementation. This allows representing the classical scalar Preisach hysteresis model as a summation of a large number of weighted hysterons which computation can be accomplished in parallel. The latter makes possible an efficient FPGA or ASIC realization of the scalar Preisach hysteresis model that can be useful for multiple applications. The signal flow which specifies the model implementation is provided in form of the block diagram. The proposed computation of Preisach hysterons, aggregated to the entire Preisach hysteresis model, is evaluated numerically and on a real-time hardware platform.

Discretization of Preisach hysteresis model

In order to reduce the partial derivative errors in Preisach hysteresis model caused by inaccurate experimental data, the concept and correlative method of discretization of Preisach hysteresis model are proposed, the essential of which is to centralize the distribution density of Preisach hysteresis model in local region as an integral, which is defined as the weight of a certain point in that region. For the input composed of an ascending segment and a descending segment, a method to determine the initial weights together with an additional method to determine present weights is given according to the number of input ascending segments. If the number of input ascending segments increases, the weights of the corresponding points in updating rectangle are updated by adding the initial weights of corresponding points. A prominent advantage of discrete Preisach hysteresis model is its memory efficiency. Another advantage of discrete Preisach hysteresis model is that there is no function in the model, and thus, it can be expediently operated using a computer. By generalizing the above updating rectangle method to the continuous Preisach hysteresis model, identification method of distribution density can be given as well.

Realization of arbitrary hysteresis by a low-dimensional gradient flow

We consider gradient systems with an increasing potential that depends on a scalar parameter. As the parameter is varied, critical points of the potential can be eliminated or created through saddle-node bifurcations causing the system to transit from one stable equilibrium located at a (local) minimum point of the potential to another minimum along the heteroclinic connections. These transitions can be represented by a graph. We show that any admissible graph has a realization in the class of two dimensional gradient flows. The relevance of this result is discussed in the context of genesis of hysteresis phenomena. The Preisach hysteresis model is considered as an example.

One-phase flow in porous media with hysteresis

This paper presents a numerical simulation of one phase flow through a porous medium showing a hysteretic relation between the capillary pressure and the saturation of the phase. The flow model used is based on mass conservation principle and Darcy's law. Boundary conditions of Neumann and Signorini type are imposed. The hysteretic relation between the capillary pressure and the saturation is described by a Preisach hysteresis operator. A numerical algorithm for the treatment of the arising system of equations is proposed. Results of numerical simulations are presented.

A New Flexure-Based <inline-formula><tex-math notation="LaTeX">$Y\theta$</tex-math></inline-formula> Nanomanipulator With Nanometer-Scale Resolution and Millimeter-Scale Workspace

In this paper, the development of a flexure-based two-degree-of-freedom (2-DOF) nanomanipulator with modified differential lever displacement amplifier is conducted, which aims to break through the millimeter-range barrier. The kinetostatics modeling of the mechanism is established by using the pseudorigid body method, also the analytical modeling of lever is built up, as well as the dimension optimizations and the mechanism performance validations are conducted by using the Particle Swarm Optimization algorithm and the finite-element analysis method, respectively. With the consideration of hysteresis effect inherent in piezoelectric ceramics actuators, the hysteresis modeling is conducted by using the Preisach theory. To enhance the mechanism positioning performance, a novel feedforward nonlinear proportion-integration-differentiation control strategy composed by the nonlinear PID controller and the inverted Preisach hysteresis compensator is proposed in this paper. Finally, a series of closed-loop motion tracking experiments have been carried out. It indicates that the developed mechanism has achieved a millimeter workspace (3.1273 mm $\;\times\;$ $26.5^{\circ }$ ), nanometer scale motion resolution (40 nm), as well as a closed-loop positioning bandwidth of over 10 Hz.

A novel claw pole memory machine for wide-speed-range applications

Memory machines with both high-power-density and wide-speed-range are becoming very attractive most recently. The purpose of this paper is to propose a novel type of memory machine, namely, claw pole memory machine. It engages an axially magnetized AlNiCo PM ring on the claw pole rotor to build the main magnetic flux in air-gap which is responsible for the electromechanical energy conversion. A magnetizing coil is equipped to online regulate the magnetization level of the permanent magnet ring, so as to achieve wide-speed-range operation. The operating principle is analyzed. The Preisach hysteresis model is combined with 3D finite element method to conduct performance assessment of the proposed claw pole memory machine. Calculation results demonstrate that the air-gap flux density can be readily adjusted by injecting DC pulse into the magnetizing coil, and the speed-range of the proposed machine can be extended as wide as six times of its base speed.

Hysteresis in column systems

In this paper one column of a telescopic construction of a bell tower is investigated. The hinges at the support of the column and at the connecting joint between the upper and lower columns are modelled with rotational springs. The characteristics of the springs are assumed to be non-linear and the hysteresis property of them is represented with the Preisach hysteresis model. The mass of the columns and the bell with the fly are concentrated to the top of the column. The tolling process is simulated with a cycling load. The elements of the column are considered completely rigid. The time iteration of the non-linear equations of the motion is evaluated by the Crank-Nicolson schema and the implemented non-linear hysteresis is handled by the fix-point technique. The numerical simulation of the dynamic system is carried out under different combination of soft, medium and hard hysteresis properties of hinges.

Nonlinear Control of Systems Preceded by Preisach Hysteresis Description: A Prescribed Adaptive Control Approach

When systems are preceded by hysteresis nonlinearities, many controller strategies have been developed with various hysteresis models, especially in the past decade. Among the hysteresis models, the Preisach model has a very general and well-established mathematical structure. However, designs of controllers that guarantee the closed-loop stability of nonlinear systems having the Preisach hysteresis representation are still a challenging issue in the literature. In this paper, we will attempt to demonstrate a solution in which a stable controller can be designed for nonlinear systems that couple with Preisach hysteresis model. The key is that by utilizing the so-called Preisach plane, the Preisach model is reexpressed into a control-oriented form, in which the input signal is explicitly expressed. It is then possible to fuse available control techniques with the Preisach model designing stable controllers. As an illustration to show the advantage of the developed control-oriented form, a prescribed adaptive control approach is adopted to ensure the transient and steady-state performance of the tracking error. The effectiveness of the control scheme is validated by the experimental results.

Dynamic Preisach model identification applying FEM and measured BH curve

Purpose – The purpose of this paper is to develop a viscous-type frequency dependent scalar Preisach hysteresis model and to identify the model using measured data and nonlinear numerical field analysis. The hysteresis model must be fast and well applicable in electromagnetic field simulations. Design/methodology/approach – Iron parts of electrical machines are made of non-oriented isotropic ferromagnetic materials. The finite element method (FEM) is usually applied in the numerical field analysis and design of this equipment. The scalar Preisach hysteresis model has been implemented for the simulation of static and dynamic magnetic effects inside the ferromagnetic parts of different electrical equipment. Findings – The comparison between measured and simulated data using a toroidal core shows a good agreement. A modified nonlinear version of TEAM Problem No. 30.a is also shown to test the hysteresis model in the FEM procedure. Originality/value – The dynamic model is an extension of the static one; an extra magnetic field intensity term is added to the output of the static inverse model. This is a viscosity-type dynamic model. The fixed-point method with stable scheme has been realized to take frequency dependent anomalous losses into account in FEM. This scheme can be used efficiently in the frame of any potential formulations of Maxwell's equations.

Parameters Calculation and Application of Preisach Hysteresis Model Based on Combination of Genetic Algorithms and Neural Networks

Based on the static mathematical model of Preisach hysteresis, this paper presents a modified method, combining Genetic Algorithm and Neural Network Method to get three conventional parameters of the Preisach hysteresis model under alternating magnetization. In the proposed method, considering the symmetry of the major hysteresis loop, a complete fitting hysteresis loop is obtained through the neural network training to find the optimization function and through the genetic algorithm to find the function extreme. The numerical fitting results obtained by this method are found to be in good agreement with the measurement data and verify the theory.

A Computationally Efficient Method to Determine Iron and Magnet Losses in VSI-PWM Fed Axial Flux Permanent Magnet Synchronous Machines

For electrical machines with a 3-D geometry, such as axial flux permanent magnet machines, the computation of iron and magnet losses in the case of pulsewidth modulation (PWM) supply could be performed by a transient 3-D finite element model (FEM) coupled with an electrical circuit. To reduce the CPU time, in this paper, these losses are computed with acceptable accuracy without using a 3-D transient FEM. The multislice technique is used with a 2-D static FEM, combined with a state space model of the machine. A Preisach hysteresis model is considered to evaluate the iron loss during minor loops. The loss in the electrical steel and in the magnets is evaluated for several PWM frequencies as well as for different segmentations of the magnets.