Hysteresis Model Research Articles

Modeling and Adaptive Output Feedback Control of Butterfly-Like Hysteretic Nonlinear Systems With Creep and Their Applications

This paper proposes a novel robust adaptive piecewise- indirect inverse output- feedback control scheme to mitigate butterfly-like hysteresis with creep in smart-material actuators. Piecewise-indirect inverse indicates that it is not a true hysteresis and creep inverse compensatorbut an on-line decoupling mechanism to accessing the approximately actual control signal from the designed hysteretic and creeping temporary control signal. In addition, a new butterfly-like relay operator is proposed for the first time, leading to the construction of a new model of butterfly-like hysteresis with creep. Finally, the experimental results on the dielectric elastomer actuator motion control platform illustrate the effectiveness of the proposed output-feedback control scheme.

A Computationally Efficient Hysteresis Model for Magneto-Rheological Clutches and Its Comparison with Other Models

The collaborative robot market has experienced rapid growth, leading to advancements in compliant actuation and torque control. Magneto-rheological (MR) clutches offer a hardware-level solution for achieving both compliance and torque control through adjustable coupling between the input and output of the MR clutch. However, the presence of frequency-dependent magnetic hysteresis makes controlling the output torque challenging. In this paper, we present a comparative study of six widely used hysteresis models and propose a computationally efficient algebraic model to address the issue of hysteresis modeling and control of the output torque of rotary MR clutches. We compare the estimated torques with experimental measurements from a prototype MR clutch, to evaluate the computational complexity and accuracy of the model. Our proposed algebraic hysteresis model demonstrates superior accuracy and approximately two times less computational complexity than the Bouc–Wen model, and approximately twenty times less memory requirement than neural network-based models. We show that our proposed model has excellent potential for embedded indirect torque control schemes in systems with hysteresis, such as MR clutches and isolators.

Empirical formulation for the estimate of the equivalent viscous damping of infilled RC frames

The direct displacement-based design (DDBD) is based on the equivalence between the nonlinear hysteretic response of a structure and a simple linear oscillator with equivalent viscous damping (EVD). Typically the EVD is calibrated for different types of structures as a function of the ductility. However, those simple relationships exhibit a huge dispersion and uncertainty since the specific properties of the structural system are not considered. This work proposes an original approach for estimating the EVD of infilled reinforced concrete (RC) frames. We focus on a ductility demand corresponding to an ultimate limit state and we investigate the effect of the properties of infilled RC frames on the EVD. A data-driven hysteresis model proposed by the authors in a previous research is implemented in OpenSees to represent the nonlinear response of infill panels. The optimal EVD at the ultimate limit state is computed using an extensive series of time-history analyses (THAs) on a dataset of 14 infilled RC frames. Afterwards, an empirical correlation law for the estimate of the optimal EVD is calibrated as a function of the geometrical and mechanical properties of infilled RC frames. This formula is meant to be a practical tool for a preliminary design of infilled RC frames. A comparison with the EVD estimated by quasi-static tests and the EVD of bare frames is made. The methods and results presented in this work may be the basis for more robust predictions of the EVD of infilled RC structures.

Quantum Stoner–Wohlfarth model of two-dimensional single-domain magnets

The Stoner–Wohlfarth model is a classical model for magnetic hysteresis of single-domain magnets. For two-dimensional (2D) magnets at finite temperatures, the Stoner–Wohlfarth model must be extended to include intrinsic strong spin fluctuations. We predict several fundamentally different hysteresis properties between 2D and 3D magnets. The magnetization switching diagram known as the astroid figure in the conventional Stoner–Wohlfarth model becomes highly temperature dependent and asymmetric with respect to the transverse and longitudinal magnetic fields. Our results provide new insights into the spintronics applications based on 2D magnetic materials.

Force-Displacement Hysteresis Model of Exterior PCRB Joints under Low Cyclic Loading.

The seismic behaviors of exterior polyvinyl chloride-carbon-fiber-reinforced polymer (PVC-CFRP) confined concrete (PCCC) column-ring-beam joints (hereafter referred to as exterior PCRB joints) under low cyclic loading were investigated. A total of 11 specimens were tested to analyze the effects of the structural parameters (i.e., the reinforcement ratio of the ring beam, the CFRP-strip spacing, the ring-beam width, the reinforcement ratio of the frame beam, and the axial compression ratio) on the failure modes and hysteretic behavior. Three different failure modes, including the failure of the frame beam, the failure of the junction between the frame beam and the ring beam, and the shear failure of the ring-beam joint, were observed. The experimental results showed that the pinching effects of the hysteresis curves decreased and that the slope of the descending stage of the skeleton curves gradually decreased with the enhancement of the reinforcement ratio of the ring beam, axial compression ratio, and ring-beam width. The effects of the CFRP-strip spacing and the reinforcement ratio of the frame beam on the hysteresis loops and skeleton curves were marginal, while the reinforcement ratio of the frame beam exerted significant effects on the failure modes. Therefore, a model for predicting the skeleton curves of exterior PCRB joints and hysteresis rules was proposed, based on the softening constitutive relation of the concrete and a regression analysis of the test data. Ultimately, a load-displacement hysteresis model of the exterior PCRB joints was established and validated by the test data, with good agreement.

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.

Underwater dynamic hysteresis modeling and feedforward control of flexible caudal fin actuated by macro fiber composites

Underwater bionic robotics and vehicles that use flexible structures as power sources have attracted considerable attention. Thus, the underwater dynamic behaviors of the flexible structure of a variable cross-section actuated by smart actuators must be further investigated. In this study, underwater dynamic hysteresis modeling and feedforward compensation of a flexible caudal fin driven by macro fiber composites (MFC) at different frequencies were investigated. The MFC-actuated flexible caudal fin is considered a Euler–Bernoulli beam. A revised hydrodynamic function governed by the thickness of the viscous layer and the gap-to-width ratio of the cross-section was developed. Then, a characteristic-frequency-dependent extended transform function model is proposed for the hydrodynamic response of a non-uniform beam. An asymmetric hysteresis model is presented to characterize the rate-independent hysteresis behavior of the MFC actuators. Further, the underwater dynamic equation of the MFC-actuated caudal fin with hysteresis is obtained by connecting the two established models in series. Experiments demonstrate the dynamic behavior between the underwater responses of the caudal fin and the input voltages have an ellipse-like shape and vary in shape and size with oscillating frequency. The ellipse-like dynamic hysteresis loop first grows, reaching its maximum at the resonant frequency, and then decreases, because of the frequency-dependent dynamic behavior. Meanwhile, a phase shift of approximately 90°between the input voltage and underwater dynamic response was observed at the resonant state. Furthermore, the experimental results demonstrate that the proposed model can describe the nonlinear underwater dynamic hysteresis behavior of the proposed caudal fin at different frequencies. The trajectory tracking performances are remarkably improved over a broad frequency range with the proposed compensator. Consequently, the effectiveness of the proposed dynamic model and compensation method was demonstrated. These results are helpful for robotic fish or autonomous underwater vehicles propelled by oscillating foils actuated by smart actuators, including MFC.

Magnetic hysteresis model using chained plays

A magnetic vector hysteresis model is presented using play hysterons as building blocks. The main difference compared to earlier play based magnetic hysteresis models is that instead of forming a superposition of plays with different coercivities, this work uses a set of identical plays which are connected in a chain so that the output of one play acts as input to the next. Like models using a superposition, this yields far more complex minor loop behavior than a single play is capable of. Comparisons are made with measurements on a nonoriented electric steel for BH curves and alternating and rotational losses, showing satisfactory agreement. The approach is found to have both advantages and disadvantages compared to models using superpositions of plays. The problem of determining model parameters becomes simpler and the model can be reversed so either magnetic field or magnetization may be used as known variable. On the other hand, there is no apparent connection to underlying physical processes.

Upscaling simulation method of fluid flow for fracturing-shut in-flowback-production process in tight oil reservoirs: Hysteresis effects of capillary pressure and relative permeability

The hysteresis effect is a key factor to accurately predict the fluid distribution and production performance of fracturing-shut in-flowback-production (FSFP) process in tight oil reservoirs. In this paper, the upscaling simulation method of fluid flow for FSFP process has been proposed. This method, which establishes the connections between the pore network model (PNM) and the reservoir numerical model, not only effectively characterizes the hysteresis effects of capillary pressure and relative permeability in tight oil reservoirs, but also realizes the upscaling process from the pore-throat scale to the reservoir scale. First, the quasi-static pore network model for tight oil reservoirs considering the boundary layer has been established. And then, the capillary pressure curves and relative permeability curves of the drainage process (non-wetting phase displacing wetting phase process) and imbibition process (wetting phase displacing non-wetting phase process) have been obtained. Moreover, the hysteresis model has been added to numerical simulation of FSFP process and the hysteresis scanning curves have been calculated. Finally, a numerical model considering different hysteresis effects for multistage-fractured horizontal well of a tight oil reservoir located at Ordos Basin, China, has been established to investigate the oil saturation change and oil recovery during the whole process of FSFP. The results show that the hysteresis effects of capillary pressure and relative permeability will increase the predicted exchange volume of oil-water between matrixes and fractures in fracturing-shut in process, and decrease the predicted oil recovery in flowback-production process. Which is proved by the actual production performance of the tight oil reservoir developed by elastic energy.

Hysteretic model for corroded reinforced concrete columns retrofitted with FRP

A hysteresis model was developed for fiber reinforced polymer (FRP)-retrofitted reinforced concrete (RC) columns with corroded reinforcing bars. The test data of 49 FRP-retrofitted corroded columns and 19 intact columns (with no corrosion or FRP wraps) under repeat-cyclic loading were collected to establish a database. A polygonal model was adopted to simulate the hysteretic behavior of FRP-retrofitted corroded columns. This was determined using backbone and cyclic parameters. For the backbone parameters, a hybrid influence factor (HIF) was introduced to incorporate the coupling effects of corrosion and FRP retrofitting. A suite of empirical equations was developed using multivariate linear regression analysis to predict the HIFs of each backbone parameter in association with the corrosion rate and important column design parameters. Moreover, an empirical relationship was developed to determine the cyclic parameters of the hysteretic model using a regression analysis. The predicted hysteretic curves were compared with the experimental results, demonstrating sufficient accuracy for both intra- and extra-database tests. Finally, the developed hysteretic model was used to establish a macro-type structural model for the FRP-retrofitted corroded RC frames. This benefitted the analysis of structural collapse under earthquakes, and the effects of the corrosion rate and FRP retrofitting schemes on the seismic collapse capacity of RC frames were examined.

Thermodynamically-Consistent Modeling of Ferromagnetic Hysteresis.

Models of ferromagnetic hysteresis are established by following a thermodynamic approach. The class of constitutive properties is required to obey the second law, expressed by the Clausius-Duhem inequality, and the Euclidean invariance. While the second law states that the entropy production is non-negative for every admissible thermodynamic process, here the entropy production is viewed as a non-negative constitutive function. In a three-dimensional setting, the magnetic field and the magnetization are represented by invariant vectors. Next, hysteretic properties are shown to require that the entropy production is needed in an appropriate form merely to account for different behavior in the loading and the unloading portions of the loops. In the special case of a one-dimensional setting, a detailed model is determined for the magnetization function, in terms of a given susceptibility function. Starting from different initial magnetized states, hysteresis cycles are obtained by solving a nonlinear ordinary differential system. Cyclic processes with large and small amplitudes are established for materials such as soft iron.

A design method for seismic retrofit of reinforced concrete frame buildings using aluminum shear panels

Despite significant progress in research and development of aluminum shear panels in recent decades, their implementation for seismic retrofit of existing reinforced concrete (RC) buildings can still be significantly extended. Their application is limited by the general lack of relatively simple and effective design criteria and proper guidelines. This paper develops a design method for the seismic retrofit of reinforced concrete buildings using aluminum multi-stiffened shear panels as dampers. Both the nonlinearity in the structure and the dampers-structure interaction are considered to give an optimal distribution of the shear panels over the height of the building. The analytical laws refer to dissipative aluminum shear panels recently tested and analyzed by the authors. The proposed procedure has been described in detail. Its applicability has been demonstrated by analyzing two typical RC buildings having drift capacity-to-demand ratios ranging from 0.505 to 0.624. The design value of the panel-to-frame stiffness ratio has been found to range from 0.594 to 1.432 as a function of the lateral stiffness of the existing building. The verification of the proposed procedure has been carried out by checking the validity of the design assumptions. The first one (i.e., the mode shapes remain the same before and after retrofit) has been checked using the modal assurance criterion that gives values ranging from 0.992 to 0.998. The second one (i.e., uniform yield drift distribution over the building height) has been checked by comparing the yield drifts with their average value giving a standard deviation ranging from about 11 to 15%. The effectiveness of the design method has been finally validated through nonlinear time-history analysis for different seismic accelerograms and hysteresis models. The results show that the seismic retrofit design procedure is effective in significantly reducing inter-story drift (maximum inter-story drift ratio demands ranging from 1.04 to 2.07%) thus satisfying the acceptance criteria of the building, and avoiding drift concentration and consequential weak story collapse.

Improved simpler R/C hysteresis model considering biaxial interaction

From practical point of view, it is evident that the seismic wave acted on structures through two mutually orthogonal components which have significant combined effect on inelastic demands of the structure. Usually a smaller amount of ground motion generally applied in only one direction than the other and in most of the cases the studies considered only limited inelasticity. Therefore, further research is needed that considers ground motion in both horizontal directions with corresponding bi-directional intensities. Study shows, the combined effects cause significant amount of degradation of strength and stiffness which in turn cause early yielding of R/C(Reinforced Concrete) structural member. Conventional uni-axial model does not consider this type of bi-directional interaction. Some existing simpler bi-axial hysteresis model which can capture biaxial interaction shows satisfactory results, but still the deviation from experimental results are very prominent. On the other hand, some existing sophisticated bi-axial hysteresis model shows better accuracy in predicting response of R/C structural elements but these types of models require large number of calibrated test results which makes them case-specific. In this backdrop, by using principle of yield surface, this study aims to incorporate bi-directional interaction over a simpler hysteresis model which primarily able to capture uni-directional loading effects. Detailed computational scheme of the enhanced simpler uni-axial hysteresis model and extension of the model to capture bi-directional interaction with its performance in prediction of inelastic cyclic behaviour of R/C structural members are presented in this paper. From the performance point of view, it is clearly visible that the proposed simple bi-axial hysteresis model can predict experimental load–displacement curves of R/C structural members under bi-directional reversible loading with acceptable accuracy. The requirement of limited number of input parameters for the present proposed bi-axial hysteresis model make it more convenient to assess the progressive seismic damage under bi-directional ground motion.

Safety-Critical Control Systems [About this Issue

This issue of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">IEEE Control Systems</i> includes one feature and one lecture note. In the feature, “Runtime Assurance for Safety-Critical Systems: An Introduction to Safety Filtering Approaches for Complex Control Systems” <xref ref-type="list-item" rid="list-itemA1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[A1]</xref> , authors Kerianne L. Hobbs, Mark L. Mote, Matthew C.L. Abate, Samuel D. Coogan, and Eric M. Feron provide an introductory tutorial of runtime assurance (RTA) concepts and their role in ensuring safety of complex control systems. Assuming an undergraduate-level understanding of control theory and state-space concepts, this article provides theory and examples for RTA architectures, four types of RTA approaches, and a number of systems engineering and practical considerations for employing RTA in safety-critical, cyberphysical systems. In the “Lecture Notes” column, “The Prandtl-Ishlinskii Hysteresis Model: Fundamentals of the Model and Its Inverse Compensator,” <xref ref-type="list-item" rid="list-itemA2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[A2]</xref> Mohammad Al Janaideh, Mohammad Al Saaideh, and Xiaobo Tan introduce the mathematical formulations of the Prandtl–Ishlinskii (PI) and Generalized PI (GPI) hysteresis models as well as their analytical inverses. These models can effectively characterize hysteresis nonlinearities in various systems, especially smart-material actuators, and their inverses can be used in feedforward compensation to mitigate the effect of hysteresis. Numerical examples of the PI and GPI models as well as their analytical inverses are also included in the article. The intended audience includes graduate students and researchers from academia and industry interested in hysteresis modeling and compensation.

Modeling of Hysteresis in Single-Crystalline Barium Titanate with Allowance for Domain Structure Evolution

Modeling of Hysteresis in Single-Crystalline Barium Titanate with Allowance for Domain Structure Evolution

The magneto-mechanic hysteresis model for giant magnetostrictive materials based on the magnetic domain theory

In the paper, a magneto-mechanic hysteresis model for giant magnetostrictive materials is suggested by considering the effect of the domain rotation and domain wall motion on the magnetization process under prestress and the applied magnetic field. The coercive force, which is magneto-mechanic dependent, is proposed instead of a pinning constant in the Jiles–Atherton model. The model can well predict the characteristics of a magnetization-applied field curve and magnetostrictive strain-applied field curve shown in the experiment, especially the “overturn phenomenon” under different compressive prestresses. Furthermore, the effect of the microstructure parameter, such as the ratio of the domain wall thickness to the internal stress wavelength, the amplitude of internal stress, the ratio of the domain wall thickness to the inclusion radius, and inclusion consistency, on coercive force under applied prestress can also be described by the model. The comparison between the results predicted by the model and experiment shows that the model is suited for a wide-ranging applied magnetic field.

Analysis of the convergence of Newton method by finite element simulation with vector hysteresis stop model

PurposeThe goal of this research is to investigate the convergence behavior of the Newton iteration, when solving the nonlinear problem with consideration of hysteresis effects. Incorporating the vector hysteresis model in the magnetic vector potential formulation has encountered difficulties. One of the reasons is that the Newton method is very sensitive regarding the starting point and states distinct requirements for the nonlinear function in terms of monotony and smoothness. The other reason is that the differential reluctivity tensor of the material model is discontinuous due to the properties of the stop operators. In this work, line search methods to overcome these difficulties are discussed.Design/methodology/approachTo stabilize the Newton iteration, line search methods are studied. The first method computes an error-oriented search direction. The second method is based on the Wolfe-Powell rule using the Armijo condition and curvature condition.FindingsIn this paper, the differentiation of the vector stop model, used to evaluate the Jacobian matrix, is studied. Different methods are applied for this nonlinear problem to ensure reliable and stable finite element simulations with consideration of vector hysteresis effects.Originality/valueIn this paper, two different line search Newton methods are applied to solve the magnetic field problems with consideration of vector hysteresis effects and ensure a stable convergence successfully. A comparison of these two methods in terms of robustness and efficiency is presented.

Seismic response evaluation of spring-based piston braced frames by employing closed-loop dynamic (CLD) testing

This paper employs the Closed-Loop Dynamic (CLD) testing method for evaluating the seismic response of Spring-Based Piston Braced Frames (SBPBF) by utilizing a combination of experimental and numerical approaches. The CLD testing procedure is an iterative process, which is initiated by conducting cyclic tests on a reduced-scale bracing element and followed by computational simulations of a full-scale braced frame. To this end, a hysteresis model is developed, based on testing the Spring-Based Piston Bracing (SBPB) element, which is incorporated into a simulated multi-story SBPBF. The time-dependent deformations of SBPBs under earthquake loadings are scaled down using similitude law, serving as a loading protocol for further testing and refining the hysteresis model. The developed model is then calibrated, scaled up, and integrated into the computational model to generate more precise deformation histories of the SBPB. The refined model is validated through aniterative process that combines experimental and numerical results. An illustrative example is presented to demonstrate the feasibility of the CLD testing method for SBPB archetypes. The efficiency of this approach is demonstrated by the remarkable match between the experimental and computational results. Additionally, a comparative numerical assessment is conducted on braced frames equipped with non-compressed and pre-compressed SBPBs, revealing their superior performance compared to the Buckling-Restrained Braced Frames (BRBFs).

Semi-Implicit Integration and Data-Driven Model Order Reduction in Structural Dynamics With Hysteresis

AbstractStructural damping is often empirically rate-independent wherein the dissipative part of the stress depends on the history of deformation but not its rate of change. Hysteresis models are popular for rate-independent dissipation; and a popular hysteresis model is the Bouc-Wen model. If such hysteretic dissipation is incorporated in a refined finite element model, then the model involves the usual structural dynamics equations along with nonlinear nonsmooth ordinary differential equations for a large number of internal hysteretic states at Gauss points used within the virtual work calculation. For such systems, numerical integration is difficult due to both the distributed nonanalytic nonlinearity of hysteresis as well as large natural frequencies in the finite element model. Here, we offer two contributions. First, we present a simple semi-implicit integration approach where the structural part is handled implicitly based on the work of Piché, while the hysteretic part is handled explicitly. A cantilever beam example is solved in detail using high mesh refinement. Convergence is good for lower damping and a smoother hysteresis loop. For a less smooth hysteresis loop and/or higher damping, convergence is noted to be roughly linear on average. Encouragingly, the time-step needed for stability is much larger than the time period of the highest natural frequency of the structural model. Subsequently, data from several simulations conducted using the above semi-implicit method are used to construct reduced order models of the system, where the structural dynamics is projected onto a few modes and the number of hysteretic states is reduced significantly as well. Convergence studies of error against the number of retained hysteretic states show very good results.