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The axial force will be altered as a result of the overturning influence exerted by both horizontal and vertical seismic events, as well as the secondary effects induced by gravitational loads. The variation of the axial force will greatly affect the seismic performance of reinforced concrete (RC) columns, thus warranting close attention. This paper proposes a hysteresis model of RC columns considering the cumulative damage effect under the action of variable axial force. First, three groups of cyclic loading tests were performed across three distinct groups. Subsequently, numerical analysis models were constructed, employing fiber-based finite element methods. Furthermore, according to the test and finite element simulation results, the existing damage value was modified to describe the degradation of the stiffness and load-bearing capacity. Next, through a regression analysis, the skeleton curve was established. Finally, the hysteresis behavior under the influence of variable axial load was ascertained. The results, when compared with the experimental data, show that the proposed hysteresis model can accurately describe the seismic performance of RC columns under the influence of variable axial force.

Shape Memory Alloys (SMAs) are used to design actuators, which are one of the most fascinating applications of SMA. Usually, they are on-off actuators because, in the case of continuous actuators, the nonlinearity of their characteristics is the problem. The main problem, especially in control systems in these actuators, is a hysteretic loop. There are many models of hysteresis, but from a control theory point of view, they are not helpful. This study used an artificial neural network (ANN) to model the SMA actuator hysteresis. The ANN structure and training method are presented in the paper. Data were generated from the Preisach model for training. This approach allowed for quick and controllable data generation, making experiments thoroughly planned and repeatable. The advantage and disadvantage of this approach is the lack of disturbances. The paper’s main goal is to model an SMA actuator. Additionally, it explores whether and how an ANN can describe and model the hysteresis loop. A literature review shows that ANNs are used to model hysteresis, but to a limited extent; this means that the hysteresis loop was modelled with a hysteretic element.

This paper develops a model for lithium-ion batteries under dynamic stress testing (DST) and federal urban driving schedule (FUDS) conditions that incorporates associated hysteresis characteristics of 18650-format lithium iron-phosphate batteries. Additionally, it introduces the adaptive sliding mode observer algorithm (ASMO) to achieve robust and swiftly accurate estimation of the state of charge (SOC) of lithium-iron-phosphate batteries during electric vehicle duty cycles. The established simplified hysteresis model in this paper significantly enhances the fitting accuracy during charging and discharging processes, compensating for voltage deviations induced by hysteresis characteristics. The SOC estimation, even in the face of model parameter changes under complex working conditions during electric vehicle duty cycles, maintains high robustness by capitalizing on the easy convergence and parameter insensitivity of ASMO. Lastly, experiments conducted under different temperatures and FUDS and DST conditions validate that the SOC estimation of lithium-iron-phosphate batteries, based on the adaptive sliding-mode observer and the simplified hysteresis model, exhibits enhanced robustness and faster convergence under complex working conditions and temperature variations during electric vehicle duty cycles.

A hysteresis motor produces output torque through the hysteresis effect of magnetic materials. It has the advantages of a simple structure, high-speed operation, high temperature resistance, low noise and self-starting capability. It can be applied to some special occasions requiring high speed and high stationarity. However, its disadvantage is low torque density, low efficiency and low power factor. The permanent magnet hysteresis motor is a compromise of the characteristics of permanent magnet motor and hysteresis motor, and it can be self-starting in the case of having a torque density comparable to that of a permanent magnet motor. In addition, there are some new structures of hysteresis motors, which open up the direction for innovative applications. Due to the complexity of magnetic properties, the calculation methods and dynamic models of hysteresis motors and permanent magnet hysteresis motors are special and also depend on the research of hysteresis materials and hysteresis models. This paper starts from the principle and classification of the hysteresis motor, and different structures and the corresponding analysis methods are reviewed. The motors with new structures and new methods are emphasized, the innovation and contribution of existing research are summarized, and the development trend of hysteresis motors is described.

Shape memory alloys (SMAs) are widely used in aerospace, automobile, and other fields because of their excellent properties, such as large driving force and large deformation. A training method with a bidirectional memory effect is proposed for SMA actuators. The trained SMA units can be heated and cooled to change their shape (shorten and extend). The trained SMA is used as an actuator to drive the deformation of a structure. Due to the obvious hysteresis characteristics of SMA, a temperature-displacement hysteresis model based on the Preisach model is proposed in order to reduce the influence of hysteresis in the process of structural deformation. The F function method (FFM) is used for Preisach numerical implementation, and a PID control method is used for the precise control of structural deformation. Compared with the PID control method without hysteresis model, this method is superior to the PID control method in response speed and control accuracy. The maximum relative error of three target points in the experiment is 5.45%, which is better than the PID control method without this model. The hysteresis model can be applied to the displacement control of a SMA-based actuator.

The fast tool servo (FTS) technology has unique advantages in the machining of complex surfaces such as special-shaped targets and free-form surfaces. In view of the shortcomings in the performance of the existing FTS device, this paper puts forward a novel FTS which uses two piezoelectric ceramics instead of flexure hinges to provide restoring force. Firstly, the feasibility of the double-drive principle is verified theoretically, and the corresponding mechanism is optimized accordingly. Then, the system control hysteresis model is established and identified, and the appropriate control strategy is designed. Finally, the performances of the proposed FTS device are tested, and a typical microstructure is machined based on the device and ultra-precision lathe. The results indicate that the proposed device effectively improves the performance of the FTS system, which is useful for the processing of microstructures and free-form surfaces.

An innovative symmetrical hysteresis model for reinforced concrete (RC) rectangular hollow columns is presented. The Bouc–Wen–Baber–Noori (BWBN) model was selected to depict the inelastic restoring forces and was improved by introducing a coefficient to describe the relationship between stiffness degradation and peak displacement. Sensitivity analysis was conducted at the local and global levels to clarify the importance of each parameter in the improved BWBN model. As such, a hybrid intelligence algorithm named PSOGSA was employed to identify the parameters of the BWBN model utilizing quasi-static tests of 16 hollow columns. The empirical formulas were regressed to bridge the connection between the BWBN model and design parameters of hollow columns. The results showed that the hysteresis curves of the improved BWBN model calibrated by the PSOGSA agreed well with the measured loops. In addition, the accuracy of the empirical prediction method of hysteretic parameters was checked through comparison with other hollow members. The calibrated improved BWBN model produced more precise hysteretic responses for RC hollow columns, since the peak and residual performance levels were simultaneously considered.

Pneumatic artificial muscle (PAM) is attractive in rehabilitation and biomimetic robots due to its flexibility. However, there exists a strong hysteretic nonlinearity in PAMs and strong coupling between the output displacement and the output force. At present, most commonly used hysteresis models can be treated as two-dimensional models, which only consider the nonlinearity between the input and the output displacement of the PAM without considering the coupling of the output force. As a result, high-precision modeling and estimation of the PAM’s behavior is difficult, especially when the external load of the system varies significantly. In this paper, the influence of the output force on the displacement is experimentally investigated. A three-dimensional model based on the modified Prandtl–Ishlinskii (MPI) model and the Nonlinear AutoRegressive Moving Average with eXogenous inputs (NARMAX) model is proposed to describe the relationship and couplings among the input, the output displacement, and the output force of the PAM. Experiments are conducted to verify the modeling accuracy of the proposed model when the external load of the PAM varies across a wide range. The experimental results show that the proposed model captures well the hysteresis and couplings of the PAM and can precisely predict the PAM’s behavior.

In the fast tool servo (FTS) system for microstructure surface cutting, the dynamic voltage hysteresis of piezoelectric actuators (PEAs) and the cutting force produced in the manufacturing affect the driving accuracy and the cutting performance. For a multi-input-single-output (MISO) cutting system, in this paper, a dynamic hysteresis model based on a rate-dependent Prandtl–Ishlinskii model is proposed. A backpropagation neural network (BPNN) is established to describe the cross-coupling effect between the applied voltage and external load. An inverse dynamic model is developed to compensate the nonlinearity of PEAs. The accuracy of the model and its inverse is discussed and the performance of the inverse feedforward compensator is validated through experiments.

Various seismic analysis methods are being used to predict the response of structures to earthquakes. Although nonlinear dynamic analysis (NDA) is considered an ideal method to represent the most realistic behavior of a structure among these various methods, correct results can be derived only when the analysis model is carefully developed by a knowledgeable person. It is particularly important to properly implement the behavior characteristics depending on the reversed cyclic load in the NDA of a building made of reinforced concrete (RC) moment frames. This study evaluated the hysteresis model suitable for NDA of existing RC moment frames, and 45 analysis models were reviewed, in which the pivot, concrete, and Takeda hysteresis models were applied differently to beams and columns. The pivot model was evaluated as the most reliable hysteresis model for each structural member by comparing and analyzing not only the responses of the entire frame but also the responses of column and beam members focusing on energy dissipation. However, this model can have practical limitations in that the parameters associated with the reinforcement detailing and applied loads need to be defined in detail. The analysis model applying Takeda to the beam, which predicted the average response at a reliable level compared to the reference model, was identified as a practical alternative when it is difficult to apply the pivot model to all frame members.

This paper proposes a new electrically controlled magnetic variable-speed gearing (EC-MVSG) machine, which is capable of providing controllable gear ratios for hybrid electric vehicle (HEV) applications. The key design feature involves the adoption of a magnetic gearing structure and acceptance of the memory machine flux-mnemonic concept. Hence, the proposed machine can not only offer a gear-shifting mechanism for torque and speed transmission, but also provide variable gear ratios for torque and speed variation. The electromagnetic design is studied and discussed. The finite-element method is developed with the hysteresis model to verify the validity of the machine design.

Hysteresis behaviors are inherent characteristics of piezoelectric ceramic actuators. The classical Duhem model (CDM) as a popular hysteresis model has been widely used, but cannot precisely describe rate-dependent hysteresis behaviors at high-frequency and high-amplitude excitations. To describe such behaviors more precisely, this paper presents a modified Duhem model (MDM) by introducing trigonometric functions based on the analysis of the existing experimental data. The MDM parameters are also identified by using the nonlinear least squares method. Six groups of experiments with different frequencies or amplitudes are conducted to evaluate the MDM performance. The research results demonstrate that the MDM can more precisely characterize the rate-dependent hysteresis behaviors comparing with the CDM at high-frequency and high-amplitude excitations.

Giant magnetostrictive actuators (GMA) driven by giant magnetostrictive material (GMM) has some advantages such as a large strain, high precision, large driving force, fast response, high reliability, and so on, and it has become the research hotspot in the field of microdrives. Research shows there is a nonlinear, intrinsic relationship between the output signal and the input signal of giant magnetostrictive actuators because of the strong coupling characteristics between the machine, electromagnetic field, and heat. It is very complicated to construct its nonlinear eigenmodel, and it is the basis of the practical process of giant magnetostrictive material to construct its nonlinear eigenmodel. Aiming at the design of giant magnetostrictive actuators, the magnetization model based on a free-energy hysteresis model has been deeply researched, constructed, and put forward by Smith, which combines Helmholtz−Gibbs free energy and statistical distribution theory, to simulate the hysteresis model at medium or high driving strengths. Its main input and output parameters include magnetic field strength, magnetization, and mechanical strain. Then, numerical realization and verification of the magnetization model are done by the Gauss−Legendre integral discretization method. The results show that the magnetization model and its numerical method are correct, and the research results provide a theoretical basis for the engineering application of giant magnetostrictive material and optimized structure of giant magnetostrictive material actuators, which have an important practical application value.

With the aim to model the seismic behavior of steel reinforced concrete (SRC) frame columns, in this research, hysteresis and skeleton curves were obtained based on the damage test results of SRC frame columns under low cyclic repeat loading and the hysteretic behavior of the frame columns was further analyzed. Then, the skeleton curve and hysteresis loops were further simplified. The simplified skeleton curve model was obtained through the corresponding feature points obtained by mechanical and regression analysis. The nonlinear combination seismic damage index, which was developed by the test results and can well reflect the effect of the loading path and the number of loading cycle of SRC frame columns, was used to establish the cyclic degradation index. The strength and stiffness degradation rule of the SRC frame columns was analyzed further by considering the effect of the accumulated damage caused by an earthquake. Finally, the hysteresis model of the SRC frame columns was established, and the specific hysteresis rules were given. The validity of the developed hysteresis model was verified by e comparison between the calculated results and the test results. The results showed that the model could describe the hysteresis characteristics of the SRC frame columns under cyclic loading and provide guidance for the elastoplastic time-history analysis of these structures.

Shape memory alloys (SMAs) offer a high power-to-weight ratio, large recovery strain, and low driving voltages, and have thus attracted considerable research attention. The difficulty of controlling SMA actuators arises from their highly nonlinear hysteresis and temperature dependence. This paper describes a combination of self-sensing and model-based control, where the model includes both the major and minor hysteresis loops as well as the thermodynamics effects. The self-sensing algorithm uses only the power width modulation (PWM) signal and requires no heavy equipment. The method can achieve high-accuracy servo control and is especially suitable for miniaturized applications.