A precision-drive hysteresis model with an equal-density weight function for GMA feedforward compensation

Giant magnetostrictive actuators(GMAs) are a widely used type of micro-nano actuator, and they are greatly significant in the field of precision engineering. The accuracy of a GMA often depends on its hysteresis model. However, existing models have some limitations,including the difficulty of identifying their parameters and the tradeoff between the quantity of modeling data required and the level of precision achieved. To solve these problems, in this paper, we propose a Preisach inverse model based on equal-density segmentation of the weight function(E-Preisach). The weight function used to calculate the displacement is first discretized. Then, to obtain a finer weight distribution, the discretized geometric units are uniformly divided by area. This can further minimize the output displacement span, and it produces a higher-precision hysteresis model. The process of parameter identification is made easier by this approach, which also resolves the difficulty of obtaining high precision using a small amount of modeling data. The Preisach and the E-Preisach inverse models were investigated and compared using experiments. At frequencies of 1 and 5 Hz, it was found that the E-Preisach inverse model decreases the maximum error of the feedforward compensation open-loop control to within 1 μm and decreases the root-mean-square error in displacement to within0.5 μm without the need to increase the number of measured hysteresis loops. As a result, the E-Preisach inverse model streamlines the structure of the model and requires fewer parameters for modeling. This provides a high-precision modeling method using a small amount of modeling data;it will have applications in precision engineering fields such as active vibration damping and ultra-precision machining.

Modeling and Tracking Control for Piezoelectric Actuator Based on a New Asymmetric Hysteresis Model

This paper presents a new asymmetric hysteresis model and its application in the tracking control of piezoelectric actuators. The proposed model is based on a coupled-play operator which can avoid the conventional Prandtl-Ishlinskii(CPI)model's defects, i.e., the symmetric property. The high accuracy for modeling asymmetric hysteresis is validated by comparing simulation results with experimental measurements. In order to further evaluate the performance of the proposed model in closed-loop tracking application, two different hybrid control methods which experimentally demonstrate their performance under the same operating conditions, are compared to validate that the hybrid control strategy with proposed hysteresis model can mitigate the hysteresis more effectively and achieve better tracking precision. The experimental results demonstrate that the proposed modeling and tracking control strategy can realize efficient control of piezoelectric actuator.

Magnetostrictive and Kinematic Model Considering the Dynamic Hysteresis and Energy Loss for GMA

Due to the influence of magnetic hysteresis and energy loss inherent in giant magnetostrictive materials （GMM）, output displacement accuracy of giant magnetostrictive actuator （GMA） can not meet the precision and ultra precision machining. Using a GMM rod as the core driving element, a GMA which may be used in the field of precision and ultra precision drive engineering is designed through modular design method. Based on the Armstrong theory and elastic Gibbs free energy theory, a nonlinear magnetostriction model which considers magnetic hysteresis and energy loss characteristics is established. Moreover, the mechanical system differential equation model for GMA is established by utilizing D＇Alembert＇s principle. Experimental results show that the model can preferably predict magnetization property, magnetic potential orientation, energy loss for GMM. It is also able to describe magnetostrictive elongation and output displacement of GMA. Research results will provide a theoretical basis for solving the dynamic magnetic hysteresis, energy loss and working precision for GMA fundamentally.

A Nonlinear Observer Approach of SOC Estimation Based on Hysteresis Model for Lithium-ion Battery

In this paper, a state of charge(SOC) estimation approach for lithium-ion battery based on equivalent circuit model and the input-to-state stability(ISS) theory has been proposed. According to the electrochemical performance of lithiumion battery, the equivalent circuit model with two RC networks is established, which includes hysteresis characteristic in inner electrochemical response process. The nonlinear relation between open circuit voltage(OCV) and SOC is obtained from a rapid test. Exponential fitting method is used to identify the parameters of the model. A novel state observer based on ISS theory is designed for lithium-ion battery SOC estimation. The designed observer is tested on AMESim and Simulink co-simulation. The simulation results show that the proposed method has a high SOC estimation accuracy with an error of about 2 percent.

STRESS-STRAIN HYSTERESIS OF POLYCRYSTALLINE SMAs─Ⅰ:A MODEL

In this paper, a theoretical model was presented to simulate the stress-strain hysteresis and the inner hysteretic behaviors, which were observed for polycrystalline Ni-Ti and Cu-based shape memory alloys (SMAs) at various temperatures. It was assumed that the stress-strum hysteresis of the grains of a polycrystalline sample of SMAs was relatively simple and easy to be calculated. The texture of the sample was characterized by a distribution function, which could be obtained from the experiments. Thercfore,the model provided a means to simulate and, for the first time, to predict the stressstrain hysteresis at different loading temperatures for polycrystalline SMAs.

Neural model-based adaptive control for systems with unknown Preisach-type hysteresis

An adaptive control scheme is presented for systems with unknown hysteresis. In order to handle the case where the hysteresis output is unmeasurale, a novel model is firstly developed to describe the characteristic of hysteresis. This model is motivated by Preisach model but implemented by using neural networks ( NN) . The main advantage is that it is easily used for controller design. Then, the adaptive controller based on the proposed model is presented for a class of SISO nonlinear systems preceded by unknown hysteresis, which is estimated by the proposed model. The laws for model updating and the control laws for the neural adaptive controller are derived from Lyapunov stability theorem, therefore the semiglobal stability of the closed-loop system is guaranteed. At last, the simulation results are illustrated.

Robust Stability of Nonlinear Plants with a Non-symmetric Prandtl-Ishlinskii Hysteresis Model

In this paper, robust stability of nonlinear plants represented by non-symmetric Prandtl-Ishlinskii （PI） hysteresis model is studied. In general, PI hysteresis model is the weighted superposition of play or stop hysteresis operators, and the slopes of the operators are considered to be the same. In order to make a hysteresis model, a modified form of non-symmetric play hysteresis operator with unknown slopes is given. The hysteresis model is described by a generalized Lipschitz operator term and a bounded parasitic term. Since the generalized Lipschitz operator is unknown, a new condition using robust right coprime factorization is proposed to guarantee robust stability of the controlled plant with the hysteresis nonlinearity. As a result, based on the proposed robust condition, a stabilized plant is obtained. A numerical example is presented to validate the effectiveness of the proposed method.

A five-parameter constitutive model for hysteresis shearing and energy dissipation of rock joints

Rock joints exhibit hysteresis shearing behavior and produce energy dissipation under shear cyclic loads,which however cannot be accurately depicted by existing constitutive models. This paper establishes a constitutive model for hysteresis shearing and associated energy dissipation of rock joints. Analytical expressions of the model during cyclic shearing processes are derived. Derivation of the model indicates no energy dissipation in the elastic stage. When the shear load exceeds elastic boundary, nonlinear energy dissipation takes place. Validations with experiments show that the proposed model provides good conformities with direct shear curves and hysteresis loops, and can predict the energy dissipation characteristics of rock joints under different working conditions. Compared to the constitutive models using Weibull's distribution, the proposed one is smooth at the elastic boundary and can accurately capture the maximum shear stress. Unlike the existing incremental-type models, the proposed one provides clear and direct analytical expressions for both shear stress and energy dissipation during the whole displacement domain, which is more convenient in application.

OPTIMAL CONTROL OF A POPULATION DYNAMICS MODEL WITH HYSTERESIS

This paper addresses a nonlinear partial differential control system arising in population dynamics.The system consist of three diffusion equations describing the evolutions of three biological species:prey,predator,and food for the prey or vegetation.The equation for the food density incorporates a hysteresis operator of generalized stop type accounting for underlying hysteresis effects occurring in the dynamical process.We study the problem of minimization of a given integral cost functional over solutions of the above system.The set-valued mapping defining the control constraint is state-dependent and its values are nonconvex as is the cost integrand as a function of the control variable.Some relaxationtype results for the minimization problem are obtained and the existence of a nearly optimal solution is established.

DYNAMIC FREE ENERGY HYSTERESIS MODEL IN MAGNETOSTRICTIVE ACTUATORS

A dynamic free energy hysteresis model in magnetostrictive actuators is presented. It is the free energy hysteresis model coupled to an ordinary different equation in an unusual way. According to its special structure, numerical implementation method of the dynamic model is provided. The resistor parameter in the dynamic model changes according to different frequency ranges. This makes numerical implementation results reasonable in the discussed operating frequency range. The validity of the dynamic free energy model is illustrated by comparison with experimental data.

一种自复位摇摆墙的改进Bouc-Wen滞回模型

Bouc-Wen模型是一种可表征结构及构件刚度、强度退化等的多功能非线性光滑滞回模型,可广泛应用于各类结构滞回行为的描述。自复位摇摆墙(Self-centering rocking wall, SCRW)结构由于其优越的抗震和自复位性能,滞回曲线呈“旗帜型”。为了更好地表征这种“旗帜型”滞回特性,在Bouc-Wen模型的基础上,建立一种具有较高精度和较好实用性的改进Bouc-Wen滞回模型。改进的Bouc-Wen模型参数是决定结构滞回性能力学特征的关键。由于该模型参数众多且选择范围不明确,为适应该类模型参数高效识别的需求,通过在MATLAB/Simulink环境中搭建程序框图,实现了对该理论模型控制参数的定性及定量分析,并运用遗传算法对10个SCRW试验结果进行参数识别,对识别结果进行统计分析,建立各参数与滞回曲线关键点的关系式,基于统计结果给出了各参数的建议取值范围;最后,通过SCRW拟静力试验对改进的滞回模型和参数取值范围进行了验证。结果表明:这种单自由度改进的Bouc-Wen滞回模型能较好地反映SCRW在往复荷载作用下无残余变形和强度、刚度退化特点的“旗帜型”滞回特性。所提出的参数取值范围显著提升了改进Bouc-Wen模型的识别精度与效率,识别过程对类似模型的参数识别具有参考价值。

Rate-Dependent Hysteresis Modeling and Compensation of Piezo-Driven Flexure-Based Mechanism

Updating parameters according to the driving rate of input, the rate-dependent Prandtl-Ishlinskii (PI) model is widely used in hysteresis modeling and compensation. In order to improve the modeling accuracy, two PI models identified at low and high driving rates separately are incorporated through a combination law. For the piezo- driven flexure-based mechanism, the very low damping ratio makes it easy to excite the structural vibration. As a re- sult, the measured hysteresis loop is greatly distorted and the modeling accuracy of the identified PI model is signifi- cantly affected. In this paper, a novel time-efficient parameter identification method which utilizes the superimposed sinusoidal signals as the control input is proposed. This method effectively avoids the excitation of the structural vibra- tion. In addition, as the driving rate of the superimposed sinusoidal signals covers a wide range, all the coefficients required for modeling the rate-dependence can be identified through only one set of experimental data. Hysteresis modeling and trajectory tracking experiments were performed on a 2-DOF piezo-driven flexure-based mechanism. The experimental results show that the combined hysteresis model maintains the modeling accuracy over the entire work- ing range of the flexure-based mechanism. The mechanism's hysteresis is significantly suppressed by the use of the inverse PI model as the feedforward controller; and better result is achieved when a feedback loop is also incorporated. The tracking performance of the flexure-based mechanism is greatly improved.

Modeling and Control for Magnetostrictive Hysteresis

To deal with the rate-dependent hysteresis presented in a magnetostrictive actuator, a new method of modeling and control is proposed. The relationship between inputs and outputs of the actuator is approximately described by a dynamic differential equation with two rate-dependent coefficients, each expressed as a polynomial of frequency. For a given frequency, the coefficients will be able to be estimated by approximating the experimental data of the outputs of the magnetostrictive actuator. Based on this model, a quasi-PID controller is designed. In the space of the coefficients and frequency, the stable domain of closed loop system with hysteresis is analyzed. The numerical simulation and experiments have born witness to the feasibility of the proposed new method.

Modeling of LiFePO4 battery open circuit voltage hysteresis based on recursive discrete Preisach model

This paper focuses on the modeling of LiFePO4 battery open circuit voltage （OCV） hysteresis. There exists obvious hysteresis in LiFePO4 battery OCV, which makes it complicated to model the LiFePO4 battery. In this paper, the recursive discrete Preisach model （RDPM） is applied to the modeling of LiFePO4 battery OCV hysteresis. The theory of RDPM is illustrated in detail and the RDPM on LiFePO4 battery OCV hysteresis modeling is verified in experiment. The robust of RDPM under different working conditions are also demonstrated in simulation and experiment. The simulation and experimental results show that the proposed method can significantly improve the accuracy of LiFePO4 battery OCV hysteresis modeling when the battery OCV characteristic changes, which conduces to the online state estimation of LiFePO4 battery.

A new model for the formation of contact angle and contact angle hysteresis

The formation mechanism of the contact angle and the sliding angle for a liquid drop on a solid surface plays an important role in producing hydrophobic surfaces. A new half soakage model is established in this paper as a substitute for Wenzel （complete soakage） and Cassie （no soakage） models. The model is suited to many solid surfaces, whether they are hydrophilic or hydrophobic, or even superhydrophobic. Based on the half soakage model, we analyse two surfaces resembling lotus, i.e. taper-like surface and corona-like surface. Furthermore, this new model is used to establish a quantitative relationship between the sliding angle and the parameters of surface morphology.

Hysteresis behavior and nonequilibrium phase transition in a one-dimensional evolutionary game model

We investigate a simple evolutionary game model in one dimension. It is found that the system exhibits a discontinuous phase transition from a defection state to a cooperation state when the b payoff of a defector exploiting a cooperator is small. Furthermore, if b is large enough, then the system exhibits two continuous phase transitions between two absorbing states and a coexistence state of cooperation and defection, respectively. The tri-critical point is roughly estimated. Moreover, it is found that the critical behavior of the continuous phase transition with an absorbing state is in the directed percolation universality class.

Modeling and identification of magnetostrictive hysteresis with a modified rate-independent Prandtl-Ishlinskii model

This paper presents a modified rate-independent Prandtl-Ishlinskii （MRIPI） model based on the Fermi-Dirac distri- bution for the asymmetric hysteresis description of magnetostrictive actuators. Generally, the classical Prandtl-Ishlinskii （CPI） model can hardly describe the asymmetric hysteresis. To overcome this limitation, various complex operators have been developed to replace the classical operator. In this study, the proposed MRIPI model maintains the classical operator while a modified input function based on the Fermi-Dirac distribution is presented to replace the classical input function. With this method, the MRIPI model can describe the asymmetric hysteresis of magnetostrictive actuators in a relatively simple mathematic format and has fewer parameters to be identified. A velocity-based sine cosine algorithm （VSCA） is also proposed for the parameter identification of the MRIPI model. To verify the validity of the MRIPI model, experiments are performed and the results are compared with those of the existing modeling methods.

Non Linear Magnetic Hysteresis Modelling by Finite Volume Method for Jiles-Atherton Model Optimizing by a Genetic Algorithm

This paper describes a generalization methodology for nonlinear magnetic field calculation applied on two-dimensional (2-D) finite Volume geometry by incorporating a Jiles-Atherton scalar hysteresis model. The scheme is based upon the definition of modified governing equation derived from Maxwell’s equations considered the magnetization M. This paper shows how to extract optimal parameters for the Jiles-Atherton model of hysteresis by a real coded genetic algorithm approach. The parameters identification is performed by minimizing the mean squared error between experimental and simulated magnetic field curves. The calculated results are validated by experiences performed in an SST’s frame.

Study on Vector Magnetic Properties of Magnetic Materials Using Hybrid Hysteresis Model

This paper presents a method to study the vector magnetic properties of magnetic materials under alternating and rotational magnetic field using 2-D vector hybrid hysteresis model.Combining Preisach model and Stoner-Wohlfarth(S-W)model,the vector hybrid hysteresis model is established for magnetic materials.The alternating and rotational hysteresis properties are calculated under different excitation frequency,respectively.And the computed results are compared with the experimental measurement ones.It is shown that the vector model can simulate the alternating and rotational magnetic properties effectively under low magnetization fields and low excitation frequency.

Hysteresis of the Magnetic Particle in a Dipolar Ising Model

Zero-temperature Monte Carlo simulations are used to investigate the hysteresis of a magnetic particle ina dipolarIsing model. The magnetic particle is described in a system of permanent dipoles, and the dipoles are locatedin a cubic lattice site. The effects of the shape and the size of the particle on the hysteresis loop at zero temperatureare obtained. For strong exchange interactions, the shapes of magnetic hysteresis loops approach rectangle. For weakexchange interactions, the effects of the size and the shape of the particle on the loops are more remarkable than thoseof strong exchange interactions case. The slope of the hysteresis loop decreases with the increase of the ratio of thesemi major axis to the semi minor axis of the ellipsoidal magnetic particle, and there is an increase of the slope of thehysteresis with the decrease of the size of the magnetic particle. The effects of the shape and size of the particle on thecoercive force at zero temperature are also investigated.