超磁致伸缩材料迟滞特性的新Hammerstein建模  

New Hammerstein Modeling of Hysteresis Characteristics of Giant Magnetostrictive Materials

作　　者：李宁 安坤 郭立山 李森 孟江[2] LI Ning;AN Kun;GUO Lishan;LI Sen;MENG Jiang(School of Electrical and Control Engineering,North university of China,Taiyuan 030051,China;School of Mechanical Engineering,North university of China,Taiyuan 030051,China)

机构地区：[1]中北大学电气与控制工程学院,山西太原030051 [2]中北大学机械工程学院,山西太原030051

出　　处：《中北大学学报（自然科学版）》2024年第5期706-715,共10页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(61774138);山西省面上自然科学基金资助项目(201801D121184)。

摘　　要：超磁致伸缩材料(Giant Magnetostrictive Material,GMM)作为一种新型功能材料,因其具有磁-机耦合系数大、响应速度快、频响特性好等优点而被广泛应用于能量采集、微位移驱动、精密定位控制等领域,但材料复杂的迟滞非线性影响了其致动器的定位精度,为了辨识超磁致伸缩材料中存在的迟滞非线性,本文提出一种新Hammerstein模型建模方法。此方法的优点在于模型可以更好地逼近迟滞非线性,提供更高的精度,减少了串联环节的参数辨识工作量。首先,构建一个基于双曲函数的迟滞算子扩展空间的极限学习机模型,用其表示新Hammerstein模型中的静态非线性部分。其次,提取极限学习机模型的全连接层的权重和偏置参数用于构建新模型中的动态线性部分的状态空间方程,减少了传统模型中串联环节的模型参数辨识的工作。最后,建立了可以描述超磁致伸缩材料迟滞特性的新Hammerstein模型。新Hammerstein模型的建模相对误差为0.86%~3.69%,平均绝对误差为2.63%,比传统Hammerstein模型均方根误差低0.8μm左右,平均绝对误差提高将近4%。仿真结果证明了新Hammerstein模型对超磁致伸缩材料复杂迟滞特性建模的有效性。Giant magnetostrictive material(GMM),as a new type of functional material,was widely used in energy harvesting,micro displacement driving,precision positioning control and other fields due to its advantages of large magneto mechanical coupling coefficient,fast response speed,and good frequency response characteristics.However,the complex hysteresis nonlinearity of the material affected the positioning accuracy of its actuator.In order to identify the hysteresis nonlinearity in GMM materials,this paper proposed a new Hammerstein model modeling method.The advantage of this method was that the model could better approximate hysteresis nonlinearity,provide higher accuracy,and reduce the workload of parameter identification in the series link.Firstly,an extreme learning machine model was constructed based on hyperbolic functions to represent the static nonlinear part of the new Hammerstein model in the extended space of hysteresis operators.Secondly,the extracted weights and bias parameters of the fully connected layers of the extreme learning machine model was used to construct the state space equation of the dynamic linear part in the new model,which reduced the workload of identifying model parameters in the traditional model with serial links.Finally,a new Hammerstein model was established to describe the hysteresis characteristics of giant mag‐netostrictive materials.The modeling relative error percentage of the new Hammerstein model is 0.86%to 3.69%,and the average absolute error percentage is 2.63%,which is about 0.8μm lower than the root mean square error of the traditional Hammerstein model,and the average absolute percentage error increases 4%.The simulation results demonstrate the effectiveness of the new Hammerstein model in modeling the complex hysteresis characteristics of giant magnetostrictive materials.

关 键 词：超磁致伸缩材料 迟滞特性 极限学习机 迟滞算子 HAMMERSTEIN模型 

分 类 号：TP389.1[自动化与计算机技术—计算机系统结构] TB381[自动化与计算机技术—计算机科学与技术]