Implementation procedure for the generalized moving Preisach model based on a first order reversal curve diagram

First order reversal curves （FORC） of nanocomposite Nd2Fe14B/Fe3B magnetic materials were measured to attain a FORC diagram, which characterizes reversible magnetization, irreversible magnetization, and magnetic interactions in a hysteresis system. Then, generalized mov- ing Preisach model （GMPM） was implemented based on the FORC diagram. Reversible and irreversible magnetizations shown in FORCs and a FORC diagram were used as an input of GMPM. Coupling interaction between reversible and irreversible magnetizations was added when calculating reversible magnetization. Meanwhile, irreversible magnetic moments＇ interaction was approximately represented by mean field interaction. The result shows that the simulated main curves mostly coincide with the experimental curves.

Discrete Methods Based on First Order Reversal Curves to Identify Preisach Model of Smart Materials

Preisach model is widely used in modeling of smart materials. Although first order reversal curves （FORCs） have often found applications in the fields of physics and geology, they are able to serve to identify Preisach model. In order to clarify the relationship between the Preisach model and the first order reversal curves, this paper is directed towards： （1） giving the reason a first order reversal curve is introduced; （2） presenting, for identifying Preisach model, two discrete methods, which are analytically based on first order reversal curves. Herein also is indicated the solution＇s uniqueness of these two identifying methods. At last, the validity of these two methods is verified by simulating a real smart actuator both methods have been applied to.

基于离散逆Preisach模型的磁悬浮系统非线性补偿研究

磁悬浮平台控制中,电磁铁铁芯材料的磁滞特性会很大程度影响控制精度,补偿磁滞特性是磁悬浮精密控制系统中必不可少的一部分,为了实现对磁悬浮精密控制系统中磁滞非线性的补偿,课题组使用离散逆Preisach模型构造了一个补偿器。首先建立了离散逆Preisach模型,再依据磁滞补偿原理,构造补偿器;根据逆模型的曲线形状,建立了基于双曲正切的分布函数验证离散逆Preisach模型构造的合理性;最后使用非负最小二乘法辨识模型。结果表明离散逆Preisasch模型描述电磁铁逆磁滞回线的最大误差为0.3%。所构造的补偿器具有良好的补偿效果,为磁悬浮系统的磁滞补偿提供了一种可行方案。

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.

解析正Preisach磁滞模型的推导与修正

准确且快速地模拟软磁材料的磁滞特性是电机、变压器等电力设备电磁场仿真及其优化设计等工作可靠展开的基本前提。然而,经典Preisach磁滞模型因包含了复杂的双重积分运算而难以达到上述要求,而现有唯一的纯解析Preisach模型存在推导失误、无法通用等问题。为此,针对该解析Preisach模型的问题,推导正确的Everett函数解析表达式,并基于Preisach基本原理,分析在其基础上考虑可逆磁化分量的本质原因,继而提出首个正确且通用的解析正Preisach模型。将仿真结果与实测结果进行对比,验证所提模型的精度。

基于R-L型分数阶导数的动态解析逆Preisach模型

准确的变压器电磁暂态模型对保障电力变压器安全意义重大,其中更为重要的是对变压器铁芯部分的建模。然而,变压器铁芯的非线性磁滞特性及动态特性的模拟仍存在不精确,误差大等问题。为此,首先通过差分法改进静态解析正Preisach模型,构造一种更利于动态模型建立的静态解析逆Preisach模型;然后,在损耗统计理论、场分离技术以及分数阶导数理论的基础上,改进动态涡流场强分量,并与静态解析逆Preisach模型以及剩余损耗分量相结合,得到改进的动态解析逆Preisach磁滞模型,同时引入量子遗传算法对分数阶导数参数进行全局寻优。最后,将准确的动态解析逆Preisach模型在不同频率与不同最大磁密下与实验数据对比,结果表明,该模型的最大平均相对误差为5.857%,验证了该方法的有效性。

解析逆Preisach磁滞模型

如何在保证模拟精度的基础上,提升逆磁滞模型的计算速度一直以来是国际电磁场领域研究的热点问题。然而,现有所提逆磁滞模型难以兼顾精度与速度的双重要求。解析形式的逆磁滞模型具有较快的求解速度,如何提出高精度的此类模型是解决上述问题的关键所在。为此,该文利用课题组所提基于解析Everett函数推导而得的解析正Preisach磁滞模型,分别推导了初始磁化曲线、磁滞回线下降支与上升支的磁导率的解析表达式,继而利用差分法,推导得到了目前唯一一个解析的逆Preisach磁滞模型。通过对比仿真与实验结果,验证了所提解析逆Preisach磁滞模型的模拟精度,并在模拟精度与计算速度两方面将其与广泛应用的逆J-A磁滞模型进行对比,发现它的平均相对误差比逆J-A磁滞模型小10%以上,且其计算速度约为逆J-A磁滞模型的2.67倍。

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.

Nonlinear hysteresis identification and compensation based on the discrete Preisach model of an aircraft morphing wing device manipulated by an SMA actuator

The conception of aircraft morphing wings thrives in aeronautics since the appearance of shape memory alloys(SMAs). An aircraft morphing wing device, manipulated by an SMA actuator, inherits the intrinsic nonlinear hysteresis from the SMA actuator, ending up with control disadvantages. Conventionally, systems with SMA actuators are constrained to bi-stable states to bypass the hysteresis region. Rather than retreating a morphing wing device to bi-stable states, this paper is dedicated to transcend the morphing wing device beyond the customary limit. A methodology of discrete Preisach modeling, which identifies the hysteresis of the morphing wing device, is proposed herein. An array of discrete equal-distance points is applied to the Preisach plane in order to derive the Preisach density over the partitioned unit of the Preisach plane. Discrete Preisach modeling is fulfilled by the discrete first-order reversible curve(DFORC). By utilizing the discrete Preisach model, the aircraft morphing wing device is simulated; the validity and accuracy of discrete Preisach modeling are demonstrated by contrasting the simulated outcome with experimental data of the major hysteretic loop and the wingspan-wise displacement over time; a comparison between simulation and experimental results exhibits consistency. Afterwards, a hysteresis compensation strategy put forward in this paper is implemented for quasi-linear control of the aircraft morphing wing device, which manifests a compensated shrinking hysteresis loop and attains the initiative of extending the morphing range to the intrinsic hysteretic region.

考虑可逆分量的解析Preisach磁滞模型及其特征参数辨识算法

基于洛伦兹函数的解析Preisach模型具有形式简便、分布函数易于确定等优势,但如果考虑可逆磁化分量,模型的复杂程度和参数会显著增加,导致用于传统模型参数辨识的解析或神经网络等方法不再适用。为此,首先通过引入可逆磁化分量,构建一种考虑可逆分量的解析Preisach模型;然后,分析了各个特征参数对磁滞回线形状的影响规律,并且结合循环迭代法与粒子群算法,提出一种针对考虑可逆分量解析Preisach模型的特征参数混合寻优算法;最后,将所提磁滞模型及其参数辨识算法得到的磁滞回线计算值与实测值进行对比。结果表明,该模型及其参数辨识算法的最大平均相对误差为4.49%,验证了该方法的准确性和有效性。

压电变形镜驱动器迟滞快速辨识与补偿研究

采用压电陶瓷作为促动机构的主动光学系统。为了对压电陶瓷驱动器固有的迟滞非线性进行有效抑制校正,以提高系统性能,该文对带变形镜镜面负载结构的压电陶瓷驱动器非线性迟滞动态进行了高效辨识建模,实现了带镜面负载的压电陶瓷驱动器相对误差1.8867%的迟滞参数辨识与建模,降低了辨识算法所需时间90%以上,同时克服了负载结构导致辨识信号信噪比低的问题。实验证明,所用方法得到的压电陶瓷迟滞模型能够有效地用于补偿校正压电陶瓷驱动器迟滞非线性动态带来的误差,通过前馈控制器可将压电陶瓷驱动器迟滞引起的镜面面形定位误差降低56.21%,有效地提升了系统性能。

压电陶瓷执行器迟滞特性的广义非线性Preisach模型及其数值实现

压电陶瓷执行器的迟滞非线性不具有经典Preisach模型的次环一致特性,直接利用该模型对压电陶瓷执行器的迟滞特性建模会产生较大误差。为了提高压电陶瓷执行器的迟滞特性建模精度,在非线性Preisach模型的基础上推导得到适用于压电陶瓷迟滞特性的广义非线性Preisach模型,并给出简化分类计算公式。广义非线性Preisach模型将经典Preisach模型表示定理中的次环一致特性修改为次环等弦长特性,放宽了对描述对象的限制要求。实验数据表明,与经典Preisach模型相比,广义非线性Preisach模型预测位移的误差绝对值的最大值降低了0.22μm,均方根误差降低了0.11μm,能够更精确地描述压电陶瓷的迟滞特性。

Preisach模型剩磁计算与抑制励磁涌流合闸角控制规律

变压器在因电力故障继电保护动作或因运行方式改变等原因而退出运行后再次投运时铁心剩磁并不是随机的。在分析磁性材料的时效特性的基础上,结合Preisach模型及其特性,推导出了分段计算铁心剩磁的方法。在此基础上,对单相变压器抑制励磁涌流的控制合闸角策略进行分析,推导出合闸角控制律,EMTP实验验证了该策略的正确性。同时,仿真实验揭示了在给定电流超调裕度下不同剩磁环境所对应的合闸角波动范围的变化规律;最后,遵循该规律,提供了设计单相变压器抑制励磁涌流装置的分段合闸角策略。

直线变压器驱动源磁芯磁化过程的仿真研究

磁芯行为对于异常工况下直线变压器驱动源(linear transformer driver,LTD)的输出特性具有很大的影响,为了预测磁芯剩磁状况,为LTD装置调试和运行提供指导,基于磁芯的测试结果构建了准确的数值模型,并应用于LTD的电路仿真。基于4级串联共用腔体LTD数值仿真研究了开关理想时序放电、开关异常自放电、开关非理想时序触发放电及去磁状况下各级磁芯的磁场强度和磁感应强度变化过程。在±70 kV充电电压下的理想时序放电后,各级磁芯最大剩磁变化量为1.27 T,稳态剩磁约为-0.38 T;在±70 kV充电电压下的单支路开关自放电引起的磁芯最大剩磁变化量为1.88 T,稳态剩磁约0.39 T,多支路开关同时自放电将使磁芯快速饱和;当触发时序系数的绝对值>1时,除最先放电的模块,其余模块磁芯先受到反向励磁,然后再正常磁化;去磁过程中越靠近负载的磁芯越早被去磁,磁场强度随着各级磁芯依次去磁而呈现阶梯式上升。该研究结果能够有效地模拟各种工况下LTD磁芯的磁化过程与剩磁状态,判断当前磁芯剩磁对下一次放电脉冲的影响。

基于Preisach修正模型的GMA前馈补偿研究

超磁致伸缩驱动器(GMA)的磁滞建模与非线性补偿是实现GMA高精度定位的基础。根据GMA的特点,提出了GMA的磁滞Preisach修正模型建模与非线性补偿方法。设计制作了一台GMA样机,对其主磁滞回线和一阶折返曲线进行了精密测量,基于实验数据建立了驱动器的Preisach磁滞修正模型。为了避免对Preisach算子求逆,提出了一种以主磁滞回线升程为基准的输入校正迭代算法,并以此设计了驱动器的前馈补偿器,实验表明,提出的GMA前馈补偿方法具有较高的精度,其定位误差不超过1%。

一种改进Preisach模型数值实现方法

探究描述压电陶瓷迟滞特性的传统Preisach数值实现方法的弊端,针对这种数值实现不具有擦除特性,提出一种具有擦除特性的改进Preisach数值实现方法,并描述其详细原理与实现过程,最后进行相关实验研究。实验结果表明,该文提出的具有擦除特性的改进Preisach数值实现方法在复杂加载过程中能相对精确地计算压电陶瓷输出位移,提高了迟滞建模精度,具有更广泛的应用范围。

混合Preisach迟滞模型及其性质研究

压电陶瓷执行器物理结构复杂,通过参数化方法辨识经典Preisach模型(CPM)描述其迟滞特性时,难以找到合适的Preisach函数,模型预测误差较大。为了提高建模精度,定义了均值迟滞模型作为CPM的补充,通过将均值迟滞模型与CPM加权叠加,得到混合Preisach模型(MPM),并将权值定义为迟滞度参数,用以描述模型的迟滞非线性强烈程度。证明了MPM具有类似于CPM的擦除特性和一致特性,给出了MPM的表示定理。最后结合神经网络方法完成了MPM的辨识过程。实验结果表明,MPM及其预测误差最大值较CPM降低了1.20μm,同时MPM的两种特性也得到了验证。

基于Lorentzian函数的Preisach磁滞模型辨识与验证

磁滞作为磁性材料的特性,在电机、变压器等设备中普遍存在,为了更好地描述材料的这种特性,有必要建立材料的磁滞数学模型。本文基于Presiach类磁滞模型,通过分别用解析和神经网络两种方法对其Lorentzian分布函数参数进行了辨识并对两种方法进行了比较,且通过实验验证了辨识结果的正确性。模型可以对无偏磁下变压器一次电流进行预测,实验采用爱泼斯坦方圈的二次电压仿真得到了方圈的一次电流,仿真与实验结果对比验证了模型的正确性。

基于双曲正切函数磁滞算子的超磁致伸缩驱动器动态Preisach模型

经典Preisach算子存在不能反映单元算子磁滞输出依赖于输入变化率的固有缺陷,为扩大Preisach磁滞模型的应用范围,提出一种基于双曲正切函数的动态Preisach磁滞算子,其形状参数为输入变化率的双曲正切函数,该算子可描述超磁致伸缩驱动器磁滞依赖输入变化率的特性.在此基础上构造出超磁致伸缩驱动器动态Preisach模型,并利用BP神经网络完成动态Preisach模型的参数辨识.进行超磁致伸缩驱驱动器磁滞输出试验研究,将驱动频率分别为40 Hz、70 Hz、100 Hz的正弦电流下超磁致伸驱动器（Giant magnetostrictive actuator,GMA）输出位移试验数据作为训练样本数据,并另取训练样本数据中未包含的100 Hz以下20 Hz、50 Hz、80 Hz与100 Hz以上120 Hz、130 Hz、150 Hz共六种频率信号下GMA输出位移试验数据对其预测能力进行检验,结果表明该动态模型能够较为精确地描述超磁致伸缩驱动器的动态磁滞现象并具有较好的模型泛化能力.在0～150 Hz频率的输入电流下,该动态Preisach模型的最大预测位移均方误差为2.87 μm,最大绝对位移误差为4.4 μin.研究结果可广泛应用于GMA实时控制系统,提高GMA器件的控制精度.

基于Preisach逆模型的压电陶瓷执行器迟滞补偿控制

为解决迟滞非线性对压电陶瓷执行器的影响,提出了基于Preisach逆补偿的闭环控制策略,利用考虑了擦除特性的分类排序方法实现了迟滞的Preisach逆模型,通过Preisach逆模型串联补偿降低迟滞作用的影响,并在逆模型前串联PI控制器,通过闭环控制抑制未能完全补偿的迟滞非线性,进而提高系统的控制精度,平均绝对误差下降到0.025μm.实验表明,基于Preisach逆补偿的迟滞补偿控制策略具有良好的控制性能.