Gauss白噪声激励下的永磁同步电动机模型的分岔分析  

Bifurcation Analysis of the Permanent Magnet Synchronous Motor Model Under White Gaussian Noises

作　　者：叶正伟 邓生文 梁相玲 YE Zhengwei;DENG Shengwen;LIANG Xiangling(College of General Education,Guangdong University of Science and Technology,Dongguan,Guangdong 523000,P.R.China;Department of Basic Course Teaching and Research,Guangdong Technology College,Zhaoqing,Guangdong 526100,P.R.China;School of Mathematics and Statistics,Kashi University,Kashi,Xinjiang 844000,P.R.China)

机构地区：[1]广东科技学院通识教育学院,广东东莞523000 [2]广东理工学院基础课教学研究部,广东肇庆526100 [3]喀什大学数学与统计学院,新疆喀什844000

出　　处：《应用数学和力学》2023年第7期884-894,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金项目(61863022)。

摘　　要：针对永磁同步电动机(PMSM)模型引入Gauss白噪声,根据极坐标变换和随机平均法得到系统It8随机微分方程,并计算出系统概率密度函数,通过数值模拟揭示了系统P-分岔的机理.此外,探讨了系统在双参数空间中的复杂动力学,仿真结果表明在参数空间中出现了大量的“鱼”形周期区域,并且这些“鱼”形周期区域不可避免地受到噪声的影响变得紊乱.值得注意的是,从数值模拟结果中发现了一个新的现象,一定的噪声强度下,可以诱导系统在周期振荡区域内的收敛行为,这也表明了噪声对系统影响的双面性.The Gaussian white noise was introduced into the permanent magnet synchronous motor(PMSM) model,to obtain the system It8 stochastic differential equation through the polar transformation and with the stochastic average method.Hence,the probability density function of the system was calculated,and the mechanism of the P-bifurcation of the system was revealed through numerical simulation.In addition,the complex dynamics of the system in the 2-parameter space was discussed.The simulation results show that,there are lots of “fish-shaped” periodic regions in the parameter space.The regions become unstable under effects of system noises.It is worth noting that,under noises of a certain intensity,the system dynamics will switch from periodic motion to convergence,indicating the dual nature of the effects of noises on the PMSM system dynamics.

关 键 词：永磁同步电动机 Gauss白噪声 随机平均法 随机分岔 

分 类 号：O211.63[理学—概率论与数理统计] TM351[理学—数学]