Gauss白噪声激励下的永磁同步电动机模型的分岔分析

叶正伟; 邓生文; 梁相玲

doi:10.21656/1000-0887.430285

Gauss白噪声激励下的永磁同步电动机模型的分岔分析

doi: 10.21656/1000-0887.430285

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

基金项目:

国家自然科学基金项目 61863022

详细信息

通讯作者:
叶正伟(1993—)，男，讲师，硕士(通讯作者. E-mail: yezhengweiff@163.com)

中图分类号: O211.63; TM351
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- 文章访问数: 391
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- PDF下载量: 66
- 被引次数: 0
出版历程
- 收稿日期: 2022-09-16
- 修回日期: 2023-04-19
- 刊出日期: 2023-07-01

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

1.
College of General Education, Guangdong University of Science and Technology, Dongguan, Guangdong 523000, P.R.China
2.
Department of Basic Course Teaching and Research, Guangdong Technology College, Zhaoqing, Guangdong 526100, P.R.China
3.
School of Mathematics and Statistics, Kashi University, Kashi, Xinjiang 844000, P.R.China

摘要

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Itô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.
- 永磁同步电动机 /
- Gauss白噪声 /
- 随机平均法 /
- 随机分岔
Abstract: The Gaussian white noise was introduced into the permanent magnet synchronous motor (PMSM) model, to obtain the system Itô 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.
- PMSM /
- Gaussian white noise /
- stochastic average method /
- stochastic bifurcation

HTML全文

图 1 随噪声强度D变化的联合概率密度图及其俯视图

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 1. The joint probability density function with the change of noise intensity D

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图 2 不同噪声强度D下的平稳概率密度图

Figure 2. The stationary probability density function with the change of noise intensity D

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图 3 不同噪声强度D下的系统分岔图

Figure 3. The bifurcation diagram with the change of noise intensity D

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图 4 不同参数平面上的分岔图(左)和Lyapunov指数图(右)

Figure 4. The bifurcation diagram(left) and the Lyapunov exponent diagram (right) in planes with different parameters

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图 5 随噪声强度D变化的最大Lyapunov指数图

Figure 5. The largest Lyapunov exponent diagram with the change of the noise intensity

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