永磁同步电机模型的随机动力学分析
Stochastic Dynamics Analysis of Permanent Magnet Synchronous Motor Model

作者: 叶正伟 , 邓生文 , 秦 旺 , 梁相玲 :兰州交通大学数理学院,甘肃 兰州;

关键词: 永磁同步电机模型Hamilton系统随机稳定性随机分岔Permanent Magnet Synchronous Motor Model Hamilton System Stochastic Stability Stochastic Bifurcation

摘要: 首先基于同步旋转坐标的永磁同步电机模型引入随机噪声项,建立永磁同步电机系统的非线性微分方程,运用中心流形定理对随机系统进行降维处理,再运用随机平均法得到Ito ̂微分方程;其次根据Lyapunov指数法讨论了系统的局部稳定性、应用奇异边界理论讨论了全局稳定性并得到稳定性条件;根据拟不可积Hamilton系统随机平均法分析了系统的D-分岔和P-分岔;最后选取合适的分岔参数进行数值模拟,并验证了分岔位置。

Abstract: Firstly, the nonlinear differential equation of the PMSM systems was established by introducing random terms into the PMSM model based on synchronous rotating coordinates. The stochastic center manifold is used to reduce the dimension of the stochastic systems, and then the Ito differ-ential equations are obtained by the stochastic average method. Then, by using Lyapunov index and singular boundary theory, the local and global stability of the systems are discussed, and the conditions of stability are obtained. The D-bifurcation and P-bifurcation behavior of the systems is analyzed based on the stochastic average method for the quasi-integrable Hamiltonian systems. Finally, the appropriate bifurcation parameters are selected for numerical simulation, and the bi-furcation positions are verified.

文章引用: 叶正伟 , 邓生文 , 秦 旺 , 梁相玲 (2020) 永磁同步电机模型的随机动力学分析。 应用数学进展, 9, 539-550. doi: 10.12677/AAM.2020.94065

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