一类永磁同步电机动力学模型的稳定性和分岔分析 Stability and Bifurcation Analysis fo

这篇文章研究了一类永磁同步电机系统的非线性动力学特性。给出了该系统的所有平衡点及其稳定性，并利用Hopf分岔定理和第一李雅普诺夫系数研究了系统产生Hopf分岔的参数条件和类型。最后利用Runge-Kutta方法对系统进行数值模拟，给出了系统的相图，，验证了理论分析的结果。得出当c > c0时，系统出现次临界分岔。
Nonlinear dynamic characteristics of the permanent magnet synchronous motor system are inves-tigated in this paper. All the equilibriums of the system and their stabilities are studied. Using the Hopf bifurcation theorem and the first Lyapunov coefficient, the conditions and the type of Hopf bifurcations for the system are investigated. With the Runge-Kutta method, the phase portraits of the system are given, which verify the analytical results.

[1]  中研普华永磁电机行业分析专家 (2015) 2015-2020年中国永磁电机行业市场深度调研与投资前景分析报告.

[2]  郭庆鼎, 孙宜标, 王丽梅 (2006) 现代永磁电动机交流伺服系统. 中国电力出版社, 北京, 11 p.

[3]  李永东, 梁艳 (2002) 高性能交流永磁同步电机伺服系统现状. 中国电工技术学会电力电子学会第八届学术年会论文集, 深圳, 1108, 1149.

[4]  Zhong, L., Rahman, M.E., Hu, W.Y., Lira, K.W. and Rahman, M.A. (1999) A direct toque controller for permanent magnet synchronous motor drives. Energy Conversion, 14, 637-642.

[5]  冯江华 (2010) 轨道交通永磁同步牵引系统研究. 机车电传动, 5, 15-18.

[6]  温文强 (2008) 永磁同步电机在电梯技术上的应用. 机械与电气, 3, 69-71.

[7]  陈巨涛, 郭焱, 郑华耀 (2006) 船舶电力推进双三相永磁同步电机的数学模型和仿真. 2006年电力系统自动化学术交流研讨会, 厦门, 中国电机工程学会, 654-656.

[8]  闫耀明, 范瑜, 王志忠 (2002) 永磁同步电机风力发电系统的自寻优控制. 电工技术学报, 6, 83-84.

[9]  唐丽婵, 齐亮 (2011) 永磁同步电机的应用现状与发展趋势. 装备机械, 1, 8.

[10]  邹国堂, 王政, 程明, 著 (2009) 混沌电机驱动及其应用. 科学出版社, 北京, 1-2, 54-60.

[11]  Hemati, N. (1994) Strange attractors in brushless DC motors. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 41, 40-45.

[12]  Li, Z., Park, J.B., et al. (2002) Bifurcations and chaos in a permanent-magnet synchronous motor. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 49, 383-387.

[13]  Alligood, K.T., Sauer, T.D. and Yorke, J.A. (1996) Chaos: An introduction to dynamical systems. Springer-Verlag, New York, 106-109.

[14]  Yu, Y.G. and Zhang, S.C. (2004) Hopf bifurcation analysis of the Lü system. Chaos, Solutions and Fractals, 21, 1217- 1220.