一类电机系统的分岔分析与 Hopf 分岔控制

doi:10.3969/j.issn.1000-1093.2013.08.021

兵工学报 ›› 2013, Vol. 34 ›› Issue (8): 1051-1056.doi: 10.3969/j.issn.1000-1093.2013.08.021

• 研究简报 • 上一篇

一类电机系统的分岔分析与 Hopf 分岔控制

张中华^1,2, 袁惠群^1,3, 张宇白¹

1. 东北大学机械工程与自动化学院, 辽宁沈阳110819;2. 东北电力大学理学院, 吉林吉林132012; 3. 东北大学理学院, 辽宁沈阳110819

收稿日期:2012-05-29 修回日期:2012-05-29 上线日期:2013-10-14
作者简介:张中华(1979—), 女, 讲师。
基金资助:
国家自然科学基金项目(51275081)

Bifurcation Analysis and Hopf Bifurcation Control of a Motor System

ZHANG Zhong-hua^1,2, YUAN Hui-qun^1,3, ZHANG Yu-bai¹

1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, Liaoning, China;2. College of Science, Northeast Dianli University, Jilin 132012, Jilin, China;3. College of Science, Northeastern University, Shenyang 110819, Liaoning, China

Received:2012-05-29 Revised:2012-05-29 Online:2013-10-14

摘要/Abstract

摘要：

针对无刷直流电机系统等效非线性动力系统,运用中心流形理论和Hopf 分岔理论研究了系统存在的分岔行为,并设计状态反馈控制器对系统进行Hopf 分岔控制,分析了控制参数对 Hopf 分岔点位置、分岔类型以及分岔周期解振幅的影响。研究结果表明:控制器中的线性控制部分能改变原系统的Hopf 分岔点位置,甚至使Hopf 分岔点消失;控制器中的非线性控制部分则可改变原系统的分岔类型及分岔周期解振幅的大小。数值仿真证明控制器设计的有效性。

关键词: 电气工程, 中心流形理论, 叉形分岔, Hopf 分岔, Hopf 分岔控制

Abstract:

For the equivalent nonlinear dynamic system of brushless DC motor, the center manifold theory and Hopf bifurcation theory are used to discuss the Hopf bifurcation behaviors of original system, the Hopf bifurcation control problem of original system is investigated using a state feedback controller, and the effects of control parameters on the position of bifurcation point, bifurcation type and amplitude of periodic solution are analyzed. The research results show that the positions of Hopf bifurcation points can be changed and even the Hopf bifurcation points are eliminated by the linear control, and the bifurcation type and the bifurcation amplitude of periodic solution can be changed by the nonlinear control. Finally, the numerical simulations show the effectiveness of the proposed controllers.

Key words: electrical engineering, center manifold theory, pitchfork bifurcation, Hopf bifurcation, Hopf bifurcation control

中图分类号:

张中华, 袁惠群, 张宇白. 一类电机系统的分岔分析与 Hopf 分岔控制[J]. 兵工学报, 2013, 34(8): 1051-1056.

ZHANG Zhong-hua, YUAN Hui-qun, ZHANG Yu-bai. Bifurcation Analysis and Hopf Bifurcation Control of a Motor System[J]. Acta Armamentarii, 2013, 34(8): 1051-1056.

参考文献

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一类电机系统的分岔分析与 Hopf 分岔控制

Bifurcation Analysis and Hopf Bifurcation Control of a Motor System

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