用基波平衡原理分析非线性振荡和混沌.PDF

第29 卷第 1 期 通 信 学 报 Vol.29 No.1 2008 年1 月 Journal on Communications January 2008 用基波平衡原理分析非线性振荡与混沌 黄炳华，黄新民，韦善革 （广西大学电气工程学院，广西 南宁 530004 ） 摘 要：用“基波平衡原理”求得注入网络的基波电流Is1 。它的流向代表网络在脱离激励源以后,为维持自激振 荡关于实功与虚功的盈亏情况，是判断网络稳定性和振荡性状的有力依据。当实功与虚功同时取得平衡时，能求 得基波解的振荡频率ω 和幅值U ，网络必然存在有对应的周期解。结论的普遍性可推广到三阶非线性微分方程。 s m 并阐明微分方程存在有多个周期解是产生混沌振荡的重要原因。其正确性可以用SIMULINK 仿真验证。 关键词：非线性；稳定性；虚功功率；极限环；混沌 中图分类号：TN 722.3 文献标识码：A 文章编号：1000-436X(2008)01-0065-06 Analysing nonlinear oscillation and chaos using fundamental-wave balance principle HUANG Bing-hua ，HUANG Xin-min ，WEI Shan-ge (Electrical Engineering School Guangxi University, Nanning 530004,China) Abstract: The fundamental-wave current Is1 can be found by the theory of fundamental harmonic balance. Its flow direc- tion represents profit and loss of active and reactive power in order to maintain self-oscillation, when the exciting source applied to the network is cut off. And it is powerfull basis of judging stability and self-excited oscillation shape and prop- erties. Oscillation frequencyω and amplitude U of fundamental- wave solution can be found, when active and reactive s m power of the network obtain balance synchronously. The respective periodic solution exist inevitably. The universality of the conclusion can be spread to third-order nonlinear differential equation. It is expounded that a differential equation possessing multiple periodic solutions is the important reason of generating chaotic oscillation.