Bifurcation and chaos in the duffing oscillator with a PID controller

被引：26

作者：

Cui, FS ^{[1
]}

Chew, CH ^{[1
]}

Xu, JX ^{[1
]}

Cai, YL ^{[1
]}

机构：

[1] XIAN JIAOTONG UNIV,INST ENGN MECH,XIAN 710049,PEOPLES R CHINA

来源：

NONLINEAR DYNAMICS | 1997年 / 12卷 / 03期

关键词：

bifurcation; chaos; Duffing oscillator; fractal basin boundary; PID controller;

D O I：

10.1023/A:1008204332684

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

We discuss in this paper the bifurcation, stability and chaos of the non-linear Duffing oscillator with a PID controller. Hopf bifurcation can occur and we show that there is a global stable fixed point. The PID controller works well in some fields of the parameter space, but in other fields of the parameter space, or if the reference input is not equal to zero, chaos is common for hard spring type system and so is fractal basin boundary for soft spring system. The Melnikov method is used to obtain the criterion of fractal basin boundary.

引用

页码：251 / 262

页数：12

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