Stability and Hopf bifurcation in an inverted pendulum with delayed feedback control

被引：6

作者：

Yang, Rui ^{[1
]}

Peng, Yahong ^{[2
]}

Song, Yongli ^{[1
]}

机构：

[1] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

[2] Donghua Univ, Dept Appl Math, Shanghai 200051, Peoples R China

来源：

NONLINEAR DYNAMICS | 2013年 / 73卷 / 1-2期

关键词：

Inverted pendulum; Discrete delay; Method of multiple scales; Hopf bifurcation;

D O I：

10.1007/s11071-013-0827-6

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

In this paper, we investigate the dynamics of the inverted pendulum with delayed feedback control. The existence and stability of multiple equilibria depending on the control strengths are studied. Taking the time delay of the control terms as a parameter, periodic oscillations induced by delay are found. By using the method of multiple scales, the effect of the control gains and the relative mass of the pendulum on the stability and direction of Hopf bifurcations are discussed. Numerical simulations are employed to illustrate the obtained theoretical results.

引用

页码：737 / 749

页数：13

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