BIFURCATION CONTROL OF A PARAMETRIC PENDULUM

被引：36

作者：

De Paula, Aline S. ^{[3
]}

Savi, Marcelo A. ^{[2
]}

Wiercigroch, Marian ^{[1
]}

Pavlovskaia, Ekaterina ^{[1
]}

机构：

[1] Univ Aberdeen, Ctr Appl Dynam Res, Sch Engn, Aberdeen AB24 3UE, Scotland

[2] Univ Fed Rio de Janeiro, Dept Mech Engn, COPPE, BR-21941972 Rio De Janeiro, RJ, Brazil

[3] Univ Brasilia, Dept Mech Engn, BR-70910900 Brasilia, DF, Brazil

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2012年 / 22卷 / 05期

关键词：

Nonlinear dynamics; chaos; control; parametric pendulum; LOCAL FEEDBACK STABILIZATION; TRANSIENT TUMBLING CHAOS; ROTATING-SOLUTIONS; PERIODIC-ORBITS; ATTRACTORS; MOTION; HOPF;

D O I：

10.1142/S0218127412501118

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we apply chaos control methods to modify bifurcations in a parametric pendulum-shaker system. Specifically, the extended time-delayed feedback control method is employed to maintain stable rotational solutions of the system avoiding period doubling bifurcation and bifurcation to chaos. First, the classical chaos control is realized, where some unstable periodic orbits embedded in chaotic attractor are stabilized. Then period doubling bifurcation is prevented in order to extend the frequency range where a period-1 rotating orbit is observed. Finally, bifurcation to chaos is avoided and a stable rotating solution is obtained. In all cases, the continuous method is used for successive control. The bifurcation control method proposed here allows the system to maintain the desired rotational solutions over an extended range of excitation frequency and amplitude.

引用

页数：14

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