阻尼控制策略抑制碰撞振动系统的分岔与混沌

吕小红

doi:10.13433/j.cnki.1003-8728.2016.0905

阻尼控制策略抑制碰撞振动系统的分岔与混沌

doi: 10.13433/j.cnki.1003-8728.2016.0905

吕小红

1.
兰州交通大学甘肃省轨道交通装备系统动力学与可靠性重点实验室, 兰州 730070

基金项目:

国家自然科学基金项目（11462012，11172119）、甘肃省科技计划项目（148RJZA034）及甘肃省高等学校科研项目（2014A-046）资助

详细信息

作者简介:
吕小红(1977-),副教授,博士研究生,研究方向为机械动力学及其控制,lvxh@mail.lzjtu.cn

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出版历程
- 收稿日期: 2014-11-12
- 刊出日期: 2016-09-05

Controlling Bifurcation and Chaos of Vibro-impact System by Damping Control Law

摘要

摘要: 以两自由度碰撞振动系统为研究对象，数值仿真了系统1/n周期运动经周期倍化分岔和Hopf分岔向混沌转迁的路径。使用微幅阻尼控制策略，对系统的分岔行为和混沌进行了控制，控制信号是根据质块M1的运动方向来改变阻尼系数而得到的。在此基础上引入反馈控制方法，即在Poincaré截面里，选择变量β*=2π或4π作为期望目标，动态地调节控制参数，把系统的多碰周期运动、概周期运动和混沌有效地控制到单碰周期轨道。仿真结果表明，输入的控制信号u=γ|x1|是一个微幅阻尼信号，达到控制的目标只消耗少量的能量。
- 碰撞振动 /
- 分岔 /
- 混沌 /
- 控制
Abstract: A two-degree-of-freedom impact oscillator is considered. Routes from doubling-periodic bifurcations and Hopf bifurcations of period-n single-impact motions to chaotic motions are illustrated by numerical simulation. Bifurcation behavior and chaotic motions are suppressed by using a small-amplitude damping control law. The control signal is obtained by varying the damping coefficient according to the velocity direction of mass M1. Choosing the variable β*=2π or 4π in Poincaré section as the desired target, the control parameter is dynamically adjusted by applying the feedback control technique. The multi-impact periodic motions,quasi-periodic motions and chaotic behavior in the system are effectively controlled to the single-impact periodic motion. Numerical results show that the control input u=γ|x1| is a small-amplitude damping signal, it is necessary to apply a small quantity of energy to the control implementation.
- vibration /
- dynamics /
- bifurcation /
- chaos

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参考文献(15)

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