Controlling Bifurcation and Chaos of Vibro-impact System by Damping Control Law
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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。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.
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Key words:
- vibration /
- dynamics /
- bifurcation /
- chaos
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