一个粘弹性振子的动力学与控制

本文详细分析了一个具有粘弹性项的非线性振子的动力学与控制.首先研究了系统平衡点的稳定性,表明系统存在复杂的无界动力学行为.然后引入时滞速度反馈对这个不稳定系统进行控制.研究结果表明速度反馈控制能镇定此不稳定的粘弹性系统.适当的选择控制增益和控制时滞,控制系统有稳定的平衡点,由Hopf分岔产生的周期解,拟周期解,并能展现出复杂的混沌解.数值模拟验证了结论的正确性.

Dynamcis and control of an oscillator with viscoelastic item

The paper presents a detailed analysis on the dynamics and delayed state feedback control of an oscillator with generalized visco elastic item. The trivial equilibrium of the model is first investigated and shows that uncontrolled model exhibits complicated unbounded behavior. Then a velocity feedback control is introduced to stabilize this unstable system. It shows that the velocity feesback control can stabilize the system. And with properly chosen delay and gain in the delayed feedback path, the velocity controlled model may have stable equilibrium, or periodic solutions resulted from the Hopf bifurcation, codimension 2 bifurcation or complex stranger attractor. Some numerical experiments verify the theoretical analysis.