一类单自由度非光滑系统混沌运动的延迟反馈控制  

DELAYED FEEDBACK CONTROL OF CHAOS IN A SINGLE DOF NON-SMOOTH SYSTEM

作　　者：张庆爽[1] 丁旺才[1] 孙闯[1] 

机构地区：[1]兰州交通大学,机电工程学院,兰州730070

出　　处：《振动与冲击》2008年第1期155-158,共4页Journal of Vibration and Shock

基　　金：国家自然科学基金(批准号:50675092,10472096);甘肃省自然科学基金(批准号:3ZS042-B25-019)

摘　　要：采用了非线性延迟反馈控制混沌的方法,运用等效线性化法对加入延迟反馈的单自由度非光滑系统微分方程进行解析求解,利用分岔图和Poincaré映射图分析了系统的动力学行为,揭示了延迟反馈对系统的混沌运动具有很好的控制效果。延迟反馈项实际上是一个作用明显的扰动项,通过选择合适的反馈控制参数R1、R2和延迟时间τ,引导非光滑系统的混沌运动转化为规则的周期运动,使得混沌受到控制;另外,通过数值仿真验证了该方法的有效性。Delayed feedback control strategy is proposed to control chaos.The motion equation of A single-degree-of-freedom and non-smooth system with delayed feedback terms is solved using the equivalent linearization method,and the bifurcation diagram and Poincare maps are used to analyze the dynamic behavior of the system.The obvious controlling effect is obtained while the delayed feedback control strategy is used to control chaos.It is shown that the delayed feedback control in fact is a perturbation term;choosing suitable feedback controlling parameters R_1 and R_2 and the delayed time τ can invert a chaotic motion to a regular periodic motion and make the chaos motion be controlled.Moreover,the numerical simulation results demonstrate the effectiveness of the control strategy proposed.

关 键 词：延迟反馈 非光滑系统 混沌控制 等效线性化法 POINCARÉ映射 

分 类 号：O322[理学—一般力学与力学基础]