THE CRITERION OF HIGHER PERIOD ON CONTROLLING CHAOS IN A VIBRO-IMPACT SYSTEM  

作　　者：张永祥[1] 林梅[2] 俞建宁[3] 

机构地区：[1]沈阳农业大学理学院,辽宁,沈阳110161 [2]空军工程大学工程学院,陕西,西安710038 [3]兰州交通大学数理与软件工程学院,甘肃,兰州730070

出　　处：《工程力学》2009年第3期31-35,共5页Engineering Mechanics

基　　金：甘肃省自然科学基金项目（3ZS051-A25-030）;沈阳农业大学青年教师科研基金项目（2006212）

摘　　要：针对工程实际中一类碰撞振动系统的混沌行为，设计了一种动态间歇反馈控制策略，仅对不碰撞时刻进行动态反馈，该方法易于操作，选择参数范围较广，能有效节约控制能量，理论分析表明混沌吸引子中的不稳定周期轨道可以稳定化，并以此控制方法为例，采用Poincare映射和功率谱相结合技术能有效判别倍化出的各种形式的时·稳定高周期轨道和nH概周期轨道。该方法能准确识别混沌控制后高倍周期数和概周期吸引不变圈数，它对于碰撞振动系统的优化设计、振动控制及安全运行提供了理论参考。The main contribution of this paper lies in the design of a dynamic intermittent feedback control strategy and the determination of higher period by combining Poincarc map and power spectrum technique. The controlling methods can save great energy and transmit the chaos in a vibro-impact system into different nP higher periodic and nH quasiperiodic orbits. A desired unstable periodic orbit, which is embedded in the chaotic attractor, is stabilized and the controlled system can maintain its stable dynamical behaviors in large windows of parameter space. The number of higher periodic orbits and quasi-periodic orbits represented by attracting invariant circles can be identified accurately. Some typical control results are given by numerical analysis, which are helpful for designing, vibration control and safety operating of vibro-impact systems.

关 键 词：碰撞振动 混沌控制 动态间歇反馈 Poincarc映射 功率谱 

分 类 号：O322[理学—一般力学与力学基础]