A Study of the Pendulum Equation with a Periodic Impulsive Force : Bifurcation and Control
A Study of the Pendulum Equation with a Periodic Impulsive Force : Bifurcation and Control
复制标题
具有周期性冲击力的摆方程的研究:分岔与控制
DOI：
--
复制
发表时间：
1995
期刊：
影响因子：
--
通讯作者：
I. Morita
中科院分区：
文献类型：
--
作者：
T. Ueta;H. Kawakami;I. Morita
研究了具有周期脉冲力的单摆方程.该模型由二阶微分方程描述，也来自步进电机的动力学。本文首先分析了一类具有周期脉冲力的广义摆方程周期解的分支现象。存在两种拓扑结构不同的解，通过改变系统参数，可以使其变为混沌。我们试图通过对参数的小扰动来稳定嵌入混沌吸引子中的不稳定周期轨道。其次，研究了两相混合式步进电动机的间歇驱动特性。我们认为，不稳定的操作称为pull-out是由分叉。最后，我们提出了一种通过改变重复频率和步进率来避免拉脱的控制方法。
The pendulum equation with a periodic impulsive force is investigated. This model described by a second order differential equation is also derived from dynamics of the stepping motor. In this paper, firstly, we analyze bifurcation phenomena of periodic solutions observed in a generalized pendulum equation with a periodic impulsive force. There exist two topologically different kinds of solution which can be chaotic by changing system parameters. We try to stabilize an unstable periodic orbit embedded in the chaotic attractor by small perturbations for the parameters. Secondly, we investigate the intermittent drive characteristics of two-phase hybrid stepping motor. We suggest that the unstable operations called pull-out are caused by bifurcations. Finally, we proposed a control method to avoid the pull-out by changing the repetitive frequency and stepping rate.