A simple feedback control system: Bifurcations of periodic orbits and chaos
A simple feedback control system: Bifurcations of periodic orbits and chaos
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DOI：
10.1007/bf01833363
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发表时间：
1996-04
影响因子：
5.6
通讯作者：
K. Yagasaki
中科院分区：
文献类型：
--
作者：
K. Yagasaki
本文考虑一个具有周期期望运动的线性反馈控制的单摆。假设单摆由小时间常数的伺服电机驱动，使得反馈控制系统可以近似为周期受迫振子。Melnikov方法已经证明了横截同宿轨道和异宿轨道的存在，并且在某些参数区域可能出现混沌。本文利用二阶平均法和Melnikov方法研究了谐波和次谐波的局部分岔。通过数值计算Melnikov函数进行Melnikov分析。数值模拟和实验测量，并与以前和现在的理论预测进行比较。观测到了单双曲周期轨道和多双曲周期轨道的同宿和异宿纠缠所导致的持续混沌运动。数值模拟与实验结果吻合较好。
We consider a pendulum subjected to linear feedback control with periodic desired motions. The pendulum is assumed to be driven by a servo-motor with small time constant, so that the feedback control system can be approximated by a periodically forced oscillator. It was previously shown by Melnikov's method that transverse homoclinic and heteroclinic orbits exist and chaos may occur in certain parameter regions. Here we study local bifurcations of harmonics and subharmonics using the second-order averaging method and Melnikov's method. The Melnikov analysis was performed by numerically computing the Melnikov functions. Numerical simulations and experimental measurements are also given and are compared with the previous and present theoretical predictions. Sustained chaotic motions which result from homoclinic and heteroclinic tangles for not only single but also multiple hyperbolic periodic orbits are observed. Fairly good agreement is found between numerical simulation and experimental results.