Control-based continuation of unstable periodic orbits
Control-based continuation of unstable periodic orbits
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DOI：
10.1115/1.4002101
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发表时间：
2009
影响因子：
2
通讯作者：
J. Sieber;B. Krauskopf;D. Wagg;S. Neild;A. Gonzalez-Buelga
中科院分区：
文献类型：
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作者：
J. Sieber;B. Krauskopf;D. Wagg;S. Neild;A. Gonzalez-Buelga
我们提出了一个实验程序来跟踪周期轨道通过折叠（鞍结）分岔，并证明它与参数激励摆实验的跟踪参数是激励的振幅。具体来说，我们跟踪初始稳定的周期一个旋转的钟摆通过其折叠分叉和沿着不稳定的分支。褶皱分叉本身对应于支持持续旋转的最小振幅。我们的计划是基于一个修改的时间延迟反馈的连续设置，我们显示了一个理想化的模型，它收敛与经典的比例加微分控制相同的效率。
We present an experimental procedure to track periodic orbits through a fold (saddle-node) bifurcation and demonstrate it with a parametrically excited pendulum experiment where the tracking parameter is the amplitude of the excitation. Specifically, we track the initially stable period-one rotation of the pendulum through its fold bifurcation and along the unstable branch. The fold bifurcation itself corresponds to the minimal amplitude that supports sustained rotation. Our scheme is based on a modification of time-delayed feedback in a continuation setting and we show for an idealized model that it converges with the same efficiency as classical proportional-plus-derivative control.