Bifurcation control of a Duffing oscillator using pole placement
Bifurcation control of a Duffing oscillator using pole placement
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DOI：
10.1177/1077546313517586
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发表时间：
2015-10
影响因子：
2.8
通讯作者：
M. Ghandchi-Tehrani;L. Wilmshurst;S. Elliott
中科院分区：
文献类型：
--
作者：
M. Ghandchi-Tehrani;L. Wilmshurst;S. Elliott
本文利用极点配置技术对受迫Duffing振子的频域分岔控制进行了数值研究。首先，Duffing振子的分岔频率范围确定使用系统和强迫参数。然后将线性状态反馈控制器应用于系统，以便将峰值谐振频率分配到指定值，使得闭环系统中的分叉被最小化或消除。附加的约束施加到极点配置，以尽量减少控制的努力，如分配在一个椭圆形区域内的复杂域的闭环极点。最后，对最大强迫水平进行了约束，使得在相对较小的强迫振幅下不会发生分叉。这些技术证明使用几个数值例子。
This paper presents a numerical study on the control of frequency-domain bifurcation in forced Duffing oscillators, through the use of pole placement techniques. First, the bifurcation frequency range of the Duffing oscillator is identified using the system and forcing parameters. A linear state feedback controller is then applied to the system, in order to assign the peak resonance frequency to a prescribed value, such that bifurcation is minimized or eliminated in the closed-loop system. Additional constraints are applied to the pole placement in order to minimize the control effort, such as assigning the closed-loop poles within an elliptical region in the complex domain. Finally, a constraint is placed on the maximum forcing level, such that bifurcation will not occur at relatively small forcing amplitudes. These techniques are demonstrated using several numerical examples.