Time delay is an obstacle in the way of actively controlling non-linear vibrations. In this paper, a rotating blade’s non-linear oscillations are reduced via a time-delayed non-linear saturation controller (NSC). This controller is excited by a positive displacement signal measured from the sensors on the blade, and its output is the suitable control force applied onto the actuators on the blade driving it to the desired minimum vibratory level. Based on the saturation phenomenon, the blade vibrations can be saturated at a specific level while the rest of the energy is transferred to the controller. This can be done by adjusting the controller natural frequency to be one half of the blade natural frequency. The whole behavior is governed by a system of first-order differential equations gained by the method of multiple scales. Different responses are included to show the influences of time delay on the closed-loop control process. Also, a good agreement can be noticed between the analytical curves and the numerically simulated ones.

中文翻译：

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时延对控制旋转叶片非线性振荡的影响

时间延迟是主动控制非线性振动的障碍。在本文中，可通过延时非线性饱和控制器（NSC）减少旋转叶片的非线性振荡。该控制器由叶片上的传感器测得的正位移信号激励，其输出是施加在叶片上执行器上的适当控制力，将其驱动到所需的最小振动水平。基于饱和现象，叶片振动可以在特定水平上饱和，而其余的能量则转移到控制器上。这可以通过将控制器固有频率调整为刀片固有频率的一半来完成。整个行为由一个通过多尺度方法获得的一阶微分方程组控制。包括不同的响应以显示时间延迟对闭环控制过程的影响。同样，可以注意到分析曲线与数值模拟曲线之间的良好一致性。