The objective of the present study is to suppress the large amplitudes of a continuous spinning shaft under an active vibration control. For this purpose, the Positive Position Feedback (PPF) control with time-delays are applied to the system via Macro-Fiber-Composite (MFC) sensors and actuators. The nonlinear dynamics of the system is explored analytically utilizing the perturbation method in the primary and one-to-one internal resonances. The steady state solutions of the system and controller in the Cartesian and polar forms are obtained. The effects of the controller gains and time delays on the stability and loci of bifurcations of the system are investigated. The controller shows its feasibility in controlling the system vibrations. Also, it is demonstrated that by increasing the controller gain coefficients the minimum amplitude regions of the system are increased. Furthermore, the safe boundary of the loop delays is studied. The results of the analytical approach are in good agreement with the numerical results of the original system of equations.

本研究的目的是在主动振动控制下抑制连续旋转轴的大振幅。为此，具有时间延迟的正位置反馈 (PPF) 控制通过宏纤维复合材料 (MFC) 传感器和执行器应用于系统。利用初级和一对一内部共振中的微扰方法分析地探索了系统的非线性动力学。得到了系统和控制器在笛卡尔和极坐标形式下的稳态解。研究了控制器增益和时间延迟对系统稳定性和分岔轨迹的影响。控制器显示了其控制系统振动的可行性。还，结果表明，通过增加控制器增益系数，可以增加系统的最小幅度区域。此外，还研究了环路延迟的安全边界。解析方法的结果与原始方程组的数值结果非常吻合。