This article aimed to control the lateral vibrations of an asymmetric vertically supported nonlinear rotating shaft system. The system is molded as a two-degree-of-freedom nonlinear system having external and multi-parametric excitations. A combination of both the linear and nonlinear proportional-derivative controller is proposed to control the system dynamics. Four poles active magnetic bearing system is utilized as an active actuator through which controllable magnetic forces are applied to stabilize the considered system. The mathematical model that governing the whole system dynamics is derived. Applying the asymptotic analysis, the slow flow equations of motions are obtained. The system oscillatory behaviors before and after control are explored. The main acquired results showed that the asymmetric rotating shaft system without control could exhibit large vibration amplitudes even for very small eccentricity because asymmetry induced parametric excitations. Moreover, the system may have a single-stable solution, bi-stable solutions, tri-stable solution, or quadri-stable solutions at the same spinning-speed depend on the shaft angular velocity ($\text{Ω}$). Besides, the system asymmetry is resulting in the appearance of backward whirling motion besides the forward whirling one. However, the proposed nonlinear controller showed its capability of eliminating the all mentioned undesired phenomena, where the controlled system responded as a linear one with very small forward whirling motion only. Finally, the conditions to prevent the occurrence of rub/impact force between the rotating shaft and the electromagnetic pole legs are discussed.

本文旨在控制非对称垂直支撑的非线性旋转轴系统的横向振动。该系统模制成具有外部和多参数激励的两自由度非线性系统。提出了线性和非线性比例微分控制器的组合以控制系统动力学。四极主动磁轴承系统用作主动致动器，通过该主动致动器施加可控制的磁力来稳定所考虑的系统。得出了控制整个系统动力学的数学模型。应用渐近分析，得到了运动的慢流方程。探索了控制前后的系统振荡行为。主要获得的结果表明，由于不对称引起的参量激励，即使在很小的偏心距下，无控制的非对称旋转轴系统也可能表现出较大的振动幅度。此外，在相同的旋转速度下，系统可能具有单稳态解，双稳态解，三稳态解或四稳态解，具体取决于轴角速度（$\text{Ω}$）。此外，系统的不对称导致除了正向旋转运动之外还出现向后旋转运动。然而，所提出的非线性控制器表现出了消除所有上述不良现象的能力，其中受控系统仅以很小的前向旋转运动作为线性系统做出响应。最后，讨论了防止在旋转轴和电磁极腿之间产生摩擦/冲击力的条件。