This article aimed to investigate the dynamical behaviours of a controlled asymmetric rotating shaft system when the rub-impact forces between the rotor and stator occur. A nonlinear position-velocity controller is proposed to control the system's lateral vibrations. The suggested control algorithm is integrated into the shaft system via four electromagnetic poles that are fixed on a fixed frame and act as active actuators. The dynamics of the asymmetric shaft, the electromagnetic coupling between the magnetic poles and the rotating shaft, and the rub-impact forces between the rotating shaft and the stator are included in the studied model. The derived dynamical model is firstly analyzed as a continuous nonlinear dynamical system utilizing the asymptotic analysis while neglecting the rub-impact forces. Different response curves are plotted to predict the conditions under which the rotating shaft may suffer from the rub-impact forces. Secondly, the whole system model is analyzed numerically as a discontinuous nonlinear dynamical system utilizing the bifurcation diagram, Poincaré map, and frequency spectrum. The main obtained results illustrated that the rub-impact forces occurrence between the uncontrolled rotating shaft and the stator induces unbounded oscillation that can destruct the rotating shaft. However, the suggested control algorithm has improved the vibratory behaviours of the considered system via minimizing the oscillation amplitudes and preventing the rub-impact forces for a wide range of the disk eccentricities. Moreover, it was found that the rotating shaft can whirl in a full annular rub mode with bounded oscillations if the proposed controller fails to prevent the rub-impact forces occurrence due to either the large disk eccentricity or the large asymmetric stiffness coefficients.

本文旨在研究当转子和定子之间发生摩擦冲击力时，受控非对称旋转轴系统的动力学行为。提出了一种非线性位置-速度控制器来控制系统的横向振动。建议的控制算法通过固定在固定框架上并用作主动执行器的四个电磁极集成到轴系统中。研究模型包括非对称轴的动力学，磁极与旋转轴之间的电磁耦合以及旋转轴与定子之间的摩擦力。首先，在不考虑摩擦力的情况下，利用渐近分析将导出的动力学模型分析为连续非线性动力学系统。绘制了不同的响应曲线，以预测旋转轴可能受到摩擦力的条件。其次，利用分叉图，庞加莱图和频谱，将整个系统模型作为不连续的非线性动力系统进行数值分析。获得的主要结果表明，在不受控制的旋转轴和定子之间产生的摩擦力会引起无限制的振荡，从而可能破坏旋转轴。但是，建议的控制算法通过最小化振荡幅度并在较大的磁盘偏心率范围内防止了摩擦力，从而改善了所考虑系统的振动性能。此外，