Nonlinear PD-controller to suppress the nonlinear oscillations of horizontally supported Jeffcott-rotor system

This paper investigates the vibration control of a horizontally suspended Jeffcott-rotor system. A nonlinear restoring force and the rotor weight are considered in the system model. The system frequency (angular speed) -response curve is plotted at different values of the rotor eccentricity. The analysis illustrated that the system has a high oscillation amplitude and exhibits some nonlinear behaviors before control. A Proportional-Derivative (PD)-controller is integrated into the system via two pairs of electromagnetic magnetic poles. The nonlinearity due to the electromagnetic coupling is considered in the system model. A second-order approximate solution is obtained by utilizing multiple scales perturbation method. The bifurcation analyses of the controlled system are conducted. The results showed the high efficiency of the controller to mitigate the nonlinear vibrations of the considered system. Numerical simulations are carried out to validate the accuracy of the analytical results. The numerical results confirmed the excellent agreement with the analytical solutions. Then, the optimal working conditions of the system are concluded. Finally, a comparative study with previously published work is reported.