Within this paper, the negative-velocity and positive-position
feedback (PPF) controllers are combined together to eliminate the
lateral vibrations of a vertically supported nonlinear Jeffcott-rotor
system. Time-delays (1 and 2 ) in the control loop are included in
the system model. The slow-flow modulating equations governing
the whole system vibration amplitudes are derived utilizing
asymptotic analyses. The maximum limits of  1 and 2 at which the
system solution remains stable are illustrated. The analyses
approved that the integration of velocity controller to the PPF one,
improves the control efficiency and stretches the stable limits of both
 1 and 2 . Finally, numerical confirmations for the obtained analytical
results are included, which are in excellent agreement with the
analytical solution