Without Rotating machines, it is almost impossible to comprehend machineries in modern engineering world. There are just too many associated parts attached with such machines . Many of these machines are required to run at very high speeds sometimes much higher than their first critical speeds. Stiffness and damping properties plays a very important role in the dynamic behaviour of these high speed rotors supported on journal bearings .Rotor-bearing systems exhibit a wide variety of phenomena pertaining to its operations which if not properly addressed and rectified may lead to catastrophic failure of the system. One such rotor-bearing phenomenon is the self-acting rotor vibrations induced by the hydrodynamic bearings and popularly known as oil-whirl and oil-whip which have severe repercussion on the functioning of the rotors. Hydrodynamic bearing and integrated model tend to be unstable due to non-conservative nature of hydrodynamic forces and stiffness coefficients. The purpose of this work is to redeem vibrations of hydrodynamic bearings with elegant control strategies. Attenuation of vibration in this work is done by using optimal control and conformal mapping based fractionalcontroller in such a way such that ultimate skeleton of the controller remains very simple to for practical deployment and also it improves the power utility and reduces overall energy cost.