In order to control the transient torsional vibration of rotational shaft system, the torsional stiffness of it has been taken into account in modelling the plant. In this paper the observer and controller has been designed in two ways. One is to consider the torsional stiffness and the other is to idealize the rotational shaft as rigid body. The third order observer considering torsional stiffness shows stable response on computer simulation. When the observer is designed on assumption of the rotational shaft being rigid body, the reduced order observer shows stable response whereas the full order observer shows unstable response.