A ship has six degrees of freedom, three of them are translational motions and three are rotational. One of the rotational motions, the rolling motion contributes much discomfort to the passengers. Different kinds of antiroll stabilizers have been employed in ships, probably the most modern being through power driven fins. The fins which look like small airplane wings protrude from each side of the ship below the water line. Either the area or the angle of attack of the fins is varied by power actuators in such a way as to produce controlling torque that opposes the torque of the sea. The rolling dynamics of the unstabilized ship is approximately represented by the transfer function given below: G(s) = s+26wns+wn This is a highly underdamped system with as low as 0.05. The roll sensor, senses the roll and provides a signal to the power actuator which drives the fins to produce controll- ing torque T,(s). The block diagram of the system is shown in Fig. P-3.8. (a) Determine the sensitivity of the system to changes in K, (for = 0). (b) Discuss the effect of feedback in stabilizing the ship against rolling motion. TD (Disturbance torque of sea) (desired roll) = 0 1 2 s + K s+K Power actuator (Controlling torque of fins) Fins Roll sensor KR Figure P-3.8. w2 3 +25ws+w Ship Roll