A ship’s roll can be stabilized with a control system. A voltage applied to the fins’ actuators creates a roll torque that is applied to the ship. The ship, in response to the roll torque, yields a roll angle. Assuming the block diagram for the roll control system shown in Figure P10.12, determine the gain and phase margins for the system.

Ship roll Fin Desired Roll Actual Transducer actuator dynamics angle error, 0(s) roll roll angle, O,(s) Voltage Torque angle, 0,(s) 0.5 9 5 s+5 s2+1.2s +9 FIGURE P10.12 Block diagram of a ship's roll-stabilizing system