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.

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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