Rolling motion of a ship can be reduced by using feedback control to vary the angle of the stabilizer fins, much like ailerons are used to control aircraft roll. Figure PI2.15 is the block diagram of a roll control system in which the roll angle is measured and used with proportional control action. Determine the phase and gain margins of the system if (a) Kp = 1, (b) KP = 10, and (c) Kp = 100. Determine the stability properties for each case. If the system is unstable, what effect will this have on the ship roll?

Ship roll dynamics 10 Actuator V0. Voltage 0.2s + 1Fint 10 Roll angle Kp angle Controller Roll angle sensor