Automatic steering of a ship would be a particularly useful application of feedback control theory [20]. In the case of heavily traveled seas, it is important to maintain the motion of the ship along an accurate track. An automatic system would be more likely to maintain a smaller error from the desired heading than a helmsman who recorrects at infrequent intervals. A mathematical model of the steering system has been developed for a ship moving at a constant velocity and for small deviations from the desired track. For a large tanker, the transfer function of the ship is

where E(s) is the Laplace transform of the deviation of the ship from the desired heading and S(s) is the Laplace transform of the angle of deflection of the steering rudder. Verify that the frequency response of the ship, E(jω)/8(jω). is that shown in Figure P8.ll.

E(s) 0.164(s 0.2)s 0.32) o(s) s+0.25)s 0.009)