P8.11 Automatic steering of a ship is a particularly use

ful application of feedback control theory [20]. In the case of heavily traveled seas, it is important to main

tain the motion of the ship along an accurate track.

An automatic system is more likely to maintain a smaller error from the desired heading than a helms

man who recorrects at infrequent intervals. A mathe

matical model of the steering system has been devel

oped 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

E(s) G(s) = 8(s) 0.164(s+ 0.2)(-s+ 0.32) s2(s+ 0.25)(s 0.009) where E(s) is the Laplace transform of the deviation of the ship from the desired heading and 8(s) is the Laplace transform of the angle of deflection of the steering rudder. Verify that the Bode plot of G(jw) is that shown in Figure P8.11.