
The natural response of the closed-loop system (K
C
¼10) is given by
u
nat
(t) ¼ c
1
e
t=0:095
þ c
2
e
t=0:255
þ e
t=2:914
[c
3
cos (0:831t) þ c
4
sin (0:831 t)] (4:285)
The closed-loop system response, when K
C
¼10, is faster than the open-loop system as evidenced
by the reduction in dominant time constant from 7.5 to 2.914 s.
Suppose the ship is maintaining a heading of 08 (with the rudder angle at 08) when it becomes
necessary to increase the heading by 58. In the open-loop system, a pulse input to the power
converter and rudder subsystem is selected to produce the new desired heading. A pulse is specified
rather than a step input because the rudder angle must