
and the submarine dynamics are approximated by the simple first-order model
t
dv
dt
þ v ¼ K
_
u
du
dt
þ K
u
u (2:175)
where v ¼v(t) is the depth rate of the submarine. Integrating the depth rate yields the depth of the
submarine
c ¼
ð
v dt (2:176)
The error signal is output from the summer as
e ¼ r c (2:177)
Equations 2.174 through 2.177 constitute the mathematical model of the simplified submarine depth
control system. The goal is to choose the parameters K
C
and K
I
, so that the submarine responds to
step changes in commanded depth in an acceptable manner.
A simulation diagram of the control system is a useful first step in helping choose a set of state
variables.