
The fast systems stat es are obtained by breaking the controller=control surface actuator transfer
function into serial first-order blocks as shown in Figure 8.41. The simulation diagrams for the first-
order b locks are drawn using the techniques introduced in Section 2.4.
The simulation diagram with the fast states x
4
, x
5
, x
6
, and x
7
is show n in Figure 8.42.
From Figures 8.39, 8.40, and 8.42, we are able to write algebraic and state derivative equation,
which eventually lead to the following state model (see Exercise 8.31).
_
x ¼ A
x þ Bu
com
(8:238)
y ¼ Cx þ Du
com
(8:239)
where the matrices A, B, C , and D are given by
A ¼
0 K
A
v
2
n
K
A
v
2
n
t
A
000 0
00 10000
0