
Given F
0
, Equations 8.294 and 8.295 can be solved in that order to find the operating point levels
H
2
, H
1
and ultimately the remaining dependent variable operating point values, namely, F
12
,
F
2
, and p
2
.
The nonlinear system model in Equations 8.286 through 8.291 can be reduced to
dH
1
dt
¼ f
1
(H
1
, H
2
, F
0
)(8:296)
¼
1
A
1
F
0
c
1
g(H
1
L
2
)
H
2
L
2
H
2
p
0
1=2
"#
, H
1
L
1
(8:297)
dH
2
dt
¼ f
2
(H
1
, H
2
, F
0
)(8:298)
¼
1
A
2
c
1
g(H
1
L
2
)
H
2
L
2
H
2
p
0
1=2
c
2
H
2
L
2
H
2
p
0
þ gH
2
1=2
"#
(8:299)
The linearized state model is
d
dt
D
H(t) ¼ ADH(t) þ BDF
0
(t)(8 :300)
D
y(t) ¼ CDH(t) þ DDF
0
(t)(8:301)
where
D
H(t) ¼
DH
1
(t)
DH
2
(t)
¼
H
1
(t) H
1
H
2
(t) H
2
"#
(8:302)
D
y(t) ¼
DH
1
(t)
DH
2
(t)
DF
12
(t)
DF
2
(t)
Dp
2
(t)
2
6
6
6