
The transfer function relating elevator input to aircraft pitc h is therefore
G
Du
Dde
(s) ¼
Du(s)
Dde(s)
¼
0:0141s
2
0:0097s 0:0005
s
4
þ 1:2700s
3
þ 0:9247s
2
þ 0:0406s þ 0:0125
(4:737)
Factoring the numerator and denominator gives
G
Du
Dde
(s) ¼
Du(s)
Dde(s)
¼
K
u
(s þ c
1
)(s þ c
2
)
(s
2
þ a
1
s þ b
1
)(s
2
þ a
2
s þ b
2
)
(4:738)
The constants in Equation 4.738, computed in M-file ‘‘Chap4_CaseStudy1.m,’’ are
K
u
¼0:0141, c
1
¼ 0:6358, c
2
¼ 0:0542, a
1
¼ 1:2440, a
2
¼ 0:0260,
b
1
¼ 0:8780, b
2
¼ 0:0143
The quadratic factors in the denominator of Equation 4.738 are both underdamped, regard less of
whether the aircraft is a small passenger plane, a commercial jet, or a high-performance mil itary