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2.2. MODELING UNCERTAIN SYSTEMS 27
Putting all the pieces together gives an engine model in the following fractional form.
P(s)=F
u
(P
mod
,∆),
where
P
mod
=
−15.87
s
7.14(s − 19.8)
s
2
141.5(1 + 1.006s)
s(s +1)
0
−9.9
s
9.9
−27.75
s
−0.9(s − 15.8)(s − 19.8)
s
3
−17.82(s − 15.8)(1 + 1.006s)
s(s +1)
,
and ∆ ∈ B∆, with the structure defined as,
∆ =
δ
v
I
2
δ
v
∈R
.
To capture the effects of unmodeled high frequency dynamics we will also include an
output multiplicative perturbation. If the output multiplicative weight is W
m
(s)then
the complete open-loop model is,
P(s)=F
u
(P
mod
,∆), (2.10)
where,
P
mod
=
−15.87
s
7.14(s − 19.8)
s
2
0
141.5(1 + 1.006s)
s(s +1)
0
−9.9
s
09.9
−27.75
s
−0.9(s − 15.8)(s − 19.8)
s
3
0
−17.82(s − 15.8)(1 + 1.006s)
s(s +1)
−27.75
s
−0.9(s − 15.8)(s − 19.8)
s
3
W
m
(s)
−17.82(s − 15.8)(1 + 1.006s)
s(s +1)