2.2. MODELING UNCERTAINSYSTEMS 27
Putting all the pieces together gives an engine model in the following fractional form.
P(s)=F
u
(P
mod,∆),
where
Pmod =
−15.87
s7.14(s−19.8)
s2
141.5(1+ 1.006s)
s(s+1)
0−9.9
s9.9
−27.75
s−0.9(s−15.8)(s−19.8)
s3
−17.82(s−15.8)(1+ 1.006s)
s(s+1)
,
and ∆ ∈B∆, with the structure defined as,
∆=δvI2δv∈R.
Toca pturethe effects o funmo deled high frequency dynamics wewill also include an
output multiplicative perturbation. If the output multiplicative weight is Wm(s)then
the complete open-loop model is,
P(s)=F
u
(P
mod,∆),(2.10)
where,
Pmod =
−15.87
s7.14(s−19.8)
s20141.5(1+ 1.006s)
s(s+1)
0−9.9
s09.9
−27.75
s−0.9(s−15.8)(s−19.8)
s30−17.82(s−15.8)(1+ 1.006s)
s(s+1)
−27.75
s−0.9(s−15.8)(s−19.8)
s3Wm(s)−17.82(s−15.8)(1+ 1.006s)
s(s+1)