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120
Real data
Fuzzy model
Simplified Fuzzy model
100
80
60
40
20
0
0
2000
4000
6000
8000
10000
Fig. 3.6
Pilot plant: comparison between original, fuzzy and simplified fuzzy system
B
T
u
m·g
Fig. 3.7
Mechanical system
s
2
,
l
1kgm
2
For simulation, the parameter will be:
g
=
9
.
8m
/
=
1m,
B
=
/
s,
m
=
1kg.
As we see, the system has a non-linearity due the sin
θ
. Linearizing around an
equilibrium point, we could model the system as
θ
=−
a
θ
−
b
θ
+
T
u
(3.46)
where
a
θ
0
). It is a second order
linear system. In order to build a Fuzzy system, we use four variables in discretemode,
to get the dynamics of a 2nd order system:
T
u
(
,
b
are parameters depending of the operating point (
−
),
T
u
(
−
), θ(
−
), θ(
−
)
.
Providing data sets for training and checking, the FIS obtained is defined by the
membership function depicted in Fig.
3.8
.
k
2
k
1
k
2
k
1
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