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Temperature
1
0.8
0.6
low
high
0.4
0.2
0
20
30
40
50
60
70
80
90
100
ºC
Valve
1
0.8
low
high
0.6
0.4
0.2
0
0
20
40
60
80
100
%
Fig. 3.5
Membership functions for the pilot plant fuzzy model
The new system is
⎛
⎞
−
0
.
04154
⎝
⎠
·
ξ(
g
˜
(
x
)
=
0
.
00001
x
)
(3.43)
0
.
00531
and
⎛
⎝
⎞
⎠
−
0
.
01020
−
0
.
00998
T
ξ(
x
)
=
a
(
x
)
·
(3.44)
−
0
.
01149
−
0
.
00976
A comparison between systems is shown in Fig.
3.6
.
3.5.2 Mechanical System
Another interesting example is the mechanical system shown in Fig.
3.7
. It could be
a simple manipulator just with one join. The system is moved by an electrical motor
which provides a torque
T
u
in order to move a bar an angle
. If we consider all the
mass (
m
) concentrated at the end of the bar, the equation that describes the system is:
θ
m
θ
l
2
B
θ
+
+
mg
sin
θ
=
T
u
(3.45)
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