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7
7
q=5.5 r=4.5
k
drag
= 5
q=5.5 r=4.5
k
drag
= 11
5
5
3
3
1
1
−1
−1
−3
−3
−5
−5
−7
−7
−12
−10
−8
−6
−4
−2
0
2
−12
−10
−8
−6
−4
−2
0
2
7
7
q=5.5 r=4.5
k
drag
= 1
q=5.5 r=4.5
k
drag
= 0
5
5
3
3
1
1
−1
−1
−3
−3
−5
−5
−7
−7
−12
−10
−8
−6
−4
−2
0
2
−12
−10
−8
−6
−4
−2
0
2
Real (s)
Real (s)
Fig. 6.4
Pole placement of the robot under fault occurrence without FTC for different possible
values of the faulty drag coefficient
6.5 Results
The two-wheel robot can be affected by parametric faults (unexpected change in the
drag coefficient
k
drag
), and sensor/actuator faults. In Fig.
6.3
, the time response of the
robot with different values of the drag coefficient is compared under the following
conditions:
•
(
−
.
,
)
the controller is designed to put the closed-loop poles in a circle of center
5
5
0
.
and radius 4
5 without taking into account the possibility of faults occurrence;
•
the Takagi-Sugeno model (
6.31
) is obtained through the
bounding box method
using the following extreme values for the state variables affecting the premise
variables:
x
min
2
x
max
2
=−
0
.
5
=
0
.
5
x
min
4
x
max
4
=−
3
=
3
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