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Table 6.1
Comparison between passive FTC and active FTC
k drag pas. (kg/m)
k drag act. kg/m
Tol. unc. ( k drag = 5 (kg/m)) %
Center
Radius
(
10
.
5
,
0
)
10
.
5
0
0
210
(
9
.
5
,
0
)
9
.
5
0
.
5
0
190
( 8 . 5 , 0 )
8 . 5
1 . 6
0
160
(
7
.
5
,
0
)
7
.
5
2
.
6
0
150
(
6
.
5
,
0
)
6
.
5
3
.
8
0
130
( 5 . 5 , 0 )
5 . 5
5 . 9
0
100
(
5
.
5
,
0
)
4
.
5
7
0
80
(
5
.
5
,
0
)
3
.
5
8
.
6
0
20
( 5 . 5 , 0 )
2 . 5
9 . 9
0
10
(
5
.
5
,
0
)
1
.
5
10
.
6
0
6
(
5
.
5
,
0
)
0
.
5
11
0
0
.
6
the tolerated uncertainty is shown too. It can be seen that there is a trade-off between
performances and tolerable fault in the passive FTC case, and between performance
and tolerable uncertainty in the active FTC case. It appears clearly that the designer
of the FTC system should choose the strategy according to the availability of an
estimation of the fault magnitude and the goodness of this estimation.
6.6 Conclusions
In this chapter, a robust Takagi-Sugeno framework has been proposed and applied to
the problem of fault tolerant control. It has been shown that the proposed framework
can lead to the design of: a passive FTC, where a single set of subsystem controllers
exhibits some robustness properties; an active FTC without controller reconfigura-
tion, where the available fault information is used to infer accordingly the controller;
and an active FTC with controller reconfiguration. In this last case, different sets of
controllers are used before fault detection, between fault detection and fault isolation,
and after fault isolation, respectively.
Some results have been obtained designing passive and active FTC for a two-wheel
differential robot simulator subject to a parametric fault, namely a change in the drag
coefficient with respect to the normal operating conditions. The obtained controllers
have been compared in terms of pole placement specifications. Such comparison
has shown that the passive FTC conservativeness results in a bigger lower bound of
the faulty drag coefficient for which fault tolerance can be achieved, with respect to
the active FTC. On the other hand, the latter is sensitive to uncertainties in the fault
estimation which can reduce the benefits of such approach.
 
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