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5
5
q=5.5 r=4.5
k
drag
= 11
q=5.5 r=4.5
k
drag
= 5
0
0
−5
−5
−10
−5
0
−10
−5
0
5
5
q=5.5 r=4.5
k
drag
= 1
q=5.5 r=4.5
k
drag
= 0
0
0
−5
−5
−10
−5
0
−10
−8
−6
−4
−2
0
Real (s)
Real (s)
Fig. 6.6
Pole placement of the robot under fault occurrence with active FTC for different possible
values of the faulty drag coefficient
On the other hand, active FTC is less conservative than passive FTC because the
fault is dealt with as if it were a scheduling variable and not an additional uncertainty
against which robustness must be enforced. A lesser conservativeness can be seen
analyzing the lower bound for the faulty drag coefficient that makes the design LMIs
feasible for the desired region of the complex plane. In Fig.
6.6
, it is shown that active
FTC is able to satisfy the desired specifications for a circle of center
(
−
5
.
5
,
0
)
and
radius 4
5 for any value of the faulty drag coefficient until 0 kg/m. The position of
the closed-loop poles does not depend on the specific realization of the state matrix.
However, a drawback of active FTC methods is that the precision of the fault
estimation can affect the performances in terms of fault tolerance. This is shown in
Fig.
6.7
, where it can be seen that as the uncertainty in the fault estimation, in this
work modeled as random noise uniformly distributed around the real value of the
faulty drag coefficient, grows, so does the variation of the closed-loop poles position.
This effect may even cause the closed-loop poles to leave the desired region of the
.
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