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Fig. 8.6
Experimental results: responses of linear fuzzy control system (
line-dotted
), of initial fuzzy
control system (
solid
) and of fuzzy control system with GSA-based tuned TS PI-FLC (
dotted
)
Considering the sensitivity reduction with respect to the process parameter
T
,
the feasible domain was set to
D
ρ
={
β
|
3
≤
β
≤
17
}×{
B
e
|
20
≤
B
e
≤
40
}×{
η
|
0
.
25
≤
η
≤
0
.
75
}
.
(8.38)
The three algorithms were run for the dynamic regimes characterized by the
r
40 rad step type modification and zero disturbance input. The adaptive GSAwith
fixed length stages leads to the parameter values of the TS PI-FLC
=
β
=
.
3
29252,
=
η
=
.
=
.
7 and to the average
number of 1829.8 evaluations of the objective function for the best five runs of the
algorithm. The implementation and application of the adaptiveGSAwith fuzzy logic-
based adaptive lengths yields the parameter values of the TS PI-FLC
B
e
40,
0
75, to the objective function
I
95287
β
=
3
.
30827,
4 and to the average
number of 1902.2 evaluations of the objective function for the best five runs of the
algorithm. The non-adaptive GSA results in the parameter values of the TS PI-FLC
β
=
B
e
=
39
.
552,
η
=
0
.
75, to the objective function
I
=
95273
.
3
.
3196,
B
e
=
40,
η
=
0
.
7498, to the objective function
I
=
95299
.
4 and to the
average number of 287.6 evaluations in the same conditions.
These results show that the adaptive GSAs lead to improved optimal values of
the objective function
I
compared to the non-adaptive GSA. The increased number
of evaluations of the objective function exhibited by the adaptive GSA with fuzzy
logic-based adaptive lengths and adaptive GSA with fixed length stages leads as well
indicates improved exploration and exploitation capabilities resulting in the overall
superior search accuracy offered by the two algorithms.
The results also show that the adaptive GSA with fuzzy logic-based adaptive
lengths ensures the best decrease of the objective functions. Although the minimum
of the objective function is not guaranteed, the three solutions obtained by these
three algorithms are different and the control system performance improvement is
obtained.
Since the parameter values of the TS PI-FLC are very close, a set of experimental
results is presented in Fig.
8.6
for one set of parameters, and they are valid for
all three GSAs. For the sake of comparison and for emphasizing the performance
improvement obtained by the GSA-based solving of the optimization problem in
Eq. (
8.5
), Fig.
8.6
gives the responses of the linear control system (with PI controller
obtained by the ESO method for which corresponds to the Symmetrical Optimum
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