Digital Signal Processing Reference
In-Depth Information
Fig. 11.18 Defuzzification
by min-of-maxima method
No engineering
sense!
1
1
max
max
0
0
y
1
y
2
y
1
y
2
y
3
y
=(
y
1
+
y
2
)/2
y
=(
y
1
+
y
2
+
y
3
)/3
Fig. 11.19 Defuzzification
with COG/weighted sum
approaches
1
1
0
0
y
1
y
2
y
3
y
y
y
¼
R
supp B
l
B
ð
y
Þ
y dy
R
supp B
l
B
ð
y
Þ
dy
:
ð
11
:
32
Þ
Instead of the integrals in (
11.32
) the weighted sum can be used, provided that
the output MF is not continuous, as it is with the Takagi-Sugeno scheme. In such a
case (
11.32
) it takes the form,
y
¼
P
supp B
l
B
ð
y
Þ
y
P
supp B
l
B
ð
y
Þ
:
ð
11
:
33
Þ
11.4 Fuzzy Logic Applications for Protection and Control
At the end of this chapter it is worth to summarize the features of FL systems as
well as to point out examples of typical applications of such schemes in power
systems. Among the most important virtues of fuzzy systems the following should
attract the reader's attention:
• ability of processing of uncertain information, inaccurate and/or corrupted data,
• possibility of expressing of non-sharp relationships and rules in a way close to
natural language (linguistic variables, IF … THEN … rules),
• quite easy interpretation of the internal signals of a fuzzy system,
• improvement of efficiency and selectivity by decision-making in protective
relays thanks to application of fuzzy settings and fuzzy decision characteristics,
• relatively simple, intuitive setting of the input/output MFs (at least for the first,
not-optimized scheme version),
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