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In-Depth Information
80
Real data
Fuzzy model
Simplified Fuzzy model
60
40
20
0
−20
−40
−60
−80
0
20
40
60
80
100
Fig. 3.9
Mechanical system: comparison between original, fuzzy and simplified fuzzy system
150
100
50
0
−50
−100
−150
Fuzzy model
Simplified Fuzzy model
−200
0
0.5
1
1.5
2
2.5
3
Fig. 3.10
Mechanical system: comparison between fuzzy and simplified fuzzy system
3.6 Conclusions
A new systematic technique have been presented in this chapter in order to reduce the
complexity of Takagy-Sugeno fuzzy systems. Using Functional Principal Compo-
nents Analysis, you can get a small number of rules. The problemwith this technique
is the lack of interpretability in the fuzzy system, due to the algebraic combination
before aggregation. If we focus on use in predictive control, that's not a problem. Even
predictive controllers with explicit solution that could be implemented in industrial
devices according to IEC-1131-3 and IEC 1131-7, there may be the possibility of
non-prototypical membership functions or algebraic operations after fuzzification.
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