Approximation of Optimized Fuzzy Logic Controller for Shunt Active Power Filter - Complex System Modelling and Control Through Intelligent Soft Computations - page 578

14

Triangular MFs
Gbell MFs
Gaussian MFs
Dsig MFs

12

10

8

6

4

2

0

Time (sec)

Fig. 16 Comparison of THD profile of source current with 49-rule FLC using various MFs

Table 4 Comparison of controllers on the basis of performance indices
Performance index MFs

Triangular Gbell Gaussian Dsig

ITAE 0.36 0.66 0.35 0.51

IAE 7.62 8.56 7.46 7.91

ISE 1,970.76 1,977.91 1,970.45 1,972.73

ITSE 11.88 13.65 12.05 12.65

(a) Integral square error (ISE),

(b) Integral absolute error (IAE),

(c) Integral time absolute error (ITAE), and

(d) Integral time square error (ITSE).

4.5 Selection of Optimal Membership Function
and Performance Analysis of Approximated
Optimized FLC

The Gaussian MFs based FLC dominates in three out of four performance indices,
and therefore the 49-rule FLC using Gaussian MFs is selected for approximation.
The approximated optimized FLC is a cascade combination of a 4-rule FLC using
optimized MFs (Gaussian, here) and a compensating polynomial derived based on
minimization of SSE. The outputs of a 49-rule FLC and a 4-rule FLC using
Gaussian MFs are compared at regular intervals in the entire range of input vari-
ables as shown in Fig. 17 .
Using the methodology of approximation discussed in Sect. 4 , a seventh order
polynomial, as given in ( 8 ), is derived, whose cascaded combination with a 4-rule
FLC approximates the control behaviour of a 49-rule FLC.