Approximation of Optimized Fuzzy Logic Controller for Shunt Active Power Filter - Complex System Modelling and Control Through Intelligent Soft Computations - page 572

Input
Variables

u 2 ( k )

u 1 ( k )

Compensating
Polynomial

4-ruleFLC

Fig. 10 Block diagram of approximation scheme

Fig. 11 Flow chart showing
design steps of approximated
FLC

Start

Load the outputs of a 49-rule FLC and 4-rule FLC

Assign order of the polynomial

Calculate the error between output of 49-rule FLC and
proposed approximated FLC with compensating polynomial

Calculate sum of error squares at various data points

Partially differentiate the sum of error squares with respect
to unknown coefficients of polynomial and equate them to
zero, solve the resulting equations to get the coefficients

Stop

The order of compensating polynomial plays a critical role in approximation.
A large order polynomial is avoided due to the following reasons:
(a) A large order polynomial needs more computational time and memory,
defeating the basic objective of designing a reduced rule approximated FLC.
(b) Higher order polynomial can be highly oscillatory and an order larger than the
exact fit case may lead to multiple solutions, resulting in a confusing state for

designer to select one solution.

cient
approximation. This situation leads towards maintaining a tradeoff between the
order of polynomial and degree of

On the contrary, a lower order polynomial may not provide the suf

fitness for adequate approximation. A 7th order
polynomial is derived in using the proposed approximation technique.