Approximation of Optimized Fuzzy Logic Controller for Shunt Active Power Filter - Complex System Modelling and Control Through Intelligent Soft Computations - page 562

In Fuzzy logic controllers (FLCs), the rule base size plays a vital role to decide
the control action. With the increase in number of rules, the partitions of universe of
discourse (UOD) become

finer, resulting in a better control action. As the number
of rules increases, the amount of information to be stored in knowledge-base also
increases. On the other hand, a smaller rule base is not able to map the non-linear
control action with same accuracy as the large rule FLC. Although, a large rule FLC
provides precise control action, but at the cost of increased complexity, large
memory requirement to store the knowledge base information and more execution
time to process a speci c control action (Singh et al. 2011b ). In this chapter, an

effort is made to overcome these limitations by proposing an approximated fuzzy
logic controller consisting of a simplest 4-rule FLC with a compensating
polynomial.
In the recent past some research on reduction of rule base size has been reported.
Some issues on design and rule base size reduction for the fuzzy control of robot
manipulators are addressed (Bezine et al. 2002 ), whereas resizing of rule base by
removing inconsistent and redundant rules for the application of vacuum cleaner is
discussed and implemented (Ciliz 2005 ). However, these two studies were appli-
cation speci

c. Hampel and Chaker ( 1998 ) provided some conclusions for mini-
mization of number of variable parameters for optimization of fuzzy controller.
Moser and Navara ( 2002 ) proposed a fuzzy controller with conditional firing rules,

where only the rule firing conditions, not the number of rules, are reduced. Zeng
and Singh ( 1994 , 1995 ) presented a mathematical description of approximation
theory of fuzzy systems for single input single output (SISO), and multi input multi
output (MIMO) systems. These works are about the approximation capabilities of
the fuzzy systems for approximating a mathematical polynomial rather than on the
rule reduction. As the reported works are either application speci

c or not focused
on rule base size reduction, provide the motivation to explore the possibility of a
process independent, less complex, approximation scheme capable of providing an
equally comparable control action as provided by a large rule FLC (Singh et al.
2011b , 2013 ; Singh and Singh 2012 ).
An approximation methodology is proposed in this chapter and its effectiveness
is validated with shunt APF providing harmonic and reactive power compensation
in an electrical distribution system supplying highly non-linear and randomly
varying loads. The proposed approximation technique is process independent, and
derived by minimizing the deviation between the responses of a large rule and a
reduced rule (4-rule) FLC in the UOD of [ 1, 1].

The objectives of this chapter are manifold, some of them are listed below:

−

￿ To understand the causes and mitigation of one of the most encountered PQ

problem, i.e., harmonics.

￿ To discuss the working principle and control scheme of shunt APF, a mitigation

device used for current harmonics compensation.

To provide a prime introduction of fuzzy logic controller (FLC).

￿