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INTRODUCTION TO FUZZY
CONTROLLERS-PART 1

• There are several ways to define the result of a rule, but one of the most
common and simplest is the "max-min" inference method, in which the
output membership function is given the truth value generated by the
premise.
• Rules can be solved in parallel in hardware, or sequentially in software.
The results of all the rules that have fired are "defuzzified" to a crisp value
by one of several methods. There are dozens, in theory, each with various
advantages or drawbacks.
• The "centroid" method is very popular, in which the "center of mass" of
the result provides the crisp value. Another approach is the "height"
method, which takes the value of the biggest contributor.
•The centroid method favors the rule with the output of greatest area,
while the height method obviously favors the rule with the greatest output
value.

The diagram below demonstrates max-min inferencing and centroid
defuzzification for a system with input variables "x", "y", and "z" and an
output variable "n". Note that "mu" is standard fuzzy-logic nomenclature for
"truth value":

Fuzzy control system design is based on empirical methods, basically a
methodical approach to trial-and-error. The general process is as follows:
1. Document the system's operational specifications and inputs and
outputs.
2. Document the fuzzy sets for the inputs.
3. Document the rule set.
4. Determine the defuzzification method.
5. Run through test suite to validate system, adjust details as required.
6. Complete document and release to production.

As a general example, consider the design of a fuzzy controller for a steam
turbine. The block diagram of this control system appears as follows:
The input and output variables map into the following fuzzy set:

where:
N3: Large negative. N2: Medium negative. N1: Small negative. Z: Zero. P1: Small
positive. P2: Medium positive. P3: Large positive.
The rule set includes such rules as:
rule 1: IF temperature IS cool AND pressure IS weak, THEN throttle is P3.
rule 2: IF temperature IS cool AND pressure IS low, THEN throttle is P2.
rule 3: IF temperature IS cool AND pressure IS ok, THEN throttle is Z.
rule 4: IF temperature IS cool AND pressure IS strong, THEN throttle is N2.

Methods1 for defuzzifying fuzzy output functions
1. Max membership principle: (Also known as the height method)where z∗is
the defuzzified value

Methods2 for defuzzifying fuzzy output functions
2. Centroid method: (also called center of area, center of gravity)

Method 3 for defuzzifying fuzzy output functions
Weighted average method: (it is usually restricted to symmetrical output
membership functions.)
Z is the centroid of each symmetric membership function

Weighted average method
As an example,

Method 4 for defuzzifying fuzzy output functions
Mean max membership: (also called middle-of-maxima)
the maximum membership can be a plateau rather than a single point).

Z ^is the centroid of each symmetric
membership function.

According to the mean max membership method, Eq. (4.7), z∗is given by
(6 + 7)/2 = 6.5 meters.

FUZZY BASED TEMPERATURE CONTROL
There are 5 steps in implementing the Fuzzy Logic.
They are :
• Defining inputs and outputs.
• Fuzzification of input.
• Fuzzification of output.
• Create Fuzzy rule base.
• Defuzzification of output.

Defining Inputs and Outputs For Fuzzy Logic Control
This step involves the declaration of the range of inputs and outputs. This
process of
declaring is called Universe of Discourse.

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