IEEE Power Electronics Magazine - December 2020 - 23

IF motor speed is high and its stator temperature is medium
  THEN set the machine stator current low.

1)	 Fuzzification of the input crisp variables (X, Y, etc.);
2)	 Application of fuzzy operator (AND, OR, NOT) in the IF
(or antecedent) part of the rule;
3)	 Implication from the antecedent to the consequent
(THEN) part of the rule;
4)	 Aggregation of the consequents of the rules;
5)	 Defuzzification to convert the fuzzy output to crisp value.
All the three rules in the figure are shown in the consecutive
horizontal rows with the input values of X = - 3 and
Y = +1.5. Since all the rules use the AND operator, the
degree of fulfilment (DOFs) from the antecedent parts of the
rules are calculated as DOF1 = 0.6 , DOF2 = 0.4 and
DOF3 = 0.4 , respectively. The corresponding fuzzy output
MFs (shaded) are PS', ZE' and NS', respectively from the
consequent part of the rules. The total fuzzy output, as
shown in the figure, is the aggregation of the consequents of
the rules. The defuzzification calculates the center of the
overlapped area (COA), where Z 0 is the defuzzified or crisp
output. Note that a practical FIS can have a large number of
input and output variables and each variable may have a
large number of MFs. A FIS can be designed with the help of
Math Works Fuzzy Logic Toolbox [5].

The fuzzy variables (underlined) in the rule are normally
represented by membership functions (MFs). Figure 3 shows
the general principle of Mamdani type fuzzy control system
(defined as fuzzy inference system or FIS) using triangular
MFs. Mamdani method is most commonly used in literature.
Here, X, Y and Z are the fuzzy variables, where X and Y are
the inputs and Z is the output. Each fuzzy variable is represented by three MFs, as indicated in the figure. The fuzzy variables can be unipolar or bipolar, and range of values of each is
defined as a " universe of discourse " . In the FIS, there are three
control rules as indicated in the figure which can be defined as
Rule 1: IF X is negative small (NS) AND Y is zero (ZE)
 THEN Z is positive small (PS)
Rule 2: IF X is zero (ZE) AND Y is zero (ZE)
 THEN Z is zero (ZE)
Rule 3: IF X is zero (ZE) AND Y is positive small (PS)
 THEN Z is negative small (NS).
For convenience, fuzzy variables are normally defined on a
per unit (pu) basis. All the rules in FIS are normally summarized as a rule matrix in the form of a table.
Because of the analogy, a FIS is often defined as fuzzy ES.
The computations in FIS consist of the following five steps to
determine the inference or conclusion
µ (X )
1

NS

Fuzzy Logic Control of Modern Wind Generation System
FL has been applied extensively in power electronic systems
[1]. The applications include robust control of drives with
parameter variation, P-I tuning of control system, system

µ (Y )
1

-6

0

µ (X )
1

6

Rule-2

ZE

-6

0

µ (Y )
1

ZE

6

0

µ (X )
1

6

Rule-3

-6

0

µ (Y )
1

PS

6
1

X = -3

0

6
ZE
ZE′

-6

0

µ (Z )
1

NS

6

NS′

DOF3 = 0.4

0.4
0 X

-6

0.6
DOF2 = 0.4

ZE

-6

PS′

µ (Z )
1

0.4
-6

PS

0.6
DOF1 = 0.6

Rule-1

0.8

µ (Z )
1

ZE

6

-6

0

Y

6

Y = 1.5

-6

0

µ (Z )
1

-6

Z

6

µ out (Z )

0
Z0

6

FIG 3 Three-rule Mamdani type FIS showing the output defuzzification.

	

December 2020	

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IEEE Power Electronics Magazine - December 2020

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