Page 75 - 2024-Vol20-Issue2

71 | Shukir

The effective values of voltage and current (r.m.s) 2. Apply Fuzzy Operator: the fuzzy operator (AND/
OR) is applied to obtain one number that represents the
V and I (r.m.s) = DCvvalues (23) result of the antecedent (an input fuzzy set represented
2 by a membership function) for the input that has more
than one part.
The efficiency of the converter and inverter is 80%, the duty
cycle of the boost converter is between (0.8 – 0.85) for stability 3. Apply Implication Method: The consequent (an out-
operation of the converter [12], and the modulation index of put fuzzy set represented by a membership function)
the inverter (m) is between (0 – 1) [13]. The inductor and is reshaped using a function associated with the an-
capacitor of the boost converter is determined depending on tecedent. Fig. 4 shows the implication process.
the equations [11, 14]:

L = Vi(Vo -Vi) (24) 4. Aggregate All Outputs: Aggregation is the process by
fs · ?I ·Vo which the consequent of each rule are combined into a
single fuzzy set.

C = Io(Vo -Vi) (25) 5. Deffuzification: The input of the defuzzification pro-
fs · ?v ·Vo (26) cess is the aggregate of the consequent of all rules. The
most popular defuzzification method is the centroid
Where: calculation, which returns the center of area under the
Current ripple(?I) = 5% of the input current curve as obvious in Fig. 5.

If µc is defined with continuous membership function, the
center of gravity is:

Voltage ripple(?V ) = 1% of the output voltage (27) Center of Gravity = µc(x) · x dx (28)
µc(x) dx
Substitute:
Input voltage = 96 V, And if µc is defined with discrete membership function, the
Input current = 128 A, center of gravity is:
Initial duty cycle (D) = 83%,
Output voltage = 452 V, Center of Gravity = ?ni=1 µc(xi) · xi (29)
Output current = 17.4 A, ?in=1 µc(xi)
Switching frequency ( fsb) = 5 kHz,
Current Ripple(?I) = 6.4 A, The membership function that used in control theory is a
Voltage Ripple(?V ) = 4.52 V, Gaussian membership function which shown in Fig. 6, and it
is defined by [17]:
Result:
L = 2.36 mH, µ(x, c, s, m) = a exp -1 x-c m (30)
C = 606 µF. 2 s

Here: c is the center, s represents width, and m is fuzzification
factor (e.g., m = 2).

V. FUZZY LOGIC CONTROLLER VI. THE MEMBERSHIP FUNCTIONS AND THE
SET OF LINGUISTIC RULES OF THE
The general construction of the FLC consists of five steps [15] CONTROLLERS
[16]: Fuzzify Inputs, Apply Fuzzy Operator, Apply Implica-
tion Method, Aggregate All Outputs, and Deffuzification. A. DC Voltage Regulator Controller
The fuzzy logic controller of error and change of error consists
1. Fuzzify Inputs: It converts a crisp input signal, er- of 3 linguistic variables as shown in Fig. 7. In output there
ror and change of error into fuzzy set by membership are 5 linguistic variables as shown in Fig. 8. The rules linking
functions, the output is a fuzzy degree of membership among input signals (error and change of error) and output
functions (0 -1). signal for the dc voltage regulator is as depicted in Table II,
Where; N negative, Z zero, P positive, SN small negative, MN
medium negative, SP small positive, MP medium positive.