i

DEVELOPMENT OF A POWER FACTOR CORRECTION

BUCK CONVERTER IN SINGLE PHASE RECTIFIER

USING FUZZY LOGIC

ASMAWI BIN MUDA@OTHMAN

A project report submitted in partial fulfillment ofthe requirement for the award of the Master of

Electrical Engineering

Faculty of Electrical and Electronic EngineeringUniversiti Tun Hussein Onn Malaysia

JULY, 2013

v

ABSTRACT

Power Factor Correction (PFC) circuits are widely used in single-phase rectifiers in

order to emulate a linear resistive behavior. The buck PFC is still the most popular

configuration due to its simplicity, but it suffers from high voltage stresses across the

power electronic devices. This thesis presents to development buck converter in

single phase rectifier used the fuzzy logic.

The methodology integrates fuzzy logic controlling the output voltage of DC-DC

converter and to improve performance of the buck converter during transient

operation. Instead of generating fast pulse-width-modulated (PWM) signal, the

digital signal processor is required to generate a slow- varying dc signal only for

determining the PWM ramp function. A model for power factor correction has been

formed by using the MALTAB software. The simulation and experimental results

show that output voltage of buck converter can be control according to the value of

duty cycle. The advantage of using the Buck Converter in power factor correction

circuit is that better line regulation is obtained with appreciable power factor.

vi

ABSTRAK

Litar faktor kuasa (PFC) digunakan dengan meluas dalam pelurus satu fasa supaya

mencontohi satu tingkah laku berintangan linear. Penukar Buck PFC adalah paling

popular digunakan disebabkan kesederhanaannya, tetapi nilai voltan meningkat

tinggi apabila merentasi alat kuasa elektronik . Projek ini adalah membangunkan

penukar buck dalam penerus fasa tunggal menggunakan kawalan fuzzy logic.

Kaedah mengintegrasikan fuzzy logic mengawal voltan output penukar AT-AT dan

memperbaiki prestasi penukar Buck semasa operasi. Daripada isyarat pulse-width-

modulated (PWM) , pemproses isyarat digital dikehendaki untuk menjana isyarat

yang boleh ubah secara pelahan-lahan untuk menentukan rangkap fungsi PWM. Satu

model bagi pembetulan faktor kuasa telah ditubuhkan dengan menggunakan perisian

MALTAB. Simulasi dan hasil percubaan menunjukkan voltan output penukar buck

boleh mengawal nilai kitar kerja. Kelebihan menggunakan penukar buck di litar

pembetulan faktor kuasa adalah peraturan talian lebih baik diperolehi berbanding

faktor kuasa ketara.

vii

TABLE OF CONTENTS

TITLE i

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

ABSTRACT v

TABLE OF CONTENTS vii

LIST OF TABLES x

LIST OF FIGURES xi

LIST OF SYMBOLS xiii

CHAPTER 1 INTRODUCTION 1

1.1 Project background 1

1.2 Problem statement 2

1.3 Project objective 3

1.4 Project scope 3

1.5 Thesis overview 3

CHAPTER 2 LITERATURE REVIEW 5

2.1 Introduction 5

2.2 Buck converter 6

2.2.1 Modes of operation 9

2.2.1.1 Continuous conduction mode (CCM) 10

2.2.1.2 Discontinuous conduction mode (DCM) 10

viii

2.2.2 Critical component value 11

2.2.3 Mathematical modeling of Buck Converter 14

2.2.3.1 State-space representation 14

2.2.3.2 Average state-space representation 17

2.2.4 Advantages of buck converter for power

factor correction 17

2.3 Power factor correction (PFC) 18

2.3.1 Need of PFC 18

2.3.2 Types of power factor correction 19

2.3.2.1 Passive power factor correction 19

2.3.2.2 Active power factor correction 20

2.4 Fuzzy logic controller 21

CHAPTER 3 METHODOLOGY 25

3.1 Project design 25

3.2 Parameter for buck converter 27

3.3 Fuzzy logic controller design 27

3.3.1 Fuzzification interface 27

3.3.2 Rule base 31

3.3.3 Fuzzy logical decision making 35

3.3.4 Deffuzzifier 35

CHAPTER 4 RESULTS AND ANALYSIS 36

4.1 MATLAB software 36

4.2 Simulation results 36

ix

4.3 Simulation for reference voltage (ref)

equal 115V 37

4.4 Output voltage for reference voltage 110V,

100V, 90V and 80V 41

4.5 Power factor for reference voltage 110V, 100V,

90V and 80V 43

4.6 Analysis for buck converter 47

CHAPTER 5 CONCLUSION AND RECOMMENDATION

5.1 Conclusion 48

5.2 Recommendation 49

REFERENCES 50

x

LIST OF TABLES

3.1 Parameter for Buck Converter 27

3.2 Rules for error and change of error 31

4.1 Analysis of power factor for reference voltage set to 115V,

110V, 100V, 90V and 80V 47

xi

LIST OF FIGURES

2.1 Circuit diagram for Buck Converter 6

2.2 Waveform for Buck Converter 7

2.3 (a) Turn on switch “Circuit Diagram Buck Converter” 7

2.3 (b) Turn off switch “Circuit Diagram Buck Converter” 8

2.4 Inductor current waveform of PWM converter 11

2.5 (a) Mode 1 14

2.5 (b) Mode 2 14

2.6 Structure of fuzzy logic controller 22

3.1 Block diagram of the Power Factor CorrectionBuck Converter in

single phase rectifier using fuzzy logic 25

3.2 Flowchart of the project 26

3.3 FIS editor 29

3.4 (a) Membership function of input variable ‘input 1’ 29

3.4 (a) Membership function of input variable ‘input 2’ 30

3.4 (c) Membership function of output variable 30

3.5 (a) Show the rule base 32

3.2 (b) Rule views for Fuzzy Logic Controller using Fuzzy Logic Toolbox 32

4.1 Block diagram of Buck Converter in single phase rectifier using

Fuzzy Logic Controller 37

4.2 Input voltage (Vin) for reference voltage (Vref) equal 115V 38

4.3 Output current (Iout) for reference voltage (Vref) equal 115V 38

4.4 Output voltage (Vout) for reference voltage (Vref) equal 115V 39

xii

4.5 Power Factor (PF) for reference voltage (Vref) equal 115V 40

4.6 (i) Output voltage (Vout) for Vref equal 110V 41

4.6 (ii) Output voltage (Vout) for Vref equal 100V 41

4.6 (iii) Output voltage (Vout) for Vref equal 90V 42

4.6 (iv) Output voltage (Vout) for Vref equal 80V 42

4.7 (i) Power factor for Vref equal 110V 43

4.7 (ii) Power factor for Vref equal 100V 44

4.7 (iii) Power factor for Vref equal 90V 45

4.7 (iv) Power factor for Vref equal 80V 46

xiii

LIST OF SYMBOLS

Symbol

Vo Output voltage

Vi Input voltage

Vref Reference voltage

R Resistor

C Capacitor

L Inductor

CCM Continuous Conduction Mode

DCM Discontinuous Conduction Mode

PWM Pulse Width Modulation

DC Direct Current

AC Alternating Current

IL Inductor Current

f Frequency

T Period

PFC Power Factor Correction

e Error

ce Change of Error

ΔQ change of charge

Cmin Minimum Capacitor

D Duty Cycle

Q Transistor

NB Negative Big

NM Negative Middle

NS Negative Small

Z Zero

PS Positive Small

PM Positive Middle

PB Positive Big

1

CHAPTER 1

INTRODUCTION

1.1 Project background

With rapid development in power electronic technology, power

semiconductor technology, modern control theory for dc to dc converter such as

buck converter and manufacturing technology for step down voltage in industry,

buck converter have been widely used in many fields. Step down buck converter are

integral to modern electronic [1]. Step down converter transfer small packets of

energy using a switch, diode, an inductor and several applications. Through

substantially larger and noisier than their linear regulator counterparts, buck

converters offer higher effiency in most cases.

The general, DC-DC converter consists of power semiconductor devices

which are operated as electronic switches. Operation of the switching devices causes

the inherently nonlinear characteristic of DC-DC converter including one known as

the Buck converter. Consequently, this converter requires are controller with a high

degree of dynamic response.

The study about fuzzy logic quickly developed in the past few decades in the

control system has made great progress. The fuzzy logic approach has been proposed

to converters. Its major advantage is that expert knowledge can regulate the output

2

voltage of the switching DC–DC Buck Converter be incorporated into the fuzzy

controller using simple linguistic rules to achieve the control objective without

involving the converter’s mathematical models. [2][3] The Fuzzy logic controller are

designed based on dimensional rule table using voltage error and change in voltage

error as input variables and change in duty cycle as control output. [4]

1.2 Problem Statement

The DC-DC converters such as Buck converter which is capable to step-

down the output voltage produce higher current ripple. This will influenced and

decreased the output voltage regulation and efficiency of the converter. These

weaknesses can be overcome by Buck converter which exhibit low input and output

current ripple.

The Fuzzy control is a practical alternative for a variety of challenging

control applications because Fuzzy logic control is nonlinear and adaptive in nature

that gives it a robust performance under parameter variation and load disturbances.

Fuzzy logic controller used in buck converter single phase rectifier circuit is

acquiring value power factor correction around 0.9 (90%) to almost 1.0 (100%).

Fuzzy logic is suited to low-cost implementations and systems of fuzzy can

be easily upgraded by adding new rules to improve performance or add new features.

3

1.3 Project objective

The major objectives of this project are:

1. To develop, describes and simulate the designed, use and analysis of Buck

Converter for power Factor Correction.

2. To develop and simulate the designed single phase rectifier using the fuzzy

logic controller for variable output voltage DC-DC buck converter.

1.4 Project scope

The scopes of this project is to simulate the proposed method of power factor

correction buck converter in single phase rectifier using using fuzzy logic controller

with MATLAB Simulink software. The analysis only covered the output voltage and

power factor correction only.

1.5 Thesis Overview

This project report is organized as follows;

a) Chapter 1 briefs the overall background of the study. A quick glimpse of

study touched in first sub-topic. The heart of study such as problem

statement, project objective, and project scope is present well through this

chapter.

b) Chapter 2 covers the literature review of previous case study based on fuzzy

logic controller background and development. Besides, general information

about Buck Converter and theoretical revision on fuzzy logic control system

also described in this chapter.

4

c) Chapter 3 presents the methodology used to design open loop Buck

Converter and fuzzy logic controller. All the components that have been used

in designing of fuzzy logic controller are described well in this chapter.

d) Chapter 4 shows the analysis for fuzzy logic controller will be with helps

from set of figures and tables.

e) Chapter 5 a conclusion for this project and recommendation for future study.

5

CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

Energy storage elements including capacitors and inductors are used for

energy transfer and work as a low-pass filter. The buck converter and the boost

converter are the two fundamental topologies of switch mode DC-DC converters.

Most of the other topologies are either buck-derived converter, because their

topologies are equivalent to the buck converters [5].

A thorough literature overview was done on the usage of fuzzy logic

controller as applied DC-DC Buck Converter.

M. Bayati Poodeh, S. Eshtehardiha, M. R. Zare (2007), proposed an

application of fuzzy logic to control the DC – DC converter using

MATLAB/SIMULINK software. This paper demonstrated the effectiveness of the

fuzzy controller applied to the state space averaging DC – DC converter using

MATLAB.

M. J Yusoff, N.F Nik Ismail, Ismail Musirin, N. Hashim, D. Johari (2010),

proposed a comparative study of fuzzy logic controller and proportional integral

derivative controller on DC – DC buck converter using MATLAB simulation

6

software. Fuzzy logic controller has advantages in fast response controlled with

higher accuracy. FLC has a potential to improve robustness of DC – DC converter.

Based on those related work, the researchers make a great efforts to propose

the good to overcome the DC-DC Converter problems. Their applications of each

method differ, thus the further investigation of this controller is needed.

2.2 Buck Converter

The step-down dc-dc converter, commonly known as buck converter, it

shown in fig. 2.1. This consists of dc input voltage source Vs, controlled switch S,

diode D, filter inductor L, filter capacitor C and load resistance R. Typically

waveform in the converter are shown in fig 2.2, under assumption that the inductor

current is always positive. The state of the converter in which the inductor current is

never zero for any period of time is called the Continuous Conduction Mode (CCM).

[4][13].

Figure 2.1 : Circuit Diagram for Buck Converter

7

Figure 2.2: Waveform for Buck Converter

It can be seen from the circuit that when the switch S is commanded to the on state,

the diode D is reverse biases, which can be shown in figure 2.3(a). When the switch

is off, the diode conducts to support an interruption current in the inductor, which

can be shown in figure 2.3(b) .

Figure 2.3 (a) : Turn on switch “Circuit Diagram Buck Converter”

8

Figure 2.3 (b) : Turn off switch “Circuit Diagram Buck Converter”

When the switch S1 is on and D is reverse biased, the dynamics of inductor current iL

abd the capacitor voltage Vc are:

(2.1)

When the switch S1 is off and D is forward biased, the dynamics of the are

(2.2)

When the switch S1 is off and D is also not conducting,

(2.3)

9

The state space representation for converter circuit configuration can be expressed

as:

(2.4)

Where X = [x1, x2]T = [Vc , iL]is the state vector and A’s and B’s are the system

matrices.

The state matrices and the input vectors for the ON and OFF periods are.

(2.5)

And U = Vin 0

2.2.1 Modes of Operation

The operation of dc-dc converters can be classified by the continuity of

inductor current flow. So dc-dc converter has two different modes of operation that

are:

(a) Continuous conduction mode (CCM) and

(b) Discontinuous conduction mode (DCM).

A converter can be design in any mode of operation according to the requirement.

10

2.2.1.1 Continuous Conduction Mode (CCM)

When the inductor current flow is continuous of charge and discharge during

a switching period, it is called Continuous Conduction Mode (CCM) of operation

shown in figure 2.4(a). The converter operating in CCM delivers larger current than

in DCM.

2.2.1.2 Discontinuous conduction mode (DCM).

When the inductor current has an interval of time staying at zero with no

charge and discharge then it is said to be working in Discontinuous Conduction

Mode (DCM) operation and the waveform of inductor current is illustrated in figure

2.4(c). At lighter load currents, converter operates in DCM. The regulated output

voltage in DCM does not have a linear relationship with the input voltage as in

CCM.

11

Figure 2.4: Inductor current waveform of PWM converter

(a) CCM (b) boundary of CCM and DCM (c) DCM

2.2.2 Critical Component Values

Since the inductor current magnitude at the end of the switching period must

equal the inductor current magnitude at the beginning of the next period at steady

state, the change in current over the switching period must equal zero.

Using this knowledge yields the following:

Δ l L.period = Δ l L.closed + Δ l L.open = 0 (2.6)

12

Substituting equations (2.1) and (2.6) into (2.7) and solving for D yields:

D = Vout (2.7)Vin

Now the average inductor current equals the average of the minimum and

maximum inductor current values, so the maximum inductor can be found using

equation (2.9) nothing that either Δ l L.closed or Δ l L.open can be used.

ILmax = IL + [Δ l L] (2.8)2

Using the rule known as amp-second balance, which states the average

current through a capacitor at steady state must equal zero, the average inductor

current must equal the average output current.

IL = I out = Vout (2.9)R

Substituting equations (2.6) and (2.9) into (2.8) and simplifying yields:

The minimum inductor current can be found in the same manner as the maximum

inductor current:

lLmin = IL - [Δ l L] (2.11)2

The minimum inductor current is an important value, because as mentioned

previously, it determines the mode of conduction. Since all previous equations were

derived using the assumption of CCM, for them to remain valid I Lmin can never go

below zero. So by setting equation (2.15) equal to zero and rearranging to solve for

L, the minimum inductor value can be found to keep the converter in CCM:

(2.10)

13

Once the inductor value is determined, the minimum capacitance to maintain

the desired output ripple voltage can be found. This can be done by finding how

much charge is supplied by the capacitor when the switch is on or off. By using amp-

second balance the average current through a capacitor must equal zero if the circuit

is in steady state.

Then by calculating the area under the current wave form either when the

switch is on or off will yield the change in charge. Since the current wave form is

triangular the area can be found by using the formula one half times the triangle’s

base times the triangles height. Where the height equals the change in current

divided by two, and the base is the switching period divided by two.

In this case the change of charge (ΔQ) is easier to calculate using the change

in current when the switch is off (Δ I L,open). Substituting equation (2.6) into (2.14)

and simplifying yields:

C = Δ Q (2.15)Δ Vout

(2.12)

(2.13)

(2.14)

14

Substituting equation (2.15) into equation (2.16) yields the equation for selecting the

minimum output capacitor for the desired output ripple voltage.

2.2.3 Mathematical Modeling of Buck Converter

2.2.3.1 State-Space Representations

The buck converter is nonlinear, time-dependent system and its operation is

described by the two modes, illustrated in Figure 2.5 (a) and (b). The system is

linearized through switch averaging method about a selected operating point, and

with respect to the transistor duty cycle, k.

Figure 2.5: (a) Mode 1 Figure 2.5: (b) Mode 2

Mode 1 of operation is described by two differential equations derived from thecircuit in Figure 2.5 (a) and consistent with transistor Q switch being turn on:

(2.16)

15

The state-space representation for mode 1 (transistor is on) is given by:

The corresponding state-space representation for mode 1 is:

During mode 2, transistor Q switch is turn off, and the voltage across diode is zero,

as illustrated in Figure 2.5 (b). Mode 2 is describe by a set of differential equations,

(2.17)

(2.18)

(2.18)

(2.19)

(2.20)

(2.21)

(2.22)

(2.23)

(2.24)

16

consistent with the transistor Q switch being turn off:

The state-space representation of mode 2 is obtained from mode 1 state-space

representation by setting all coefficients of Vg to zero:

(2.25)

(2.26)

(2.27)

(2.28)

(2.29)

17

2.2.3.2 Average State-Space Representation

The two linear systems are averaged with respect to their time span during

the switching period [1]:

This system representation is an approximation of the time-varying system,

in which a new input variable is introduced: duty cycle k(t). Thus, a new input vector

u’(t) is defined:

The non-linear time-invariant system obtained, with state vector x(t), input

vector u’(t) and output y(t) is written in a general format as:

Defining the deviations from an operating point, a straight forward linearization is

applied:

2.2.4 Advantages of Buck Converter for Power Factor Correction

i. It requires only one transistor and is simple.

ii. It has high efficiency, more than 90%.

iii. The inductor limits the rate of change of load current.

(2.30)

(2.31)

(2.32)

18

But, the input current is discontinuous and a smoothing input filter is required. Buck

converter provides one polarity of output voltage and unidirectional output current.

In systems such as universal line AC-DC converters [5], it is very difficult to

improve power factor where high efficiency is required throughout the entire line. A

Power Factor Correction circuit using Boost Converter possesses 1% to 3% lower

efficiency at 100 Volts than that at 230 Volts. This is due to increased input current

that produces higher losses in semiconductors and input filters. Also the high output

voltage of Boost Converter in 380-400 Volts range has a detrimental effect on its

switching losses and on the size and efficiency of the isolation transformer.

2.3 Power Factor Correction (PFC)

Power factor correction is the method of improving the power factor of a

system by using suitable devices. The objective of power factor correction circuits is

to make the input to a power supply behave like purely resistive or a resistor. When

the ratio between the voltage and current is a constant, then the input will be resistive

hence the power factor will be 1.0. When the ratio between voltage and current is

other than one due to the presence of non-linear loads, the input will contain phase

displacement, harmonic distortion and thus, the power factor gets degraded [7]. [12]

2.3.1 Need of PFC

The rise in the industrial, commercial and residential applications of

electronic equipment’s has resulted in a huge variety of electronic devices requiring

mains supply. These devices have rectification circuits, which is the prominent

reason of harmonic distortion. These devices convert AC to DC power supply which

causes current pulses to be drawn from the ac network during each half cycle of the

supply waveform. Even if a single device for example, a television may not draw a

lot of reactive power nor it can generate enough harmonics to affect the supply

19

system significantly, but within a particular phase connection, there may exist

several such devices connected to the same supply phase resulting in production of a

large amount of reactive power flow and harmonics in line current [8].

2.3.2 Types of Power Factor Correction

Power Factor Correction can be classified as two types:

i. Passive Power Factor Correction

ii. Active Power Factor Correction

2.3.2.1 Passive Power Factor Correction

In Passive PFC, in addition to the diode bridge rectifier, passive elements are

introduced to improve the nature of the line current. By using this, power factor can

be increased to a value of 0.7 to 0.8 approximately. As the voltage level of power

supply increases, the sizes of PFC components increase. The idea of passive PFC is

to filter out the harmonic currents by use of a low pass filter and only allow the 50

Hz power frequency wave to increase the power factor [7], [8].

a) Advantages of Passive PFC :

It has a simple structure.

It is reliable and rugged.

The cost is very low because only a filter is required.

The high frequency switching losses are absent and it is not sensitive to

noises and surges.

The equipment used in this circuit don’t generate high frequency

b) Disadvantages of Passive PFC :

For achieving better power factor the size of the filter increases.

20

Due to the time lag associated with the passive elements it has a poor

dynamic response.

The voltage cannot be regulated and the efficiency is low.

Due to presence of inductors and capacitors interaction may take place

between the passive elements and the system resonance may occur at

different frequencies.

Although by filtering the harmonics can be filtered out, the fundamental

component may get phase shifted thus reducing the power factor

The shape of input current is dependent upon what kind of load is connected

[7],[ 8].

2.3.2.2 Active Power Factor Correction

An active PFC is a power electronic device designed to control the amount of

power drawn by a load and obtains a power factor as close as possible to unity.

Commonly any active PFC design functions by controlling the input current in order

to make the current waveform follow the supply voltage waveform closely (i.e. a

sine wave). A combination of the reactive elements and some active switches

increase the effectiveness of the line current shaping and to obtain controllable

output voltage [7], [8].

The switching frequency differentiates the active PFC solutions into two classes.

i) Low frequency active PFC:

Switching takes place at low-order harmonics of the line-frequency and it is

synchronized with the line voltage.

ii) High frequency active PFC:

The switching frequency is much higher than the line frequency.

21

The power factor value obtained through Active PFC technique can be more

than 0.9. With a suitable design even a power factor of 0.99 can be achieved

easily. Active PFC power supply can detect the input voltage automatically,

supports 110V to 240V alternative current, its size and weight is smaller than

passive PFC power supply [7], [8].

a) Advantages of Active PFC :

The weight of active PFC system is very less.

The size is also smaller and a power factor value of over 0.95 can be obtained

through this method.

It reduces the harmonics present in the system.

Automatic correction of the AC input voltage can be obtained.

It is capable of operating in a full range of voltage [7], [8].

b) Disadvantages of Active PFC :

The layout design is somewhat more complex than passive PFC.

It is very expensive since it needs PFC control IC, high voltage MOSFET,

high voltage ultra-fast choke and other circuits [7], [8].

2.4 Fuzzy logic Controller

The most important specifications of fuzzy control method are their fuzzy

logical ability in the quality perception of system dynamics and the application of

these quality ideas simultaneously for power systems [9]. A simple block diagram of

a fuzzy system is shown in figure 2.6.

22

Figure 2.6: Structure of fuzzy logic controller

a) Input

The inputs are most often hard or crisp measurement from some measuring

equipment is converted into fuzzy values for each input fuzzy set with the

fuzzification block. [10]

b) Fuzzification

The fuzzification block performs the following tasks:

Measures the value of input variables.

Performs a scale mapping that transfers the range of values of input variables

into the corresponding universes of discourse.

Performs the function of fuzzification, which converts input data into suitable

linguistic values that may be viewed as labels of fuzzy sets.

Knowledge Based /Rule Base

Fuzzy LogicalDecision Maker

Fuzzification Defuzzifacition

input output

23

c) Knowledge based/rule base

The collection of rules is called a rule base. The rules are in “If Then” format

and formally the If side is called the conditions and the Then side is called the

conclusion. The computer is able to execute the rules and compute a control signal

depending on the measured inputs error (e) and change in error.(dE). In a rule based

controller the control strategy is stored in a more or less natural language. A rule

base controller is easy to understand and easy to maintain for a non- specialist end

user and an equivalent controller could be implemented using conventional

techniques. [10]

d) Fuzzy logical

The fuzzy engine is the kernel of a fuzzy logic controller, which has

capability of simulating human decision making based on fuzzy concepts and of

inferring fuzzy control actions using fuzzy implication (fuzzy relation) and the rules

of inference in fuzzy logic. This means that the fuzzy inference engine handles rule

inference where human experience can easily be injected through linguistic rules.

e) Defuzzication

Defuzzification is when all the actions that have been activated are combined

and converted into a single non-fuzzy output signal which is the control signal of the

system. The output levels are depending on the rules that the systems have and the

positions depending on the non-linearity’s existing to the systems. To achieve the

result, develop the control curve of the system representing the I/O relation of the

systems and based on the information; define the output degree of the membership

function with the aim to minimize the effect of the non-linearity.[10]

24

f) Output

The output is output gain that can be tuned and also become as an integrator.

The output crisp value can be calculated by the centre of gravity or the weighted

average. [8]

50

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51

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