fuzzy logic

VISVESVARAYA TECHNOLOGICAL UNIVERSITY

JNANA SANGAMA, BELGAUM-590 014

A Technical Seminar Report on

“SPEED CONTROL OF DC MOTOR BY FUZZY LOGIC”

By

MANASA NAIK

1NT09EE023

DEPT OF EEE

Under the Guidance of

Prof. SRIDEVI H R

Senior lecturer,

DEPT OF EEE

Department of ELETCTRICAL AND ELECTRONICS ENGINEERING

NITTE MEENAKSHI INSTITUTE OF TECHNOLOGY

BANGALORE-64

1 DEPT OF EEE | NMIT

NITTE MEENAKSHI INSTITUTE OF TECHNOLOGY

BANGALORE – 64

(An autonomous college under VTU, Belgaum)

Department of Electrical and Electronics Engineering

CERTIFICATE

Certified that Ms. Manasa Naik, 1NT09EE023, a bonafide student of Nitte Meenakshi Institute of Technology, Bangalore has submitted the technical report on the seminar entitled ‘SPEED CONTROL OF DC MOTOR BY FUZZY LOGIC’ in partial fulfillment for the award of Bachelor of Engineering in Electrical and Electronics Engineering during the year 2012-2013.

Signature of the Reviewer Signature of the Incharge Signature of the HOD


ABSTRACT

Fuzzy logic is a powerful problem solving methodology with wide range of application in

industrial control. This paper concentrates on the speed control of D.C Motor using fuzzy logic.

An attempt is made in developing efficient rule based constant speed dc drive by fuzzifying the

controller input.The idea behind the Fuzzy logic controller is to fuzzify the controller inputs then

infer the proper control decision based on defined rules. The fuzzy logic controller (FLC) output

is then produced by defuzzifying this inferred control decision. Thus fuzzification, rule definition

and defuzzification forms the basic process of fuzzy logic controller.A FLC uses motor speed as

input and measures difference of speed with respect to target speed. Assuming symmetrical and

50% overlapping with adjacent triangular membership function for five linguistic variables;

controller gives the voltage proportional to fall in speed. When the motor is loaded, this voltage

is fed to armature to make the motor to run at rated speed.A well accepted separately excited

D.C.Machines mathematical model is used for the simulation. As the load current increases, due

to armature resistance voltage drops across it increases and hence the speed of the motor

decreases. Speed of dc motor using FLC at different load currents is obtained which reveals that

almost constant speed is maintained at its operating range


CONTENTS

1.INTRODUCTION ……………………………………………………… (5)

2. LITERATURE REVIEW ……………………………………………………………..(7)

2.1 DIFFERENT CONTROLLING METHODS ……………………………………….(7)

2.2 FUZZY SYSTEM………………………………………………………………………(9)

MEMBERSHIP FUNCTION…………………………………………………………(11)

WORKING OF A FUZZY SYSTEM ……………………………………………….(12)

3. MATHEMATICAL MODEL OF A DC MOTOR ……………………………………(15)

4. DESIGN OF F.L. …………………………………………………………………………(21)

4.1 INTRODUCTION ………………………………………………………………………(21)

4.2BLOCK DIAGRAM OF FLC…………………………………………………………..(21)

4.3IMPLEMENTATION OF FLC …………………………………………………………(23)

CONSTRUCTION OF MEMBER FUNCTION ……………………………………….(24)

5. RESULTS AND DISCUSSIONS …………………………………………………………(29)

6. CONCLUSIONS ………………………………………………………………………… (31)

BIBLOGRAPHY…………………………………………………………………………...(32)


ABSTRACT:

Fuzzy logic is a powerful problem solving methodology with wide range of application in

industrial control. This paper concentrates on the speed control of D.C Motor using fuzzy logic.

An attempt is made in developing efficient rule based constant speed dc drive by fuzzifying the

controller input.The idea behind the Fuzzy logic controller is to fuzzify the controller inputs then

infer the proper control decision based on defined rules. The fuzzy logic controller (FLC) output

is then produced by defuzzifying this inferred control decision. Thus fuzzification, rule definition

and defuzzification forms the basic process of fuzzy logic controller.A FLC uses motor speed as

input and measures difference of speed with respect to target speed. Assuming symmetrical and

50% overlapping with adjacent triangular membership function for five linguistic variables;

controller gives the voltage proportional to fall in speed. When the motor is loaded, this voltage

is fed to armature to make the motor to run at rated speed.A well accepted separately excited

D.C.Machines mathematical model is used for the simulation. As the load current increases, due

to armature resistance voltage drops across it increases and hence the speed of the motor

decreases. Speed of dc motor using FLC at different load currents is obtained which reveals that

almost constant speed is maintained at its operating range

1.INTRODUCTION

In the present era of utility, degradation and complication many utility and industrial customers

are concerned about reliable operation of electric motor and quality of power. Recently speed controls are

used for wide variety of operation used in industry domestic and research works. Most of the drives work

on this rotating machine.

Speed control means intentional change of the drive speed to a value required for performing the

specific work process as per the requirement. The desired change in speed is accomplished by acting

accordingly on the drive motor or on the transmission connecting it to the unit it serves to drive.

Electric motors are used to drive loads of varying characteristics. Precise speed control of electric

motors in either direction or their constant speed operation under varying load conditions is required in

different applications in industries, electric traction and machine tool etc to attain a high rate of

production, high quality of products and at the same time to achieve economy in production.

Speed control is required to a high degree of accuracy. Some of the features like range,

smoothness, economic justifiability, and stability of operation and direction of speed control have to be

considered. The operation of speed control was first carried out through some of the mechanical methods.


Speed can be adjusted mechanically by means of stepped pulleys, set of change gears, variable speed

friction clutch mechanisms and other mechanical devices.

Speed can also be controlled by some of the electrical methods such as varying flux per pole (flux

control), resistance of the armature circuit (rheostatic control); applied voltage (voltage control).these

methods are applied to shunt, compound and series motor.

The electrical speed control has many economical as well as engineering advantages over mechanical

speed control methods. The traditional control model does not handle a variety of objects with differing

material characteristics very well and are based on mathematical models in which the control system is

described using one or more differential equations that define the system response to is inputs. Such

systems are often implemented as “proportional integral derivative” (PID) controllers. They are the

products of decades of development and theoretical analysis and are highly effective.

But these traditional speed control methods have got their own drawbacks, which can be

efficiently over come by applying fuzzy logic control.

The concept of fuzzy logic was conceived by lotfi Zadeh, a professor at the University of

California at Berkley. An organized method for dealing with imprecise data is called fuzzy logic. The

data are considered as fuzzy sets. Fuzzy sets allow partial membership. Fuzzy logic provides a means of

calculating intermediate values between absolute true and absolute false with resulting values ranging

between 0.0 and 1.0.

A fuzzy logic controller uses fuzzy logic as a design methodology, which can be applied in linear

and non-linear system for embedded control. The idea behind the fuzzy logic controller is to fuzzify the

controller inputs than infer the proper fuzzy control decisions based on defined rules. Defuzzifying this

inferred control decision then produces the fuzzy logic controller output.

Fuzzy logic is a problem solving control system methodology that lends itself to implementation

in systems ranging from simple, small, embedded micro controllers to large, networked multi channel PC.

It can implement in hardware, software or a combination of both. Fuzzy logic provides a simple way to

arrive a definite conclusion based upon vague, noisy or missing input information. Simplicity of fuzzy

logic in FLC enables the control designers to realize a control in less development time, at lower

development cost and with better performance.

A fuzzy logic based controller (FLC) has been developed to perform the function of speed

controller by providing controlled voltage to the D.C. machine. The complete range for variation of

controller input is represented by five decisions.


The application of speed control of drives using fuzzy logic was first introduced in the controlling

of kiln controllers in cement mills. Later it finds an important place in controlling of many industrial

drives such as steel mills, coal mills etc. It also finds its use in household appliances such as vacuum

cleaners, washing machines etc. even the field of automobiles is not beyond the reach of fuzzy logic.

2. LITERATURE REVIEW

2.1 DIFFERENT CONTROLLING METHODS:-

Speed control can be done manually by the operator or by means of some automatic

control device. There are number of methods of mechanically varying the speed of the driven

load when the driving motor is operating at a constant speed, these are typically belt drive, chain

drive, gear box, idler wheel drive.

In these methods, coupling ratio alters the speed of the driven load. These mechanical

methods allow a dynamic speed variation but are less common and more expensive.

Some of the electrical methods to control the speed of D.C.Motor are Field rheostat

control method, armature resistance control method and voltage control method.

FIELD RHEOSTAT CONTROL METHOD:-

In this method, speed variation is accomplished by means of a variable resistance inserted

in series with the shunt field. An increasing controlling resistance reduces the field current with a

consequent reduction in flux and increase in speed. This method of speed control is very simple,

convenient and most economical and is therefore, extensively used in modern electric drives.

This method of speed control is independent of load on the motor and permits remote control of

speed.

ARMATURE RESISTANCE CONTROL:-


This method consists simply of a variable resistance connected in series with the

armature. The speed at full load may be reduced to any desired value depending on the amount

of resistance. With this method, the voltage across the armature drops as the current passes

through the series resistance and the remaining voltage applied to the armature is lower than the

line voltage. Thus the speed is reduced in direct proportion to this voltage drop at the armature

terminals. Wide range of speed can be obtained by this method and at the same time motor will

develop any desired torque over its operating range, since the torque depends upon the armature

current, flux remaining unchanged.

ARMATURE VOLTAGE CONTROL: -

This method of speed control requires a variable source of voltage separate from the

source supplying the field current. This method avoids the disadvantages of poor speed

regulation and low efficiency. The adjustable voltage for the armature is obtained from an

adjustable voltage generator or from an adjustable electronic rectifier. This method gives a large

speed range with any desired number of speed points. It is essentially constant torque system,

because the output delivered by the motor decreases with a decreasing applied voltage and a

corresponding decrease in speed.

Speed of a motor can also be varied by using mechanical methods depending upon the

type of drives and braking phenomenon to be evolved. These mechanical methods allow for a

dynamic speed variation but these are less common and more expensive.

The traditional control model does not handle a variety of objects with differing material

characteristics very well and are based on mathematical models in which the control system is

described using one or more differential equations that define the system response to is inputs.

Such systems are often implemented as “proportional integral derative” (PID) controllers. They

are the products of decades of development and theoretical analysis and are highly effective.

.Furthermore, fuzzy logic is well suited to low cost implementation based on cheap

sensors, low resolution analog to digital converters and 4-bit or 8- bit one chip micro controllers,


and such systems can be easily upgraded by adding new rules to improve Performance or add

new features and even extra layer of intelligence to the current control method.

2.2 FUZZY SYSTEM:

A fuzzy system can be represented with the help of a block diagram as shown in figure 1.

Fig.1

Any fuzzy system consists of four major modules of the system

1. Fuzzification module.

2. Inference engine,

3. Knowledge base and

4. Defuzzification module.

The fuzzification module transforms the crisp input(s) into fuzzy values. These values are

then processed in fuzzy domain by inference engine based on knowledge base (rule base and

procedural knowledge) supplied by the domain expert (s). Finally the processed output is

transformed from fuzzy domain to crisp domain by defuzzification module.

FUZZIFICATION MODULE:-

Fuzzification is a process of mapping input values in crisp sets to values in fuzzy set. The

fuzzification module performs the following function.


Receives the crisp inputs. The input variables are scale mapped that transfers the range of

values of input variables into corresponding universe of discourse.

Transforms the input crisp variables to fuzzy variables. The universe of discourse of

fuzzy variables is divided into fuzzy subsets. The input variable is mapped into these subsets

with varying grade of membership.

KNOWLEDGE BASE:-

This module contains the knowledge of the application domain and the procedural

knowledge such (as attendant control goals in the case of a fuzzy controller). It consists of a

database and linguistic (fuzzy) control rule base or production rules.

The data base provides the necessary definitions, which are used to define linguistic

control rules and fuzzy data manipulation in an FLC.

The rule base characterizes the control goals and control policy of the domain expert by a

set of linguistic control rules.

INFERENCE ENGINE:-

This module simulates the decision making capabilities of human brain. Based on input

from fuzzifier, domain knowledge and set of control rules the output decisions or the necessary

control actions are evaluated in fuzzy domain. Since usually more than the rules fire there are

more than one outputs at a given instant. Inference engine also takes into account this fact by

combining a number of fuzzy outputs into a single fuzzy set. This process of combining a

number of fuzzy sets into single fuzzy sets is called aggregation.

DEFUZZIFICATION MODULE:-

The defuzzification module performs the following functions:-


A scale mapping that converts the range of values of output variables into corresponding

universe of discourse.

Defuzzifcation that transforms fuzzy outputs o corresponding crisp outputs for suitable

action.

MEMBERSHIP FUNCTION:-

In the Fuzzification, process of transferring the crisp control variables to corresponding

fuzzy variables. It is more common in the literature to use the output error and the derivatives of

the output as controller input .but for convenience, speed (N) has been selected as controller

input for the present problem.

Each of the FLC input and output signals are interpreted into a number of linguistic variables.

The number of linguistic variable varies according to the application and usually an odd number

is used .however, increasing the number of linguistic variables results in a corresponding

increase in the number of rules and also decrease the fuzzy characteristics. Adopting a

compromise, the reasonable number is five .Each linguistic variable has its fuzzy membership

function. The membership function maps the crisps values into fuzzy variable .A set of

membership defined for negative big (NB), negative minimum (NM), zero (Z), positive medium

(PM), positive big (PB) respectively.

The membership function is a graphical representation of the magnitude of participation

of each input. It associates a weighting with each of the inputs that are processed, define

functional overlap between inputs, and ultimately determines an output response.The rules use

the input membership values as weighting factors to determine their influence on the fuzzy

output sets of the final output conclusion. Once the functions are inferred, scaled, and combined,

they are defuzzified into a crisp output which drives the system. There are different memberships

functions associated with each input and output response.

Membership function is to be treated as the heart of the program where in all the major

part of calculation is done using the previous data’s obtained. Generally membership function is

expressed graphically and tends to illustrate how a complete crisp variable belongs to fuzzy set.


WORKING OF A FUZZY SYSTEM:-

To illustrate the working principle of a fuzzy system we consider here the computational

inferencing systems. A fuzzy systems working under the frame work of compositional

mechanism performs its computing as shown in figure 2, in the following 5 steps.

Fig.2

STEP 1:- FUZZIFICATION OF THE INPUTS

Fuzzification is the process of transformation of crisp input values to the corresponding

values in fuzzy domain (fuzzy values), in this step fuzzifier takes the inputs and determines the

degree to which they belong to each of the appropriate fuzzy sets via membership functions. The

input (s) is always a crisp numerical value.

STEP 2:- FUZZY OPERATORS


APPLY FUZZY OPERATOR

APPLY IMPLIFICATION METHOD

AGGREGATE ALL OUTPUTS

DEFUZZIFY

FUZZIFY INPUTS

It is also called composition. Usually the antecedent of a given rule has more than one

part; hence the fuzzy operators are applied to obtain one number that represents the result of the

antecedent for that rule. This number will then be applied to the output function. The input to a

fuzzy operator is two or more membership values from fuzzified input variables. The output is

single truth-value. Two commonly used fuzzy operators are MIN and MAX operators.

STEP 3:- IMPLICATION METHODS:-

The shaping of the consequent based on the antecedent is termed as implication. The

input for the implication process is a single number given by the antecedent, and the output is a

fuzzy set (i.e. output of a fuzzy operator), implication is applied for each rule. Two commonly

used implication methods for AND are min (i.e. truncation) and product (i.e. scaling the height

of the fuzzy set). There are a large number of implication operators such as mamdani, Larsen,

godelian which are listed in the table shown below

IMPLICATION OPERATION AGGREGATION OPERATOR

Mamdani Union ( ¿ )

Larsen Union ( ¿ )

Lukasiewicz Intersection ( ¿ )

Kleen-Dienes Intersection ( ¿ )

Standard Sequence Intersection ( ¿ )

Drastic Product Union ( ¿ )

Zadeh Intersection ( ¿ )


Bounded product Union ( ¿ )

Gougen Intersection ( ¿ )

Godelian Intersection ( ¿ )

STEP4:-AGGREGATE OF OUTPUTS:-

Aggregation is a process by which several fuzzy sets are combined in desirable way to

produce a single fuzzy set. Aggregation is obtained by combining all the fuzzy sets that represent

the output of each rule into a single fuzzy set. Aggregation only occurs once for each output

variable. For our model the input of the aggregation process is the list of truncated output

functions returned by the implication process for each rule. The output of the aggregation

process is one fuzzy set for each output variable. Designing of an aggregation process is trival,

because the coupling between implication operators and aggregation operators are suggested in

interaction. Aggregation operator performs either a union (OR) or an intersection (AND) among

the implication results. The Mamdani implication operator is used with union aggregation or

maximum inference.

STEP5:-DEFUZZIFICATION

Defuzzification transforms the fuzzy values (sets) to crisp values. The input for the

defuzzification process is a fuzzy set and the output is a single crisp number. Given a fuzzy set

that encompasses a range of output values; one number needs to be returned thereby moving

from a fuzzy set to a crisp output. The process of defuzzification in fuzzy systems is not a


standard one. There are numerous defuzzification methods available; however the popular

methods are listed below. Unfortunately, there is no theory to justify their behaviour, other than

commonsense reasoning such that the defuzzified output must represent a weighted, voted or

most suitable solution.

Centre of gravity

Centre of sums

Height defuzzication

Centre of largest area

Min max approach

Weighted average.

From the above mentioned defuzzification methods the MIN MAX approach has been adopted.

The MIN MAX method tests the magnitudes of each rule and selects the highest one. The

horizontal coordinate of the "fuzzy centric" of the area under that function is taken as the output.

This method does not combine the effects of all applicable rules but does produce a continuous

output function and is easy to implement.

Defuzzification is especially necessary for hardware applications, because conventional

systems operate based on crisp data exchange.

3. MATHEMATICAL MODEL

EQUIVALENT CIRCUIT OF A SEPARATELY EXCITED D.C. MOTOR:-


Fig.3

The equivalent circuit of D.C. Motor showing the field and armature winding is as shown in fig.3.

The armature has a certain amount of resistance,

Ra

. When voltage is applied, a current,

I a

flows

through the armature. This armature current generates a magnetic field that interacts with the shunt

field (

φ) causing rotation.

As the flux is constant throughout the operation, the field winding is directly connected across

the supply mains; therefore we can treat the system as a separately excited D.C. Motor.

MATHEMATICAL MODEL OF D.C MOTOR:-

When the armature and field are suitably connected to the supply the motor armature rotates,

the armature conductors cut the lines of force of the field, and as a result, they have emf induced in

them. The direction of one such induced e.m.f in an individual conductor given by Fleming’s right hand

rule and according to this rule the e.m.f is outwards to the current direction that is opposed to the

current. This induced e.m.f in the case of motor is therefore called the back e.m.f.


If the induced e.m.f in the armature is opposite in direction to the current then the

machine is motoring; if it is in the same direction as the current, the machine is generating; the

magnitude of the back emf is given by the expression for the generated emf calling the back

emf, we have

Eb=φ ZNP60 A ………………………….. (1)

Where,

Eb =back emf in volts

N = speed in r.p.m.

φ =flux in webers

Z=number of armature conductors

P=number of poles

A=number of parallel paths

The voltage applied across the motor has to

1. Overcome the back emf Eb and

2. Supply the armature ohmic dropI a Ra

V = Eb +I a Ra ……………………………. (2)


Eb = V - I a Ra and I a = (V−Eb

Ra)……….. (3)

This is known as voltage equation of motor.

From the equations (2) and (3), back e.m.f depends among other factors, upon the

armature speed. If the speed is high,

Eb

is large hence the armature current

I a

, as seen from the

equation (3) is small. If the speed is less, then

Eb

is less hence more current flows which

develops motor torque. So, we find that

Eb

acts as a governor.

In order to express the back e.m.f. equation in terms of voltage constant K v , equation

(1) is modified by Multiplying both the numerator and denominator by angular acceleration ‘ω

’ we get,

Eb=

φ ZNP60 A

¿(ωω )

Substituting ω =2πN

Eb=φ ZNP60 A ¿

( 2πN2πN )

= (φZP

2πA )×( 2 π60 )

In the above equation,(φ ZP

2πA ) is a constant called as voltage constant K v in volts/rad/sec.


Eb =K v¿ N×( 2π

60 )where N is the armature speed in r.p.m

i.e,Eb=( Kv×setspeed×π

30 )As the supply voltage is normally constant, the back emf is almost equal to the applied

voltage during the no-load condition.

The back e.m.f under no-load condition is given by,

Eb 0 = V - I a Ra

Where, Eb 0 = no-load back e.m.f in volts.

V = terminal voltage in volts.

I a = armature current in amperes.

Ra = armature resistance in ohms.

The speed under no-load condition is related to back e.m.f as,

Ebo ∝N0 ………….. (4)

When load is applied on the motor, the armature current will increase due to which the

back emf will decrease thereby decreasing the speedof the motor normally to a value which is

not equal to the target speed.


The corresponding speed under load conditions is deduced below

Eb 1∝N1 ……………………. (5)

(5)/ (4) gives ( Eb 1

Ebo)=( N 1

NO)

N1=( Eb1

Ebo)NO

………………… (6)

To attain target speed we have to make the back emf sufficiently enough. The fuzzy or

crisp outputs will produce necessary values as outputs so that the back emf which is sufficiently

enough to attain target speed is obtained.

Eb 2=Eb 1+( crispoutput )

By using the back emf and speed relation to deduce relation for the target speed,

Eb 2∝N2

Where N2 is the target speed

Ebo ∝NO

( N2

N0)=(Eb 2

Ebo)

Therefore,


Motor

One step delay

U

N2=( Eb2

Eb0)NO

Hence as seen from the above equation, the target speed of the motor ‘

N2

’ is obtained by

using the fuzzy or crisp outputs.

4. DESIGN OF FUZZY LOGIC

4.1 INTRODUCTION:

Design is a process of creating something new by implementing new concepts and new

arrangements. The essential part of fuzzy system design is the application of fuzzy sets and fuzzy

logic to a solution, provided in the conventional non fuzzy form.

It is generally valid that there are three sources of solutions for all kinds of problems.

These three sources also indicate three domains of knowledge representation: Natural language,

numerical data and closed form of mathematical formula.

The design challenge is to translate the knowledge given in one of these forms into fuzzy

IF-THEN rules.

A fuzzy logic controller uses principle of fuzzy logic as a design methodology wherein a

program is written to measure the input and control the output, which can be applied in

developing linear and non-linear system for embedded control.

4.2 BLOCK DIAGRAM FOR FLC:-


Fig.4

For the system described, the output of the system is speed of the motor. Hence the

system is to be controlled in closed loop. Therefore the output speed (N) is fed as the feedback

signal for the closed loop.

FUZZY SYSTEMS:

A fuzzy inference system (or fuzzy system) basically consists of a formulation of the

mapping from a given input set to an output set using FL. This mapping process serves as basis

for which the inference or conclusion can be made. A fuzzy inference process consists of the

following five steps.

Step.1: fuzzification of input variables.

Step.2: application of fuzzy operator (AND, OR, NOT) in the IF (antecedent) part of the rule.

Step.3: implication from the antecedent to the consequent (THEN part of the rule).

Step.4: aggregation of the consequence across the rules.

Step.5: Deffuzification.

A fuzzy system is defined as a system (mechanical, electrical) with operating principles

based on fuzzy information processing and decision-making. Designing a fuzzy system refers to

developing mechanism for fuzzy information processing and decision making within a digital

platform and soft computing environment.

4.3 IMPLEMENTATION OF FLC:-



fig.5

FUZZIFICATION:-

Fuzzification is the process of transformation of crisp control variable to corresponding

fuzzy variables.

In this project, we have selected speed (N) as the controller input variable.

This input is used for fuzzification. In this step, fuzzifier takes the speed input and determines the

degree to which they belong (i.e. the region in the speed triangle) to each of the appropriate

fuzzy sets via membership functions. A set of membership functions is defined for five linguistic

variables negative big (NB), negative medium (NM), zero (Z), positive medium(PM), positive

big( PB).

CONSTRUCTION OF TRIANGULAR MEMBERSHIP FUNCTIONS FOR FIVE

LINGUISTIC VARIABLES:

The number of linguistic variables varies according to the application and usually an odd

number is used.

Following assumptions are made in construction of membership functions for five

linguistic variables to both input variable and control output.

1. symmetrical membership functions

2. 50% overlapping with adjacent functions

However increasing the number of linguistic variables resulting in corresponding

increases in the number of rules and also decrease the fuzzy characteristics. Adopting a

compromise the reasonable number is five. Each linguistic variable has its fuzzy membership

function. The membership function maps the crisp values into fuzzy variables. A set of

membership defined for five linguistic variables NB, NM, Z, PM, PB which stands for negative

big, negative medium, zero, positive medium, positive big respectively as shown in fig.

Assuming symmetrical membership function and 50% overlapping with adjacent function.


PROCEDURAL STEPS FOR CONSTRUCTION OF TRIANGLE ARE AS STATED

BELOW:-

Initially we require mean of the linguistic variables and is calculated by using formula.

Mean, x =

x1+x2+x3+. .. . .. xn

n

Where, x1 ,x2 , x3 .. .. . .. .. .xn are linguistic variables.

n is total number of linguistic variables.

x is the mean of linguistic variable.

Thus the mean obtained will be used for the further calculation of deviation which is given by,

Deviation, d1 =x1 - x

Where,

x1

is the first data of linguistic variable .similarly deviation is calculated for all the data.

The average deviation is calculated by using formula,

D =

|d1|+|d2|+. . .. .. . .+|dn|n

D =

∑|d|n


Where, D is the mean deviation

d1 , d2 . .. . .. ..dn are the deviation of the linguistic variables corresponding to x1 ,

x2 , x3 .. .. . .. .. .xn

n is total number of linguistic variables.

Finally standard deviation will be calculated as below :

σ=√ d12+d2

2+. . .. .. .+dn2

n =∑

d i2

n

where σ = standard deviation.

The standard deviation obtained from the linguistic data s is used for construction of

triangle where in base of each triangle is 2σ which gives more efficiency in fuzzy reasoning.

Thus the maximum and minimum range of speed is calculated using 2σ the formula

given below:-

Xmin = x - 2σ

Xmax = x + 2σ

μi



fig.6

Rule evaluation:

In general, fuzzy system maps input fuzzy sets to output fuzzy sets. Fuzzy rules are the

relation between input and output fuzzy sets. They are usually in the form of IF A THEN B.

where A is the rule antecedent and B is rule consequence. Each rule defines a fuzzy path in the

Cartesian product A x B (system space representation). The antecedents of each fuzzy rule

describe a fuzzy input region

For a system of one control variable with five linguistic variables, five rules are defined which

are as follows:

Rule 1: if speed is very low then v_set must be very high

Rule 2: if speed is low then v_set must be high.

Rule 3: if speed is set speed then v_set must be zero

Rule 4: if speed is high then v_set must be low.

Rule 5: if speed is very high then v_set must be very low

When the motor is running at the set speed (say at 1000 r.p.m), the incremental voltage to

be supplied from FLC is zero but if the speed of the motor decreases (i.e low), the incremental

voltage to be supplied is high (i.e. 6.75 V) which speeds up the motor to run at target speed.


Fig.7

fig.8


Implication method:-

The shaping of the consequent based on the antecedent is termed as implication. The input

for the implication process is a single number given by the antecedent, and the output is a fuzzy

set. Implication is applied for each rule.

In the implication process, two out of five rules will be activated based on the input variable.

Example;- if the speed of the motor is running at 900rpm, then N lies in the region

between SET and NM in the speed triangle hence depending on that speed two out of five rules

activated are as follows.

If speed is low then v_ set must be high.

If speed is set speed then v_ set must be zero.

AGGREGATION :( Rule grade Or Max .or Min. Inference)

The process of obtaining the overall consequent (conclusion) from the individual

consequents contributed by each rule in the rule base is known as aggregation of rules.

Aggregation operator performs either a union (OR) or an intersection (AND) among the

implication results. In aggregation process, two out of five rules which are implicated earlier are

aggregated into one fuzzy set.

An each rule activated above represents an individual output .the individual out puts

obtained are combined in to a single fuzzy set called as output fuzzy set.

DEFUZZIFICATION:

Defuzzification is a process of transforming the fuzzy values to the crisp values. The

input for the defuzzification is a fuzzy set and the output is a single crisp number.

Defuzzification is especially necessary for hardware applications, because conventional systems

operate based on crisp data exchange.


In defuzzification process, an action will be activated for aggregated fuzzy set. Both rule

strength from the membership function and the activated action are substituted in the below

formula to get the desired crisp output.

This crisp output obtained is the controlling voltage,which is propotional to the fall in

speed which upon feeding to the armature makes the motor to run at target speed.

5. RESULTS AND DISCUSSIONS

This section discusses the results obtained from the speed control of separately excited

D.C. motor using FLC.

A separately excited motor has separate field and armature windings. The speed output of

the motor is varied by controlling the excitation on the armature winding while maintaining full

D.C. voltage on the field. The ratings of the machine used are given below

Applied voltage=220V

Armature resistance Ra = 0.3 ohms

No-load current,I a =3 amps

Set speed=1000 r.p.m


output ( crisps )=∑l=1

N

(rulegrade×action sin gleton )

∑l=1

N

(rulegrade )

When the rated voltage is applied across the motor armature it has to overcome back emf

and supply the armature ohmic drop. I a Ra

V = Eb +I a Ra

This is known as voltage equation of a motor.

The armature current is given by,

I a = (V−Eb

Ra)

The speed v/s armature current of separately excited D.C. motor with and without using FLC are

as shown in fig.9

fig.9


From the characteristics curve (without using FLC) as load on motor increases, armature

current will increase and back emf decreases. As the back emf is directly proportional to speed,

speed will decrease.

From the above graph, it is observed that the speed of the drive drops with increase in load.

Hence this type of speed control is not suitable where a constant speed operation is required.

Speed control using FLC techniques have been adopted to achieve the constant speed of

operation which is shown in the characteristic curve.

For small load, the controller is less accurate to provide the incremental feed back voltage, so

that the speed is slightly greater than the target speed. Speed remains almost constant till the

magnetic saturation. Once the magnetic saturation occurs, armature reaction will increase and

speed will decrease for any value of load current.

CONCLUSION

This paper describes a simple implementation of fuzzy logic to control the speed of

dcmotor. Through the course of this project, FLC design steps and a procedure to improve the

speed characteristics are explained.

The FLC output is based on fuzzy logic, which requires some numerical parameters and

fuzzy rules to operate.

Simulation studies for different load currents with FLC based controller demonstrate its

effectiveness in maintaining almost constant speed within its operating range.

Fuzzy logic implementation techniques are conceived as a better method for sorting and

handling data which has proven to be an excellent choice in the applications of industrial drives

and control systems.


BIBLOGRAPHY

1. Electric drives and traction

-N.A.De and P.K.Sen

2. Theory and performance of electrical machines

-J.B.Gupta

3. Just plain folks

-George Bojadziev

4. Encoder

-Steven.D Kaehler.

5. Development and Implementation of fuzzy logic based constant speed

D.C.Drive

-S.Mishra,A.K.Pradhan,P.K.Hota.

6. Applied soft computing,SOCO-2005

- Center for advanced technology,Haryana engineering

College.

7. Theory of electrical machines

-H.Cotton

8. Fuzzy system design and principles

-Riza.C.Berkow,Sheldon.L.Trubatch.



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