An Educational Toolfor Fuzzy Logic Controllerand Classical Controllers

M. A. AKCAYOL,1 C. ELMAS,2 O. A. ERDEM,3 M. KURT4

1Department of Computer Engineering, Faculty of Engineering & Architecture, Gazi University, Ankara, Turkey

2Department of Electrical Education, Faculty of Technical Education, Gazi University, Ankara, Turkey

3Department of Electronics & Computer Education, Faculty of Technical Education, Gazi University, Ankara, Turkey

4Department of Industrial Engineering, Faculty of Engineering & Architecture, Gazi University, Ankara, Turkey

Received 29 September 2003; accepted 15 December 2003

ABSTRACT: In this study, an educational tool has been presented to teach fuzzy logic

controller (FLC) and classical controllers to undergraduate and graduate level students, so that

students could establish a thorough understanding and be able to compare FLC with classical

controllers. The tool has flexible structure and user-friendly graphical interface. Direct current

(DC) motor speed control has been presented to help students learn and compare the FLC and

classical controllers. Students practice on both controller, interpret and draw conclusions

related to system parameters by changing parameters of FLC and classical controller with

various working conditions. � 2004 Wiley Periodicals, Inc. Comput Appl Eng Educ 12: 126�135, 2004;

Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20007

Keywords: educational tool; teaching technologies; fuzzy logic control

INTRODUCTION

In engineering courses today, there is a growing

movement to integrate into the curriculum several

aspects of real world including design, teamwork, and

communication skills. Traditionally, classroom and

laboratory has been used to teach these courses. A

common difficulty in explanation and analysis of such

problems is how to describe insight of the systems.

Either the instructor provides a description that is

almost word-by-word like one given in a textbook’s

table or the students have widely varying perceptions

as to what the situation is. In either case, students are

unable to demonstrate engineering judgment.

With the development of technology and the

computer in particular, the virtual classroom or virtual

laboratory, which is the computer-related definition of

that which is created through the imagination, be-

comes a possible option that facilitates teaching and

learning.Correspondence to M. A. Akcayol (akcayol@gazi.edu.tr).

� 2004 Wiley Periodicals Inc.

126

Current technology makes available the possibi-

lity of using computers. The scene can be manipulated

to show ‘what if . . . ?’ scenarios that can be used for

classroom comparisons. The purpose of the tool is to

develop a realistic scene and demonstrate applications

that relate engineering judgment to real world

problems and to provide a space in which the learning

can take place.

The presence of computers and the Internet offer

many possibilities to students, researchers, and

lecturers. Many colleges are now offering fuzzy logic

courses due to successful applications of FLCs in

nonlinear systems. However, teaching students a

fuzzy logic controller (FLC) in a laboratory, or

training technical staff is time consuming and may

be an expensive task. In general, experience and

expertise are required for the implementation of

fuzzification in a complex system, which yields more

time required for learning and application. The best

solution for the choice of control parameters is the

trial and error method, which could be done in a

simulation environment. Then students may perform

real experiments in a laboratory to verify theory, to

interpret and discuss the results.

Fuzzy logic or fuzzy set theory was first presented

by L. A. Zadeh [1]. Since the introduction of fuzzy

logic, many researchers have studied modeling of

complex systems, and FLCs have been broadly used

to control ill-defined, nonlinear, or imprecise systems

[2,3]. In the area of the electrical machines’ drive

systems, FLCs have been applied to switched

reluctance motors [4], induction motor [5], brushless

DC motors [6], and the other types of AC motors

successfully [7]. There are also several software

packages in the areas of fuzzy logic and neural

networks. These include ARISTOTLE [8], fuzzy-

TECH [9], O’INCA [10], Togai Infra Logic [11], and

Fuzzy Logic Development Kit (FULDEK) [12].

These software packages, however, are developed

for limited capability and are not well suited for easy

learning and to provide comparison between FLC and

classical controllers.

Well-known commercial software packages such

as MATLAB/Simulink offer fuzzy logic toolboxes

[13]. Although students who use MATLAB/Simulink

could learn the modeling process, classical and fuzzy

control system designs in a sequence, only a few

advanced students could achieve it in a limited time.

These software solutions do not save time for learning

of FLC. These solutions might be costly and time

consuming for both instructors and students.

In this study, an educational tool to teach FLC has

been presented for cost-effective education and train-

ing. The tool helps students to learn and to compare

the application of FLCs and classical controllers. The

tool has a flexible structure and graphical interface.

Direct current (DC) motor speed control has been

presented as an application. FLC and classical

controller parameters can be changed easily under

different operating conditions.

FUZZY LOGIC CONTROLLER (FLC)

Fuzzy logic, based on fuzzy set theory first formulated

by Zadeh, has found recently wide popularity in

various applications [14,15]. In the technical domains,

FLC is used in two application fields: (i) design of

controllers for ill-known systems and (ii) design of

non-linear controllers for modelisable systems. In the

former case, we take the advantage that no mathema-

tical modeling is required for the FLC design. In the

latter case, we utilize the non-linear characteristics of

FLC to improve the performance of conventional

controllers, which operate in the linear way. Hence

fuzzy logic can be considered as an alternative

approach to conventional feedback control.

A conventional FLC consists generally of three

stages: fuzzification, fuzzy inference, and defuzzifica-

tion as shown in Figure 1.

The FLC used in this study accepts speed error oe

and change in speed error oce as input variables.

The output variable is the change in the reference

current Di.

Fuzzification

Multiple measured crisp inputs first have to be

mapped into fuzzy membership functions. This

process is called fuzzification. Fuzzy logic’s linguistic

terms are most often expressed in the form of logical

implications, such as If-Then rules. These rules define

a range of values known as fuzzy membership

functions. Fuzzy membership functions may be in

the form of a triangle, a trapezoid, a bell (as seen in

Fig. 2), or another appropriate form.

Figure 1 Fuzzy logic controller block diagram.

AN EDUCATIONAL TOOL FOR FLC AND CLASSICAL CONTROLLERS 127

Triangle membership functions’ limits are

defined by Val1, Val2, and Val3. Triangle membership

function is defined with the equation as:

mðuiÞ ¼

ui�Val1Val2�Val1

; Val1 � ui � Val2

Val3�uiVal3�Val2

; Val2 � ui � Val3

0; otherwise

8>><>>:

Trapezoid membership function is defined with

the equation at below. Trapezoid membership func-

tions’ limits are defined by Val1, Val2, Val3, and Val4.

mðuiÞ ¼

ui�Val1Val2�Val1

; Val1 � ui � Val2

1; Val2 < ui < Val3

Val4�uiVal4�Val3

; Val3 � ui � Val4

0; otherwise

8>>>>><>>>>>:

Bell membership functions are defined by para-

meters Xp, w, and m as follows

mðuiÞ ¼ 1= 1þ jui � Xpjw

� �2m !

where Xp is mid-point, and w is width of bell function.

m� 1, and describes the convexity of the bell

function.

Fuzzy Inference

The second phase of the FLC is its fuzzy inference

where the knowledge base and the decision-making

logic reside. The rule base and the database form the

knowledge base. The database contains descriptions

of the input and output variables. The decision-

making logic evaluates the control rules. The control

rule base can be developed to relate the output actions

of the controller to the obtained inputs.

There are several types of fuzzy reasoning in

fuzzy inference systems. The most important of them,

in the literature, are max dot method, min max

method, Tsukamoto’s method, and Takagi and

Sugeno method. These reasoning types have been

presented in the tool and students can choose a type

for application.

Max dot method. The final output membership

function for each output is the union of the fuzzy

sets assigned to that output in a conclusion after

scaling their degree of membership values to peak at

the degree of membership for the corresponding

premise [16]. Figure 3 shows max dot method of fuzzy

reasoning.

Min max method. The final output membership

function is the union of the fuzzy sets assigned to

that output in a conclusion after cutting their degree of

membership values at the degree of membership for

the corresponding premise. The crisp value of output

is, most usually, the center of gravity of resulting

fuzzy set [3]. Min max method is given in the Figure 4.

Tsukamoto’s method. The output membership func-

tion has to be monotonically non-decreasing [17].

Then, the overall output is the weighted average of

Figure 2 Triangle, trapezoid, and bell membership functions.

Figure 3 Max dot method.

128 AKCAYOL ET AL.

each rule’s crisp output induced by the rule strength

and output membership functions. Figure 5 shows

Tsukamoto’s method of fuzzy reasoning.

Takagi and Sugeno method. Each rule’s output is a

linear combination of input variables. The crisp output

is the weighted average of each rule’s output [18].

Takagi and Sugeno method is shown in Figure 6.

Defuzzification

The output of the inference mechanism is fuzzy output

variables. The FLC must convert its internal fuzzy

output variables into crisp values so that the actual

system can use these variables. This conversion is

called defuzzification. One may perform this opera-

tion in several ways. We will describe here four of

them namely, the center of gravity method, the mean

of maximum method, Tsukamoto’s method, and the

weighted average method. These defuzzification

methods have been presented in the tool and student

can choose a type for application.

The center of gravity method. This widely used

method generates a center of gravity (or center of

area) of the resulting fuzzy set of a control action. If

we discretize the universe it is:

z ¼

Pni¼1

rizi

Pni¼1

zi

where n is the number of quantisation levels, ri is the

amount of control output at the quantisation level i,

and zi represents its membership value [19].

The mean of maximum method. The mean of

maxima method generates a crisp control action by

averaging the support values which their membership

values reach the maximum. In the case of discrete

universe:

z ¼Xli¼1

rl

where l is the number of the quantized r values which

reach their maximum membership [3].

Figure 4 Min max method.

Figure 5 Tsukamoto’s method.

Figure 6 Takagi and Sugeno method.

AN EDUCATIONAL TOOL FOR FLC AND CLASSICAL CONTROLLERS 129

Tsukamoto’s method. If monotonic membership

functions are used, then the crisp control action can

be calculated as follows:

z ¼

Pni¼1

wizi

Pni¼1

wi

where n is the number of rules with firing strength, wi

is greater than zero, and zi is the amount of control

action recommended by the rule i [17].

The weighted average method. This method is used

when the fuzzy control rules are the functions of their

inputs [20] as shown in Figure 6. If wi is the firing

strength of the rule i, then the crisp value is given by:

z ¼

Pni¼1

wif ðxi; yiÞ

Pni¼1

wi

CONTROLLER DESIGNFOR THE DC MOTOR

From the energy conservation law and the assumption

of magnetic linearity, the mechanical equation of the

machine is given by

ðJmJLÞdodt

¼ �Boþ T � TL

dydt

¼ o

where o is the speed, B is the friction coefficient, jm is

the inertia of the rotor, jL is the inertia of the

mechanical load, TL is the load torque, and T is the

electromagnetic torque. Students via interface can

easily change these parameters, so that they observe

the system with different working parameters.

Fuzzy Logic Controller for the DC Motor

The FLC accepts speed error o and change in speed

error oce as input variables. The output variable is the

change in the reference current Di. The speed error oe

and change in speed error oce are defined as:

oe ¼ oref � o

oce ¼ oe � oeo

where oref is the reference speed, o is the actual

speed, oeo is the previous speed error. The block

diagram of the fuzzy logic controlled DC motor is

presented on Figure 7.

The control unit consists of a FLC and a

switching signal generator (turn-on angle yon, turn-off angle yoff, and pulse width modulation duty cycle).

The FLC output is change in the current Di. Feedback

signals are the position y, and the phase current i. In

this application, the position signal is used to calculate

the speed. The shape and count of the membership

functions of oe and oce can be changed by students.

The defuzzifier collects the fuzzy outputs from all

rules to derive the actual crisp output Di based on the

defuzzification method which is chosen by students.

Classical Controller for the DC Motor

The classical controller accepts speed error oe as input

variable. The output variable is the change in the

reference current Di. The speed error oe is defined as:

oe ¼ oref � o

The three types of classical controller have been

presented in the tool namely, PI, PD, and PID.

PI control. Theoretically, Proportional-Integral (PI)

control of the motor would provide a system that is

more responsive. Unfortunately, this is often too

responsive and thus produces overshoot and ringing in

the final output. The following equation describes the

discrete control equation implemented for PI control

of the motor.

Di ¼ Kpoek þ Ki

Xkj¼0

oej

where oek is speed error which is found by subtracting

speed from reference speed, Kp and Ki are constant for

proportional and integral, respectively.

Figure 7 Fuzzy logic controller for the DC motor.

130 AKCAYOL ET AL.

PD control. Using just Proportional-Derivative (PD)

control in the model theoretically provides for a

system that settles out faster than with just Propor-

tional or PI control. The following equation describes

the discrete control equation implemented for PD

control of the motor.

Di ¼ Kpoek þ KDðoek � oek�1Þ

where oek is speed error which is found by subtracting

speed from reference speed, Kp and KD are constant

for proportional and derivative, respectively.

PID control. Finally, PID control was implemented.

PID control provides for the tightest closed-loop

control as compared to any other combination. The

following equation is the discrete control equation

implemented.

Di ¼ Kpoek þ Ki

Xkj¼0

oej þ KDðoek � oek�1Þ

Figure 8 shows the block diagram of the DC

motor with classical controller.

THE OPERATIONAL PROCEDUREOF THE EDUCATIONAL TOOL

The tool works in Windows environment. The drive

system operation can be observed on a PC monitor

and can be modified by choosing appropriate win-

dows. A control window and another selected window

can be seen simultaneously by pressing desired button

on the top of the screen. A view of the main program

window is shown in Figure 9. The main window is

divided into two sections, namely, the control window,

which is on the left, and the menu window on the

right. The contents of the control window do not

change when the program is running. In the control

window, operation of the entire system, [i.e., position

of the rotor, reference and actual speed values, speed

error and change in the error (both can be seen

analytically and graphically)], can be observed. By

using buttons at the bottom, the user may control the

simulation process.

The menu window has four sub-windows, and the

contents of the menu window changes according to

the chosen window from the menu. When one of the

windows is chosen, the chosen window replaces the

previous menu window. These windows are shown in

Figures 10�13. Although a student may start the tool

directly by using default values of the program given

for a specific DC motor and a FLC, to start a new

simulation, parameters related to the motor, fuzzy

controller, and simulation should be entered by the

user. Once the simulation has been started, the user

may select any window to see how the system is

working.

Motor and FLC setup windows enable users to

define motor and FLC parameters. At the beginning of

the simulation, both motor and FLC setup windows

are used to define parameters used in simulation.

The Motor Setup Window

In the motor setup window (Fig. 10), motor and load

parameters are defined according to the simulation

type. For example, a motor can be simulated

according to the chosen load type, i.e., pulse, no load,

half load, or full load conditions. Moreover, a user

may define a load function and speed function

between specified time intervals during the simulation

time. Simulation parameters and data can be saved in

a user defined text file by selecting check boxes.

Moreover, the user can save simulation data with a file

extension .dat, .txt, or .mat. This procedure enables a

person to use any DOS or Windows based editor (i.e.,

EXCEL, WORD), or a specific program such as

MATLAB to view and to plot simulation results.

The FLC Setup Window

In the FLC setup window (Fig. 11), fuzzy controller

parameters are defined. Since FLC depends on user

experience, a flexible rule base can be defined. Count

of the membership function is defined in this window.

Three types of membership functions are given in the

program for the error and the change in the error.

These are triangle, trapezoid, and bell functions. Each

Figure 8 Block diagram of the DC motor with classical controller.

AN EDUCATIONAL TOOL FOR FLC AND CLASSICAL CONTROLLERS 131

membership function can be defined by the user.

Triangle membership functions’ limits are defined by

Val1, Val2, and Val3. Trapezoid membership func-

tions’ limits are defined by Val1, Val2, Val3, and Val4.

Bell membership functions are defined by parameters

Xp, w, and m.

By selecting the appropriate circle each func-

tion’s values can be set, or altered. Membership

function for error and for change in the error may be

composed of only one function, or either two

functions, or three membership functions, i.e., trian-

gle, trapezoid, or bell function. Fuzzy control rules for

the output are also defined as table in the window. The

table values are stored in a database file. Reasoning

type of fuzzy inference and defuzzification method

also defined in this window. In the program there are

three files named Default, SetupFile1, and SetupFile2.

The user may configure these files and save in another

file name or may create a new file.

The Simulation Window

Simulation window (Fig. 12) shows fuzzy control

rules for the output created in the FLC setup window

and other graphics which are speed, load, membership

function for the error, membership function for the

change in the error, and the defuzzification process

according to the selected method.

During the simulation, speed error and the change

in the error and weight can be observed. Also

reference speed and load can be changed by selecting

the appropriate circle.

The FLC Graphics Window

In the FLC graphics window (Fig. 13), distribution

graphics for the rule base, weight distribution for the

speed error, and weight distribution for the change in

the error are given. In addition, on the left of the

Figure 9 The main window. [Color figure can be

viewed in the online issue, which is available at

www.interscience.wiley.com.]

Figure 10 Motor setup window. [Color figure can be

viewed in the online issue, which is available at

www.interscience.wiley.com.]

Figure 11 FLC setup window. [Color figure can be

viewed in the online issue, which is available at

www.interscience.wiley.com.]

132 AKCAYOL ET AL.

window, used rules density in the rule base table,

weight distribution density for the speed error, and

weight distribution density for the change in the error

are given. The eraser symbol is used to clear graphics

in the window.

THE EVALUATION OF THEEDUCATIONAL TOOL

The first exposure of the tool to student usage was in a

forth year electrical engineering course of 30 students,

in which one of the modules taught focused on FLC.

One of the laboratory assignments was control with

FLC. Before studying with the tool, the students are

required to attend three 2-h theoretical sessions. One

session was about the DC motor’s construction,

operation principle, modeling of the motor, and the

drivers. One session was about fuzzy sets theory and

FLC. At last session, 2-h lecture is spared for the

description of the tool.

After lectures on fuzzy logic, the students

performed a series of tests with the educational tool

and presented the results in a report with 1-week

deadline. The students were asked to obtain FLC for

the motor drive system and reported the results. The

tool assignment would provide reinforcement of what

was expected for the actual test as well as give each

student the opportunity to spend time with the tool and

obtain a thorough understanding of the responses of

the motor under different speeds and loads. Then

students were conducted to motor-control lab where

the motor is controlled by the PIC16F877 microcon-

troller set to observe operation and control of the

motor.

The tool is expected to achieve following

educational goals. One who uses this tool should be

able to:

* Relate system parameters to system response.* Do virtual experiments on a PC to be ready for

real laboratory experiments.* Improve his/her knowledge on fuzzy control.* Develop an appropriate fuzzy rule base for the

drive system.* Save in time while developing his/her knowl-

edge.* Interpret and draw conclusions related to system

parameters.

Afterward results obtained by the use of the tool

and the results obtained without using the tool were

compared. Student’s response to the use of the tool

was obtained through evaluation sheets. The feedback

from the introduction of the educational tool was very

positive. The scores for the laboratory assignments

were higher than previous years and the understanding

of this material seemed to be more uniform across the

class as a whole. The lecturers also may develop new

ideas and teaching methods by using the tool. With

this philosophy, it is aimed that the tool is available for

Figure 13 FLC graphics window. [Color figure can

be viewed in the online issue, which is available at

www.interscience.wiley.com.]

Figure 12 Simulation window. [Color figure can be

viewed in the online issue, which is available at

www.interscience.wiley.com.]

AN EDUCATIONAL TOOL FOR FLC AND CLASSICAL CONTROLLERS 133

everyone who wants to use or try it so that students

may use it in a laboratory or at home.

CONCLUSIONS

In this study, an educational tool to teach FLC has

been presented for cost-effective education and

training. The tool helps students improve their learn-

ing and be able to compare the application of FLCs

with classical controllers. DC motor speed control has

been presented for an application. Students practice

on both controller, interpret and draw conclusions

related to system parameters by changing FLCs

parameters and classical controller parameters under

different operating conditions. The tool has flexible

structure and graphical interface and FLC and

classical controller parameters can be changed easily.

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134 AKCAYOL ET AL.

BIOGRAPHIES

M. Ali Akcayol received the BS degree in

electronics and computer education from

Gazi University, Ankara, Turkey, in 1993

and 1998, respectively, and MSc and PhD

degrees from the Institute of Science and

Technology at Gazi University, in 2001. He

is currently teaching computer engineering

at Gazi University, Faculty of Engineering.

His research interests include intelligent

control, fuzzy logic, neural networks,

genetic algorithm, web-based distance learning, and digital signal

processing.

Cetin Elmas received the BS degree in

electrical and electronics education and the

MSc degree in electrical education from

Gazi University, Ankara, Turkey, in 1986

and 1989, respectively, and the PhD degree

in electronic and electrical engineering from

the University of Birmingham, Birmingham,

UK, in 1993. From 1987 to 1989, he was a

research assistant with Gazi University,

Faculty of Technical Education. From 1994

to 1995, he was an assistant professor at Gazi University, and he was

an associate professor from 1995 to 2001. He is currently a full

professor and the head of the Department of Electrical Machinery.

His research interests include power electronics, electrical machines

and drives, intelligent control, digital signal processing, and

engineering technology education.

O. Ayhan Erdem received the BS and MSc

degrees in electronics and computer educa-

tion from Gazi University, Faculty of

Technical Education, Ankara, Turkey, in

1983 and 1988, respectively, and the PhD

degree from Institute of Science and

Technology at Gazi University, in 2000.

He is currently teaching at Gazi University,

Faculty of Technical Education. His

research interests include intelligent con-

trol, fuzzy logic, education tools, and computer systems.

Mustafa Kurt received the BS and MSc

degrees in industrial engineering from Gazi

University, Faculty of Engineering & Archi-

tecture, Ankara, Turkey, in 1979 and 1985,

respectively, and the PhD degree from

Institute of Science and Technology at Gazi

University, in 1994. He is currently teaching

at Gazi University, Faculty of Engineering.

His research interests include classroom

tools and fuzzy logic.

AN EDUCATIONAL TOOL FOR FLC AND CLASSICAL CONTROLLERS 135