Adaptive Fuzzy Type-2 in Control of 2-DOF

Helicopter

Djaber Maouche and Ilyas Eker Department of Electrical and Electronic Engineering, Çukurova University, Adana, Turkey

Email: maouchedjaber@gmail.com, ilyas@cu.edu.tr

Abstract—In the present article, type-2 fuzzy controllers

(T2FLC) are designed to control position of yaw and pitch

angles of the Twin Rotor Multi-input Multi-output System

(TRMS) characterized with nonlinear dynamics and

uncertainties. Type-2 fuzzy control method is preferred to

capture uncertainties and input and output external

disturbances. In the presented approach, two independent

type-2 fuzzy controllers are designed. Performance of each

control scheme is examined under a number of simulations,

furthermore some performance indexes to highlight the

advantages of the controllers. The results of tracking and

disturbance/load rejection tests are compared with the

results obtained from conventional fuzzy controller and PID

controller. It is the fact that presented diagrams and

tabulated results showed that present control approach

provided significant advantages over the compared

controllers.

Index Terms—PID, type-1 fuzzy, type-2 fuzzy, dynamic

modeling, TRMS, nonlinear

I. INTRODUCTION

Twin Rotor Multi-Input Multi-Output Systems (TRMS)

are widely used control platforms (developed by

Feedback Ltd) [1] due to their high non-linearity and the

coupling between axial motions. The system, which is

driven vertically and horizontally through its two joined

rotors placed at the end of the TRMS beam, is

characterized with two degrees of freedom (DOF) [2], [3].

These challenges make it a preferred control system set-

up for investigating, testing, and validating of the control

theories those have challenges to keep the system

stabilized [4], by reaming its two angles yaw and pitch on

to the desired positions area under any internal or external

disturbances [5].

The nonlinear, unstable and underactuated structure

makes the control of TRMS a challenging problem.

Control of such systems is an active subject in automatic

control and robotic for both practical and theoretical

interest. Various control design methodologies to solve

tracking problem of TRMS have been investigated.

Until recently, the control and system engineering

framework offers several tools based on nonlinear control

techniques, soft computing based adaptive and intelligent

control techniques [6], and conventional linear control

techniques [7].

Manuscript received February 27, 2016; revised September 15, 2016.

Fuzzy control is a versatile control technique that

allows controlling through the descriptions of system

behavior in terms of linguistic variables constituting the

rule base [8]. The reason motivating us to experiment

fuzzy control technique is mainly because of the

appropriateness of the behaviour of the helicopter system.

Furthermore, fuzzy controller can be used as an adaptive

methodology as well it is combined with traditional

control strategies to improve the stability, increase the

robustness, and reduce the fuzzy rule base. As a general

example, the combinations between Fuzzy and PID

controllers (Fuzzy-PID) are widely used to control

nonlinear systems by improving the control performance

efficiency. While considering a feedback system with a

fuzzy controller, there may be some uncertainties both in

the controlled system and in the membership rules part of

the fuzzy logic. However, the conventional fuzzy logic

system or so-called fuzzy type-1 logic system cannot deal

with such uncertainties [9], [10]. Recently, many

researches have been focused to increase the performance

of fuzzy logic controllers and to overcome the uncertainty

problems. In order to achieve robustness, an interval

fuzzy type-2 strategy was introduced, as a new generation

of fuzzy logic. The main structural difference between

these two types of fuzzy logic controller is in the

defuzzifier composited block, where a type reduction

block is used during the defuzzification in type-2 fuzzy

logic [9]. This work is organized as following. TRMS

components, system description and a detailed modelling

is addressed in the next section. Then, a synthesis and

applications of various control strategies, namely,

classical PID controller, type-1 fuzzy-PID controller and

type-2 fuzzy PID controller are demonstrated. Finally,

concluding observations and remarks are given in the last

section.

II. SYSTEM DESCRIPTION AND MODELLING

The system, which consists of several rigid parts such

as propellers, engines, and control surfaces, is depicted in

[11]. The test set-up is composed from a beam pivoted on

its base where it gives the TRMS the ability to rotate

freely in both vertical and horizontal directions. The

aerodynamic forces are controlled by changing the speed

of rotors which also controlled by variable electric motors

that enable changes in the pitch and yaw angle [11].

TRMS is modelled by dividing the whole system into

International Journal of Electronics and Electrical Engineering Vol. 5, No. 2, April 2017

©2017 Int. J. Electron. Electr. Eng. 99doi: 10.18178/ijeee.5.2.99-105

three sub-models for both the horizontal and vertical

plane, DC motors, aerodynamics, and mechanical sub-

model. All six sub-models are modelled separately.

A. DC Motors Dynamics

The main rotor is employed to drive the TRMS on

vertical plane and tail rotor is employed for the horizontal

plane [6]. The model of the motor-propeller dynamics can

be described as a first order model [1]:

1

vv

vv v

mr

duu u

dt T (1)

1

hh

hh h

tr

duu u

dt T (2)

where vvu , hhu are the input voltages, mrT ,

trT are the

time constants, and mrK ,

trK are the static gain of the

main, tail motor respectively. The rotational speed is

expressed as [12]:

6

11( ) ( )i

m vv vviu t P i u t

(3)

6

11( ) ( )i

t hh hhiu t P i u t

(4)

The angular velocitiesm ,

t of the rotational

dynamics can be described by an approximated

polynomial as the following [1]:

6 5 4

3 2

90.99 599.73 129.26

1238.64 63.45 1283.4

m vv vv vv vv

vv vv vv

u u u u

u u u

5 4 3

2

2020 194.69 4283.15

262.27 3796.83

h hh hh hh hh

hh hh

u u u u

u u

The nonlinear propulsive forces on the vertical plane

and horizontal planes are:

5

1( ) ( )i

v m miF t P i t

(5)

5

1( ) ( )i

h t tiF t P i t

(6)

The propulsive forcevF ,

hF those drive the joined

beam to move in the vertical and horizontal direction

described by nonlinear functions of the angular velocities

[1]:

14 5 11 4 7 3

4 2

3.10.10 1.595.10 2.511.10

1.808.10 0.8080

h h h h h

h h

F

12 5 9 4 6 3

4 2 2

3.48.10 1.09.10 4.123.10

1.632.10 9.544.10

v v v v v

v v

F

B. TRMS Newtonian-Based Model

In this study, the method adopted for dynamic

modelling of TRMS is Newton-Euler method, which is

easy to understand and accepted physically despite of the

compact formulation and generalization shown by Euler-

Lagrange method. Dynamic modelling strategy is

described in the following subsequent sections.

1) Vertical plane

The total torque vM in the vertical plane is described

as: 5

1

( ) ( )v vi

i

M t M t

(7)

( ) ( ) ( ) ( ) ( ) ( )v g fp pv c frictM t M t M t M t M t M t (8)

where gM is moment of the gravity forces,

pfM is

moment of propulsive forces applied to the beam, pvM is

the moment generated by the force from the tail rotor,

frictM is the moment of Friction depending on angular

velocity of beam around horizontal axis, and c

M is the

moment of the centrifugal forces corresponding to motion

of beam around vertical axis [1].

2

( ) cos ( ) sin ( ) ( ) ( )

( ) sin ( )cos ( ) ( )

v v v m v v t t

h m t c v v v v

M t A B t C t l F t t k

t Al Bl Cl t t t k

(9)

where

2

t

tr ts t

mA m m l

2

m

mr ms m

mB m m l

2

b

b cb cb

mC l m l

The moments of inertia vJ can be described as [13]:

2 2

2 2 2

2

2 2 2 2

 3 3

3 2 2

m t

v mr m m tr t t cb cb

b ms ts

b ms ms m ts ts t

l lJ m l m l m l m m l

l m mm r m l r m l

(10)

Then the system equations in vertical plane are: 5

2

1

2

( )( ) ( ) vi

v v i

v

M td t dS t

dt dt J

(11)

( ) ( )( ) v tr t

v

v

S t J tt

J

(12)

where vS the angular momentum,

v the angular

velocity and v the angular rotation in vertical plane of

the beam.

2) Horizontal plane

The total torque hM in the horizontal plane can be

described as: 4

1

( ) ( )h hi

i

M t M t

(13)

/( ) ( ) ( ) ( ) ( )h fp frict spri p hM t M t M t M t M t (14)

where fpM is the moment of propulsive forces applied

to beam, frictM is the moment of Friction

spriM spring

and /p hM propeller depending on the angular velocity of

beam around the vertical axis [8], [12].

/( ) ( ) ( ) cos ( ) ( ) ( ) ( )h h t t v h h h spri t p hM t F t t l t t k t k t k

(15)

International Journal of Electronics and Electrical Engineering Vol. 5, No. 2, April 2017

©2017 Int. J. Electron. Electr. Eng. 100

The moments of inertia h

J in the vertical plane can be

described as [13]:

2 2( ) cos ( ) sin ( )

h v vJ t D t E t F (16)

where

2 2

3

b

b cb cb

mD l m l ,

2 2

2

ts

ms ms ts

mF m r r (17)

2 2

3 3

m t

mr ms m tr ts t

m mE m m l m m l

(18)

Then the system’s equations in horizontal plane are: 2

2

( ) ( ) ( )

( )

h h h

h

d t dS t M t

dt dt J t

(19)

( ) cos ( ) ( )( )

( )

h mr v m

h

h

S t J l t tt

J t

(20)

where hS the angular momentum,

h the angular

velocity and h

the angular rotation in the horizontal

plane of the beam.

III. CONTROLLER DESIGN

A. PID Controller Design

In the first proposed controller of the TRMS, two

simple PID controllers are designed to control each of the

vertical plane and the horizontal plane independently.

The TRMS Simulink model consists two inputs are the

control voltages and two output are the angular positions.

The error is calculated by subtracting the feedback output

of the angular position from the reference input which is

represented the desired position. The error is entered later

to the control block as it is shows in the following picture.

In order to tune PID controller parameters, Ziegler–

Nichols open loop tuning approach is used and the

controller parameters are given in Table I.

TABLE I. PID CONTROLLER PARAMETERS

Tuning by Ziegler–Nichols Method

p

K i

K d

K τdead τ

Main rotor Controller 9.7 1.21 6.76 7.3 1.54

Tail rotor Controller 8.2 1.01 7.23 3.6 1.15

B. Fuzzy Type-1 Logic System Controller Design

The central notion of the fuzzy control is to incorporate

the experiences of an expert into the design or the come

up with a design that is based mostly on the physics of

the process, all in the domain of linguistic labels. The

design of adaptive type-1 fuzzy-PID controller is

consisted of two sub-controllers. First controller is

designed for the yaw motion, and second controller is

designed for the pitch motion by speed adjustment of the

main and tail rotor, respectively.

In the rule base; VNB, NB, NM, NS, VNS, ZE, VPS,

PS, PM, PB denotes very negative big, negative big,

negative medium, negative small, zero, very positive

small, positive small, positive medium, positive big and

very positive big, respectively. The fuzzy rules are

presented in Table II. Triangular membership functions

are employed because it is defined by three parameters,

two of them indicate left and right endpoints of the

triangular, and the other indicates the central point which

allow us easily to resize its shape, the ranges of the inputs

membership functions are as following: VNB [-1, -0.7],

NB [-1, -0.4], NS [-0.7, -0.2], VNS [-0.4, 0], ZE [-0.2,

0.2], VPS [0, 0.4], PS [0.2, 0.7], PB [0, 0.3], VPB [0.4, 1].

And for the second input NB [-100, -100], NM [-1, 0], ZE

[-0.1, 0.1], PM [0, 0.3] and PB [-0.2, 0.2]. The defuzzifier

parameters are chosen between -1, -0.7, 0, 0.7, 1, which is

determined according the observations from the already

studied control schemes. The centroid Takagi-Sugeno

(TS) defuzzification technique is employed during the

defuzzification process due to being able to describe a

highly nonlinear system.

TABLE II. FUZZY TYPE-1 RULES-BASE

Δe e

NB NM ZE PM PB

VNB N N NM NM NS

NB N NM NM NS NS

NS NM NM NS NS NS

VNS NS NS Z Z Z

ZE NS Z Z Z PS

VPS Z Z Z PS PS

PS PS PS PS PM PM

PB PS PS PM PM P

VPB PS PM PM P P

C. Interval Fuzzy Type-2 Logic System Controller

A typical type-2 fuzzy membership functions is consist

of two type-1 fuzzy membership functions as shown in

Fig. 1 [14].

Figure 1. (a) Membership function of type-1 fuzzy controller and (b) membership function of type-2 fuzzy controller

The uncertainty in the primary membership of a type-2

fuzzy set X can be defined as a bounded region so-called

Footprint of Uncertainty (FOU) [15], [16] between these

two type-1 fuzzy membership functions, one is a “upper

membership function” (UMF) and the other is “lower

membership functions” (LMF), mathematically FOU can

be described as the union region between LMF and UMF,

footprint can be described as:

x

x

x D

FOU X J

(21)

where, X is an interval type-2 fuzzy when all ,X

x u

=1 [17]. As described in type-1 fuzzy logic system, a

International Journal of Electronics and Electrical Engineering Vol. 5, No. 2, April 2017

©2017 Int. J. Electron. Electr. Eng. 101

type-2 fuzzy contains also a fuzzifier block, rule-base,

inference engine and substitute defuzzifier at the output

processor. This last includes furthermore a type-reducer

[18], and it generates a regular type-1 output [19].

1) The vector of crisps inputs 𝑥T

=(𝑥1,.,𝑥p)T is fuzzified

firstly under the fuzzifier block as the same way with the

type-1 fuzzy where it is mapped into a type-2 fuzzy sets

X .

2) As indicated for the type-1 fuzzy, a Type-2 Fuzzy

System has also IF-THEN rule structure however the

consequent in fuzzy type-2 is described as follows [20]:

1 1: if is and...and is , isn n n n

p pR x X x X then y Y

n=0,1,…, L L N

where n

pX (𝑖=1,...,P) are interval type-2 fuzzy system and

𝑌𝑛 is the interval output. For an input vector 𝑥=(𝑥1, 𝑥2, …,

𝑥p) of the pth

inputs, n is the number of rules.

3) In the type-2 fuzzy system, the inference engine gives

a mapping from the fuzzified input type-2 fuzzy sets to

the defuzzification block after combining it with the rules

by using the minimum or product t-norms operations, the

ith

activated rule Fl(X’) gives us the interval that is

determined by tow extreme l

f and l

f [19]:

' ' ', ,

l l l l lF X f X f X f f (22)

where

1

' ' ' ' '

1*...*

l l

p

l

pF Ff X x x (23)

and

1

' ' ' ' '

1*...*

l l

p

l

pF Ff X x x (24)

4) The function for center of sets, called Ycos is expressed

as [18]:

cos

,l r

Y X y y (25)

1 1 1 1, , ... ,

M M

l r l r l ry y y y y y y y

1 1 1

1

1

1, ... , .

M M M

l r l r M

i i

i

M

i

i

f f f f f f

f y

f

(26)

And consequent set can be described as:

11

1

1

1... ,

iN

i i

y N J l rNG

i i

i

N

i

i

C J J y y

y

(27)

Eq. (26) should be evaluated before the calculation of

Ycos (x).

1

1

M

i i

l l

i i

l M

i

l

i

f y

y

f

(28)

and

1

1

M

i i

r r

i i

r M

i

r

i

f y

y

f

(29)

A Karnik and Mendel type reducer is used for the type

reduction algorithm. It should be noted that, although

other type reducer algorithms are tested, Karnik and

Mendel algorithm shows satisfactorily performance [21].

5) An interval set, which is called Ycos, can be obtained

from the type-reducer. In order to defuzzify this set an

average of yl and yr is used, by the way defuzzifier output

is given as:

( )

l ry y

y Xr

(30)

6) Design of type-2 fuzzy logic system controller

The design of fuzzy type-2 controller is similar in

structure to the type-1 which we designed by two sub-

controllers. The first controller is corresponding to the

pitch motion, and the other controller is corresponding to

the yaw motion. Both of the two sub-controllers are

designed by fuzzy-PID strategies. A developed software

is called Type-2 Fuzzy Logic Toolbox is used a collection

of MATLAB based M-files algorithms [15]. In the type-2

fuzzy rule two inputs were chosen by representing the

error and the error variation under the linguistic

representations as rule base; N, NM, ZE, PM, P denotes

negative, negative medium, zero, positive medium and

positive, respectively as shown in Table III. For both of

the error the FOU is chosen between 1 and 0.5 for all the

membership functions, also for the error derivation which

is the second input the FOU is chosen between 1 and 0.72

for all the membership functions but for the zero ZLMF

and ZUMF that it is chosen between 1 and 0.5. Triangular

membership functions are chosen as introduced

previously, then fuzzy inference engine infers the input

variables to a suitable fuzzy set, as it can be seen in Fig. 2

the first input and Fig. 3 shows the second input. And, an

output signal is obtained by defuzzification. Takagi-

Sugeno (TS), is chosen as method of fuzzy inference with

an output range of -1/+1 for the negative and positive

respectively and -0.8/0.8 for the negative medium and

positive medium respectively as shown in Fig. 4.

TABLE III. FUZZY TYPE-2 RULES-BASE

Δe

e

VN N Z P VP

VN N N N N NM

N N NM Z NM Z

Z NM Z Z Z PM

P PM PM Z PM P

VP PM P P P P

International Journal of Electronics and Electrical Engineering Vol. 5, No. 2, April 2017

©2017 Int. J. Electron. Electr. Eng. 102

Fuzzifier

Rules

Inference

Type-reducer

Defuzzifier

Figure 2. Error membership functions type-2 fuzzy controller

Figure 3. Error derivation membership functions type-2 fuzzy controller

Figure 4. Output membership functions type-2 fuzzy controller

7) Stability analysis

Generally in the real and hardware application the

reliability of a controller is taken in consideration much

more than the stability issued [9], furthermore the last is

proved in the set-point oriented control such in the

conventional controller where the fuzzy is classified as a

task oriented controller. However, guaranteeing a robust

interval fuzzy type-2 and proofing its stability is yet a big

challenge objective for researchers because of its

complicated structure, therefore the information taken

from the (FOU) is used to develop some membership

functions conditions which through them we can handle

the stability analysis where the FOU here gives us the

chance to generate different stages of nonlinear control

curves to use while also providing a certain robustness

which cannot found in type-1 [22]. Different approaches

were used to realize the stability in fuzzy type-2, the well-

known Lyapunov based approach [22] and the other is the

bounded input bounded output (BIBO) based approach

[23] Consider the system shown in Fig. 5. Let the

subsystems H1 and H2 represent the type-2 controller and

the plant under control. 1 ,

1 the gain of H1, H2. And

1 , 2 are constants,

1 ≥ 0, 1 ≥ 0 so that

1 1 1 1 1 1y H e e (31)

2 2 2 2 2 2y H e e (32)

Regarding to (31) and (32) as stability conditions and

according to the small gain theorem, that any bounded

input pair (u1, u2) generates a bounded output pair (y1, y2),

the system is BIBO stable if y1y2 < 1 [23].

Figure 5. Feedback control [23]

IV. SIMULATION RESULTS AND DISCUSSION ON

CONTROL PERFORMANCE

A. Tracking Performance

In this last section, a TRMS model has been realized

on Matlab/Simulink environment, by using the above

mathematical equations mentioned in the modelling part,

the numerical parameters of the model were obtained

from the company provider [6]. The performance of the

controllers have been examined using different

performance indexes such as the integral of squared error

(ISE), the integral of absolute error (IAE), the integral of

time multiply squared error (ITSE) and the integral the

multiply absolute error (ITAE). The overshoot response

and the integral square of control input (ISCI) are used as

well. The results are presented in Table IV for the vertical

plane (pitch motion) and Table V for the horizontal plane

(yaw motion).

TABLE IV. PERFORMANCE INDEXES OF THE PITCH MOTION

IATE IAE ISE ITSE ISCI Overshoot

PID 58.36 2.46 0.71 8.17 55.13 7%

T1FLC 41.34 2.42 1.01 7.66 52.32 3%

T2FLC 24.25 1.92 1.02 6.30 54.49 02%

TABLE V. PERFORMANCE INDEXES OF THE YAW MOTION

IATE IAE ISE ITSE ISCI Overshoot

PID 3.22 0.11 0.003 0.006 1.51 0.9%

T1FLC 2.70 0.13 0.003 0.008 0.79 3.1%

T2FLC 1.29 0.09 0.001 0.002 0.84 1.2%

5 10 15 20 25 30 35 40

-0.8

-0.6

-0.4

-0.2

0

0.2

Time (sec)

Ve

rtic

al p

ostio

n (

rad

)

PID

Ref

T2FLC-PID

T1FLC-PID

Figure 6. Response of the vertical position

International Journal of Electronics and Electrical Engineering Vol. 5, No. 2, April 2017

©2017 Int. J. Electron. Electr. Eng. 103

10 20 30 40 50 60

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Time (sec)

Ho

rizo

nta

l p

ostio

n (

rad

)

Ref

PID

T2FLC-PID

T1FLC-PID

Figure 7. Response of the horizontal position

Two different set-points are used to test the system’s

response, for the vertical plane a square wave was applied

firstly with a frequency of 0.01 (Hz) and -0.2/+0.2 (rad)

as magnitude as shown in Fig. 6. And a sinusoidal signal

with a 0.01Hz frequency and -0.2/+0.2 (rad) magnitude is

applied. As illustrated in Fig. 7, type-2 fuzzy controller

needs less time than the type-1 fuzzy and the PID to

making the system settling with less than 2% of

overshoot. Also type-2 as similar as to type-1 has smaller

oscillations and steady-state error comparing to the PID.

Fig. 8 and Fig. 9 show the variation in the control

inputs for the vertical and horizontal plane respectively,

of the three used controllers.

10 20 30 40 50 60 700

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Time (sec)

Ve

rtic

al co

ntr

ol in

pu

t

PID

T1FLC-PID

T2FLC-PID

Figure 8. Vertical control input

10 20 30 40 50 60 70-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Time (sec)

Ho

rizo

nta

l co

ntr

ol in

pu

t

PID

T1FLC-PID

T2FLC-PID

Figure 9. Horizontal control input

The control input of the PID controller contains high

oscillations which causes a significant steady state error.

With type-2 fuzzy the control is more stable includes

some impulsions as same as with the type-1 fuzzy.

B. Disturbance Rejection Performance

A sudden load disturbance as shown in Fig. 10 is

applied to test the performance responses of the

controllers at the 32nd

second [5].

Figure 10. Disturbance load added to the output of the system

5 10 15 20 25 30 35 40 45 50

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Time (sec)

Ve

rtic

al p

ostio

n (

rad

)

PID

ref

T2FLC-PID

T1FLC-PID

Figure 11. Response of the vertical position to load disturbance (at 32nd sec)

10 20 30 40 50 60

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Time (sec)

Ho

rizo

nta

l p

ositio

n (

rad

)

Ref

PID

T2FLC-PID

T1FLC-PID

Figure 12. Response of the horizontal position to load disturbance (32nd

sec)

The disturbance load is illustrated in Fig. 11 and Fig.

12. As can be seen from performance comparisons, the

model-free PID control system yields favorable control

performance superior to that of Fuzzy-PID control.

Furthermore, the controllers are compared via several

illustrations and numerical measures. In this sense, fuzzy-

PID controller, which is highly sensitive to perturbations

and uncertainties, has a drawback and it may cause a

International Journal of Electronics and Electrical Engineering Vol. 5, No. 2, April 2017

©2017 Int. J. Electron. Electr. Eng. 104

performance degradation. In the meanwhile, applied on

the same class of systems as described previously, the

fuzzy-PID control has higher tracking errors, especially

when disturbances arise.

V. CONCLUSION

Although the difficulties in both understanding and

design of the type-2 logic systems comparing to other

controllers, the first stays still as a preferred research area

in the recent years, due to its robustness through the

uncertainties and disturbances. In this sense, PID

controller, which is highly sensitive to perturbations and

uncertainties, has a drawback and it may cause a

performance degradation. In the meanwhile, applied on

the same class of systems as described previously, the

PID and fuzzy control have higher tracking errors,

especially when disturbances arise. In this study, the

proposed designed controllers successfully designed

several controllers for trajectory tracking control of

TRMS model on MATLAB/Simulink, among these

designed controllers, an interval type-2 fuzzy logic

system is presented. According to the results, type-2

fuzzy logic controller produce better results than the PID

and fuzzy type-1 controller in terms of tracking precision

in the presence of the disturbances.

ACKNOWLEDGMENT

Authors would like to thank Mr. Necdet Sinan Ozbek

and Mr. Adel Hamid Kharbachi for their valuable

discussion. And thank Çukurova University scientific

research department for their support.

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2014.

Djaber Maouche received the B.Sc. degree in Electronics Engineering

from M’sila University, M’sila, Algeria, in 2010. He is currently

pursuing the M.Sc. degree in electrical and electronics engineering at Çukurova University. His research interests include system theories and

automatic control.

İlyas Eker received the B.Sc. in electrical and electronic engineering (EEE) from (METU)/Turkey in 1988. He joined Industrial Control

Centre, University of Strathclyde, Glasgow, UK in 1992, where he received his Ph.D. degree in 1995. Currently, he is a full professor at

EEE, Çukurova University/Turkey. His current research interests are

selftuning control adaptive control, fuzzy control, sliding mode control, fault detection, linear and nonlinear control, and their applications.

International Journal of Electronics and Electrical Engineering Vol. 5, No. 2, April 2017

©2017 Int. J. Electron. Electr. Eng. 105

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Type-2 Fuzzy Logic in Intelligent Control Applications,

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