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: [email protected], [email protected]
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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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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