DEVELOPMENT AND IMPLEMENTATION OF A ADAPTIVE FUZZY CONTROL SYSTEM FOR A VTOL VEHICLE IN HOVERING MODE

International Journal of Control Theory and Computer Modeling (IJCTCM) Vol.7, No.1/2, April 2017
DOI : 10.5121/ijctcm.2017.7201 1
DEVELOPMENT AND IMPLEMENTATION OF A
ADAPTIVE FUZZY CONTROL SYSTEM FOR A VTOL
VEHICLE IN HOVERING MODE
Ehsan. Abbasi
Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
ABSTRACT
The studies in aerial vehicles modeling and control have been increased rapidly recently. This paper
presents the modeling and control of a four rotor vertical take-off and landing (VTOL) vehicle. The
modeling of the VTOL vehicle will be described by using Euler-Newton equations. In order to stable this
vehicle and control the attitude of that, classical PID controller and a fuzzy system that adjusts the PID
controller gains, have been designed. Although fuzzy control of various dynamical systems has been
presented in literature, application of this technology to aerial vehicle control is quite new. This system has
nonlinear characteristics where classical control methods are not adequate for stabilize that. On the other
hand, fuzzy control is nonlinear and it is thus suitable for nonlinear system control. Matlab Simulink has
been used to test, analyze and compare the performance of the controllers in simulations. Finally this
presented controller will be implemented on a real vehicle and performance of that will be showed. This
study showed that although, both of the classical PID and the fuzzy self-tuning PID controllers, can control
the system properly, the second controller performed better than the classical PID controller.
KEYWORDS
VTOL, Fuzzy control, Modeling, Attitude control, PID controller.
1. INTRODUCTION
unmanned aerial vehicles has attracted a great amount of attention among scientists over the last
decades, due to, the widespread area of applications, e.g. near-area surveillance, crop dusting
firefighting, exploration both in military and commercial in- and outdoor applications, and so on.
Helicopter design has been the center of attention since the beginning of the 20th century. First
full-scale four rotor helicopter (quadrotor) was built by Debothezat in 1921 [1]. Other examples
are Breguet Richet helicopter, Oemnichen helicopter, Convertawings Model A and Curtis Wright
VZ-7 [2,3]. At those early times due to the lacking control and sensing technologies, it was not
possible to build an unmanned vehicle. Advances in sensors, control technology and electronics
enable the possibility of that. Currently, there are various commercial and experimental
autonomous unmanned VTOL vehicles are being developed at universities, research centers, and
by hobbists [4-7].
The studies in quadrotor modeling and control have been increased rapidly recently. A number of
examples of these studies can be summarized as following; Altuğ et al. modeled a quadrotor
using Euler-Newton method and worked on vision based stabilization and output tracking control
[8]. Suter et al. also studied on image based visual servo control for quadrotors [9]. Dunfied et al.
created a neural networks controller for a quadrotor [10]. Earl et al. used a Kalman filter to
estimate the attitude of a quadrotor [11]. Lee et al. presented feedback linearization vs. adaptive
sliding mode control for a quadrotor helicopter [12]. Bora et al. used a hybrid fuzzy logic

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controller for a quadrotor [13]. Astha et al. presented a fuzzy logic controller for a quadrotor and
compared it to conventional PID controller [14].
The fuzzy logic control is an active field in last couple of decades, and it has been implemented
on various dynamical systems [15-20]. The fuzzy logic has also been implemented in helicopter
control [21-23]. In more recent papers [24,25], the researcher used a fuzzy controller for the
altitude and hovering control of an unmanned helicopter. Although fuzzy control of dynamical
systems has seen presented extensively in literature, application of this to quadrotor helicopter
control is quite new.
Although the quadrotor has the advantages in easy mechanical construction against the traditional
helicopter, but there are still issues that prevent it from being widely used in many of the
suggested fields and applications. For example, the stabilizing control and guidance of the
quadrotor is a difficult task because of the nonlinear dynamic behavior. Conventional control
methods use linear theory that is suitable for linear systems only. Fuzzy control is nonlinear and it
is thus suitable for nonlinear system control.
This paper will be presented a fuzzy system for control the quadrotor. Additionally, detailed
model of the quadrotor is given. The performances of the fuzzy controllers are compared to
classical PID controllers using Matlab simulations. And in real world this controller will be tested
on the real quadrotor and performance of that will be showed.
The paper is structured as followings: In section 2 the mathematical model of the quadrotor is
described. The controllers are presented in section 3. The simulations supporting the objectives of
the paper are presented in section 4. Results of the implementation of the presented controller will
be showed in section 5. And finally concluding remarks are presented in section 6.
2. MATHEMATICAL MODEL OF THE QUADROTOR
Generally, the quadrotor can be modeled with a four rotors in cross configuration. The throttle
movement is provided by increasing (or decreasing) all the rotor speeds by the same amount. It
leads a vertical force u1 (N) with respect to body-fixed frame which raises or lowers the
quadrotor.
The roll movement is provided by increasing (or decreasing) the left rotor's speed and at the same
time decreasing (or increasing) the right rotor's speed. The pitch movement is provided by a same
way but with other two motors. The front and rear motors rotate counter-clockwise while other
two motors rotate clockwise, so yaw command is derived by increasing (or decreasing) counter-
clockwise motors speed and at the same time decreasing (or increasing) clockwise motor speeds.
Figure 1. Configuration, inertial and body fixed frame [26].

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In order to model the quadrotor dynamics, two frames have to be defined as showed in figure. 1.
The orientation of the quadrotor is given by the three Euler angles, which are roll angle , pitch
angle and yaw angle .
These three Euler angles form the vector . The position of the vehicle in the
inertial frame is given by the vector . The transformation of vectors from the body
fixed frame to the inertial frame is given by the rotation matrix R where for example denotes
and denotes .
The thrust force generated by rotor is , where is the thrust factor and
is the rotational speed of rotor . Then the thrust force applied to the airframe from
the four rotors is given by
(2)
Now the first set of differential equation that describes the acceleration of the quadrotor can be
written as:
(3)
With inertia matrix (which is diagonal matrix with the inertias and on the main
diagonal), the rotor inertia , the vector that describes the torque applied to the vehicle's body
and the vector of the gyroscopic torques we obtain a second set of differential equations:
(4)
The vector is defined as:
(5)
The four rotational velocities of the rotors are the input variables of the real vehicle, but with
regard to the obtained model a transformation of the input is suitable. Therefore, the artificial
input variables can be defined as follows:
(6)
(7)
(8)

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(9)
Where (6) denotes the thrust force applied to the quadrotor airframe; denotes the force
which leads to the roll torque; for the pitch torque and for the yaw torque.
However, also the gyroscopic torques depend on the rotational velocities of the rotors and hence
on the vector of the transformed input variables. We assume that:
(10)
And then evaluation of (4) and (5) yields the overall dynamic model in the following form:
(11)
(12)
(13)
(14)
(15)
(16)
Equations (11) to (16) represent the full mathematical model of the quadrotor.
3. ATTITUDE CONTROL ALGORITHM DESIGN
In this section two controllers for the stabilization of the quadrotor will be presented; the
proportional Integral Derivative (PID) controller, and a fuzzy system that tunes the PID gains.
As mentioned before the inputs chose like equations (6) to (9). Where controls the motion
along the z-axis, controls rotation along the x-axis (roll angle), controls the rotation along
the y-axis (pitch angle) and controls rotation along the z-axis (yaw angle). The designed
controllers should set values to parameters which determines the four rotor speed parameters
by (6) to (9).
3.1. CLASSICAL PID CONTROLLER
Due to their simple structure and robust performance, proportional-integral-derivative (PID)
controllers are the most commonly used controllers in industrial process control. The equation of
a PID controller has the following form:
(17)
Where , and are called the propositional, integral and derivative gains, respectively.
For adjusting the controller parameters the Ziegler-Nichols method will be used and response of
the system with this adjusting will be showed in the result section.

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3.2. FUZZY SYSTEM FOR TUNING THE PID GAINS
The success of the PID controller depends on an appropriate choice of the PID gains. Tuning the
PID gains to optimize performance is not a trivial task. In practice, the PID gains are usually
tuned by experienced human experts based on some "rule of thumb". In the next we will first
determine a set of tuning rules (fuzzy IF-THEN rules) for the PID gains, and then combine these
rules into a fuzzy system that is used to adjust the PID gains on-line [15].
A fuzzy PID controller takes the classical PID controller as the foundation which uses the fuzzy
reasoning and variable universe of discourse to regulate the PID gains. The characteristics of a
fuzzy system such as robustness and adaptability can be successfully incorporated into the
controlling method for better tuning of PID gains.
The term self-tuning refers to the characteristics of the controller to tune its controlling
parameters on-line automatically so as to have the most suitable values of those gains which
result in optimization of the process output. Fuzzy self-tuning PID controller works on the control
rules design on the basis of theoretical and experience analysis. Therefore, it can tune the gains
, and by adjusting the other controlling parameters and factors on-line. This, in result
makes the precision of overall control higher and hence gives a better performance than the
classical PID controller or a simple fuzzy PID controller without self-tuning ability.
The self-tuning fuzzy PID controller, which takes error "e" and rate of change-in-error "ed" as the
input to the controller makes use of the fuzzy controller rules to modify PID gains on-line. The
self-tuning the PID controller refers to finding the fuzzy relationship between the three gains of
PID, , and and "e" and "ed", and according to the principle of fuzzy control modifying
the three gains in order to meet different requirements for control gains when "e" and "ed" are
different and making the control object produce a good dynamic and static performance. For
selecting the language variables of "e" and "ed", is choose seven fuzzy values (NB, NM, NS, ZO,
PS, PM, PB) which NB denotes Negative Big, NM denotes Negative Medium, Negative Small
(NS) , Zero (ZO) , Positive Small (PS), Positive Medium (PM) and PB denotes Positive Big, and
for the outputs we are choose seven fuzzy values (VVS, VS, S, M, B, VB, VVB) which VVS
denotes Very Very Small, Very Small (VS), Small (S), Medium (M), Big (B), Very Big (VB) and
VVB denotes Very Very Big.
The figure. 2 shows the block diagram of a fuzzy self-tuning PID controller. As it can be seen
from the block diagram, the fuzzy system takes two inputs (e and ed) and gives three outputs ( ,
, ) (Figure. 3). This block diagram just shows control of one degree of freedom of a
quadrotor and we are used two other controllers like this controller for attitude control of
quadrotor.
The membership functions of the all inputs and outputs have been chosen identical. Figure. 4
shows these membership functions. This membership functions are combined of triangular and
Gaussian. The width of the fuzzy sets used for controllers are not same and they have been
determined by trial and error experience. The width of the fuzzy sets for output, , have been
chosen [0.2 0.7], , have been chosen [0.001 0.01] and for , [0.1 0.15]. And for inputs, the
range for the error have been chosen [-1 1] and for error rate have been chosen [-10 10] and if
these inputs put out of these ranges we are used a saturation for put those in the range.
The set of linguistic rules is the essential part of a fuzzy controller. In many cases it is easy to
translate an expert's experience into these rules and any number of such rules can be created to

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define the actions of the controller. In some other cases this rules can come from some trial and
error approaches. Table.1 and Table.2 shows the fuzzy rules for tuning the PID gains.
Figure. 2 Basic structure of plant whit controller
Figure. 3 Basic structure of a fuzzy controller
Figure.4 Membership functions for the all inputs and outputs
Table 1. Fuzzy rules for and
ERROR
PB
PM
PS
ZO
NS
NM
NB
ERROR
RATE
M
S
VS
VVS
VS
S
M
NB
B
M
S
VS
S
M
B
NM
VB
B
M
S
M
B
VB
NS
VVB
VB
B
M
B
VB
VVB
Zo
VB
B
M
S
M
B
VB
PS
B
M
S
VS
S
M
B
PM
M
S
VS
VVS
VS
S
M
PB

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Table 2. Fuzzy rules for
ERROR
PB
PM
PS
ZO
NS
NM
NB
ERROR
RATE
M
B
VB
VVB
VB
B
M
NB
S
M
B
VB
B
M
S
NM
VS
S
M
B
M
S
VS
NS
VVS
VS
S
M
S
VS
VVS
Zo
VS
S
M
B
M
S
VS
PS
S
M
B
VB
B
M
S
PM
M
B
VB
VVB
VB
B
M
PB
The rules presented at Tables. 1 and 2 can be read as follows:
For example, IF the error is NB and the error rate is PS THEN is VB and is VB and is
VS. The output of the fuzzy system logic is fuzzy.
We cannot provide these fuzzy outputs to a dynamical system as control inputs directly.
Defuzzification process is needed to convert these fuzzy outputs to numbers that can represent the
fuzzy output. The control signal should be continuous, any variation in input should not produce
big changes in output signal. The defuzzification algorithm should be clear and the process to
determine the output signal should be identified clearly. Also, the defuzzification should be
logical, should have high membership degree and it should correspond to the approximately
middle of the graph. For the reason discussed above we have selected center average defuzzifier
for the controllers.
4. RESULTS AND SIMULATION STUDY
The mathematical dynamical model of the quadrotor vehicle as well as the controllers have been
developed in Matlab Simulink for simulation. The goal of this analysis is to test how well the
controllers can stabilize the quadrotor. We are supposed the quadrotor starts with 6 (rad) pitch, 3
(rad) roll and -2 (rad) yaw angle in the hovering mode. The quadrotor is commanded to change
these angles to zero and stable itself. Both of the controllers are run on these two scenarios and
the results are compared.
For adjusting classical PID controller gains we are used Ziegler-Nichols method. Due to this
method we are choose for the PID gains.
And by using the fuzzy system for tuning the PID gains, the PID gains change along the
simulation that you can see results of this changing in Figure. 5, for example changing the PID
gains in roll angle.
The results of two methods for three Euler angles are showed in Figure. 6 to Figure. 8. In Figure.
6 you can see response of the quadrotor for the roll angle, Figure. 7 shows the response for the
pitch angle and Figure. 8 shows response of the quadrotor for the yaw angle. Additionally figures
show differences between two methods, classical PID controller and fuzzy PID controller.

8
From the figures clearly can be understand that by using the fuzzy system for tuning the PID
gains the performances improved. Overshoot in three Euler angles is less than classical PID gains.
The setting time of three angles by using the fuzzy system, obviously decreased. In the yaw angle
there is no big different between two methods but in it the overshoot decreased. In two other
angles you can see big different between classical PID controller and fuzzy PID controller.
5. EXPERIMENTAL RESULTS
After the design of controller, this controller implemented on a real quadrotor. The main rig of
this test setup is a quadrotor equipped with IMU sensor type GY80 measures the roll, pitch and
yaw angle of quadrotor . Moreover, an Arduino Board (UNO) has been used as a
microcontroller which its duties are sending, receiving and operating data in order to stabilize the
quadrotor (Figure.9).
Figure. 5 Changing the PID gains along the simulation for roll angle
Figure. 6 The roll angle control of the quadrotor using classical PID (solid line) and fuzzy PID (dashed line)
controllers
Figure. 7 The pitch angle control of the quadrotor using classical PID (solid line) and fuzzy PID (dashed
line) controllers

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Figure. 8 The yaw angle control of the quadrotor using classical PID (solid line) and fuzzy PID (dashed
line) controllers
In order to eliminate noise from IMU data, 260 Hz and 256 Hz low pass filter are applied to the
accelerometer and gyro data correspondingly. Generally, the accelerometer is very noisy while
the gyro drifts over time. In other words, the gyroscope data can be used on a short term while the
accelerometer data can be utilized on a long term. To treat this, a Kalman filter is then designed
and implemented in which a combination of accelerometer and gyro data are employed to achieve
a better roll, pitch and yaw angle estimation along with removing unwanted residual noise.
Figure. 10 and Figure. 11 shows performance of applying filter to have satisfactory data of the
roll angle.
Figure. 9 Prototype equipped quadrotor
The measured roll, pitch and yaw angles by IMU sensor, are transferred to Arduino board. After
some numerical computations like filtering and buffering of sensor data, the values of 3 Euler
angles are sent to computer. This information is employed in MATLAB software and using them,
suitable control signal is computed by designed algorithm. The algorithm output (PID controller
parameters) comes back to Arduino board and then using the electrical speed controller, the
quadrotor’s attitude is changed (Figure. 12).
Two experimental tests are performed to evaluate the effectiveness of the fabricated Fuzzy-PID
controller.

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0 2 4 6 8 10 12 14 16
-60
-40
-20
0
20
40
60
Time (s)
Roll
Angle
(deg)
Accelorometer
Gyro
Kalman
Figure. 10 Accelerometer, Gyro Roll data before applying low pass filter and roll angle with kalman filter
0 2 4 6 8 10 12 14 16
-20
-15
-10
-5
0
5
10
15
20
Time (s)
Roll
Angle
(deg)
Accelerometer
Gyro
Kalman
Figure. 11 Accelerometer, Gyro Roll data after applying low pass filter and roll angle with kalman filter
Figure. 12 Exchanging data between different equipments.
5.1. FIRST TEST
We get the quadrotor in a situation such that pitch angle starts at +20 (deg) in hovering mode. The
quadrotor is commanded to change these angles to zero and stable itself. In the below figures you
will see results of this test for controlling roll and pitch angle. In first two figures shows changes
of PID parameters during the test for both roll and pitch angles (Figure. 13 and 14). Other two
figures shows the result of controller performance (Figure. 15 and 16).
It is necessary to say for stabilize of IMU data we should spend about 2 seconds. Thus in these
figures quadrotor starts after 2.2 seconds.
5.2. SECOND TEST
In the final test, has been tried to show performance of the presented controller, when two heavy
weights have been connected to corners of the quadrotor. These two weights make the quadrotor

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be unstable. A 370 (gr) weight has been connected to one corner of the quadrotor to distort the
roll angle and a 400 (gr) weight will be distorted the pitch angle. Now the controller will be tried
to stable the quadrotor. Results of this test showed in figure. 17.
1 2 3 4 5 6 7 8 9 10
0
0.1
0.2
0.3
0.4
0.5
0.6
Time (s)
Gain
(Roll)
Kd
Ki
Kp
Figure. 13 Changing the PID gains along the test for roll angle
1 2 3 4 5 6 7 8 9 10
0
0.1
0.2
0.3
0.4
0.5
0.6
Time (s)
Gain
(Pitch)
Kd
Ki
Kp
Figure. 14 Changing the PID gains along the test for pitch angle
1 2 3 4 5 6 7 8 9 10
-30
-20
-10
0
10
20
30
Time (s)
Roll
(deg)
Fuzzy-PID
Classical PID
Figure. 15 The roll angle control of the quadrotor by using fuzzy PID _ angle (solid line) and classical PID
controller (dashed line)

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1 2 3 4 5 6 7 8 9 10
-30
-20
-10
0
10
20
30
Time (s)
Pitch
(deg)
Fuzzy-PID
Classical PID
Figure. 16 The pitch angle control of the quadrotor by using fuzzy PID _ angle (solid line) and classical
PID controller (dashed line)
2 4 6 8 10 12 14 16 18 20 22 24
-50
-40
-30
-20
-10
0
10
20
30
40
50
Time (s)
Angle
(deg)
Roll
Pitch
Figure. 17 The roll (solid line) and pitch (dashed line) angle control of the quadrotor by using fuzzy PID
6. CONCLUSION
In this paper, modelling, a classical PID controller and a fuzzy supervisory controller for tuning
the PID controller gains has been presented. Although fuzzy control of dynamical system has
been presented extensively in literature, application of this technology to quadrotor control is
quite new. In the first step we modeled the quadrotor with Euler-Newton equations. In the next
we used a classical PID controller to attitude control of the quadrotor. For first time we used
Ziegler-Nichols method for adjusting the PID gains and after that introduced a fuzzy supervisory
controller for tuning the PID gains and attached this controller to the classical PID controller. We
used three sets of these controllers for control of the quadrotor's three Euler angles. Various
simulations based on the Matlab Simulink, were performed to test and compare the two control
algorithms. When comparing these two types of controller we should note that the selection of the
membership functions and the rules of the fuzzy controller are based on the experience of the
designer and furthermore using a few trial and error approach.
The dependence of the fuzzy controller on the quadrotor model is much less than the classical
controllers used. The fuzzy controller is nonlinear and it is thus more suitable for nonlinear
system control. The control performances of the fuzzy PID controller was greatly better than the
classical PID controller as you can see in the result section. The biggest advantages of the fuzzy
PID controller is eliminating overshoots than the big overshoots in the classical PID controller
and the other one is smaller setting time than the classical PID controller.
In the next step we implemented this control methods to the real quadrotor and performed some
tests to show abilities of the presented controller. Results of this tests showed and you can see that
this results verify the simulation results.

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In next studies we will develop some other control methods to the quadrotor both in simulation
and experiment and will compare this control methods and will select the best controller in the
real experiment tests.
APPENDIX
Some constant's values which used in the simulation of the quadrotor are showed in Table. 3. This
constant's values selected from a real quadrotor in laboratory of mechatronic in the University of
Tehran.
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Table 3 Table of constants
Symbol Description and unit value
Roll angle (rad) _
Pitch angle (rad) _
Yaw angle (rad) _
Mass of the quadrotor (Kg) 1.25
Center of quadrotor to center of propeller
distance (m)
0.2
Body moment of inertia around the x-axis
( )
0.002353
Body moment of inertia around the y-axis
( )
0.002353
Body moment of inertia around the z-axis
( )
0.004706
Thrust factor
Drag factor
Rotor inertia ( )

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Automate-Based Model: A Rocking Block-Based Approach." IEEE Sensors Journal 16.14 (2016):
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10 Conference (TENCON), 2016 IEEE. IEEE, 2016.
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Regeneration of Gait Pattern." IEEE Transactions on Automation Science and Engineering (2016).
[32] Semwal, Vijay Bhaskar, et al. "An optimized feature selection technique based on incremental feature
analysis for bio-metric gait data classification."Multimedia Tools and Applications: 1-19.
[33] Semwal, Vijay Bhaskar, Pavan Chakraborty, and Gora Chand Nandi. "Less computationally intensive
fuzzy logic (type-1)-based controller for humanoid push recovery." Robotics and Autonomous
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AUTHORS
Ehsan Abbasi received M.s degree in Mechanical Engineering from University of Tehran,
Tehran, Iran in 2014. Now he studies at Isfahan University of Technology for receiving PhD
degree. His current research interests include controlling of dynamical systems and robotics
and mechatronics.

DEVELOPMENT AND IMPLEMENTATION OF A ADAPTIVE FUZZY CONTROL SYSTEM FOR A VTOL VEHICLE IN HOVERING MODE

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