International Review of Applied Sciences and Engineering
Volume/Issue:
Volume 13: Issue 2
Neural networks on-line optimized PID controller with wind gust rejection for a quad-rotor
Authors:
Chiraz Ben Jabeur University of Tunis, RIFTSI, ENSIT, University of Tunis El Manar, ISI, 2, Rue Abou Raihane Bayrouni, 2080, Ariana, Tunisia

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https://orcid.org/0000-0002-4763-8074
and
Hassene Seddik University of Tunis, Department of Electrical Engineering, RIFTSI, ENSIT, 5, Av. TahaHussein, 1008, Tunis, Tunisia

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Pages:
133–147
Online Publication Date:
11 Nov 2021
Publication Date:
16 Jun 2022
Article Category:
Research Article
DOI:
https://doi.org/10.1556/1848.2021.00325
Keywords:
quad-rotor control; BLADE Inductrix FPV+; robustness and stability; hostile environment; trajectory tracking; disturbances rejection
Open access

Abstract

In this paper a complete methodology of modeling and control of quad-rotor aircraft is exposed. In fact, a PD on-line optimized Neural Networks Approach (PD-NN) is developed and applied to control the attitude of a quad-rotor that is evolving in hostile environment with wind gust disturbances and should maintain its position despite of these troubles. Whereas PD classical controllers are dedicated for the positions, altitude and speed control. The main objective of this work is to develop a smart Self-Tuning PD controller for attitude angles control, based on neural networks capable of controlling the quad-rotor for an optimized performance thus following a desired trajectory. Many problems could arise if the quad-rotor is evolving in hostile environments presenting irregular troubles such as wind gusts modeled and applied to the overall system. The quad-rotor has to rapidly achieve tasks while guaranteeing stability and precision and must behave quickly with regards to decision making fronting turbulences. This technique offers some advantages over conventional control methods such as PD controllers. Simulation results are achieved with the use of Matlab/Simulink environment and are established on a comparative study between PD and PD-NN controllers founded on wind disturbances application. These obstacles are applied with numerous degrees of strength to test the quad-rotor comportment. Experimental results are reached with the use of the V-REP environment with which some trajectories are tracked and then applied on a BLADE Inductrix FPV+. These simulations and experimental results are acceptable and have confirmed the efficiency of the proposed PD-NN approach. In fact, this controller has fairly smaller errors than the PD controller and has an improved ability to reject troubles. Moreover, it has confirmed to be extremely vigorous and efficient fronting disturbances in the form of wind disturbances.

Abstract

In this paper a complete methodology of modeling and control of quad-rotor aircraft is exposed. In fact, a PD on-line optimized Neural Networks Approach (PD-NN) is developed and applied to control the attitude of a quad-rotor that is evolving in hostile environment with wind gust disturbances and should maintain its position despite of these troubles. Whereas PD classical controllers are dedicated for the positions, altitude and speed control. The main objective of this work is to develop a smart Self-Tuning PD controller for attitude angles control, based on neural networks capable of controlling the quad-rotor for an optimized performance thus following a desired trajectory. Many problems could arise if the quad-rotor is evolving in hostile environments presenting irregular troubles such as wind gusts modeled and applied to the overall system. The quad-rotor has to rapidly achieve tasks while guaranteeing stability and precision and must behave quickly with regards to decision making fronting turbulences. This technique offers some advantages over conventional control methods such as PD controllers. Simulation results are achieved with the use of Matlab/Simulink environment and are established on a comparative study between PD and PD-NN controllers founded on wind disturbances application. These obstacles are applied with numerous degrees of strength to test the quad-rotor comportment. Experimental results are reached with the use of the V-REP environment with which some trajectories are tracked and then applied on a BLADE Inductrix FPV+. These simulations and experimental results are acceptable and have confirmed the efficiency of the proposed PD-NN approach. In fact, this controller has fairly smaller errors than the PD controller and has an improved ability to reject troubles. Moreover, it has confirmed to be extremely vigorous and efficient fronting disturbances in the form of wind disturbances.

1 Introduction

Up to now, flying robots enjoy great popularity and the control of these systems is the main subject in robotics research, in military and space studies. Unmanned Air Vehicle can be remotely controlled or can fly independently [1]. In fact, autonomous Unmanned Air Vehicles are becoming more and more popular. By regulating the motors power, the quad-rotor can be capable of achieving several tasks. That is to say the control of a quad-rotor is not a minor task because of the six degrees of freedom, the high nonlinearities presented in the responses, the strong coupling multivariable and the under actuated conditions, especially with only four motors. Some studies worked on the control of such a system in a wide field of applications such as trajectory tracking control and obstacle avoidance control [2, 3]. In the mission of trajectory tracking, certain applications are based on conventional techniques such PD and PID [4–7], and others are based on artificial intelligence, such as Fuzzy Logic, Neural Networks and Neuro-Fuzzy systems [8–10]. In [8], four cooperative PD controllers were replaced by four Neural Networks with which each Neural Network imitated the actions of a PD controller and Fuzzy logic was used to adjust PID controllers' gains. In addition, in [9], fuzzy logic is used to design a robust Self-Tuning PID controller. It was a task to optimize PID gains with fuzzy logic for heading and position trajectory tracking control to manipulate the external disturbances caused by the payload weight variation for the period of flight. Moreover, in [10], the control of an unmanned aerial vehicle in tracking a moving object is exposed with the use of three fuzzy logic units that are implemented to permit the engine following the desired position and inclination.

PID controller has become an essential technical tool and is successfully applied in robotic systems and especially in quad-rotors control strategies. Nevertheless, to get ideal control effect, it is required to optimize its three parameters: proportional coefficient   K P , integral coefficient   K I , and derivative coefficient K D before placing it into simulation.

It is relevant to affirm that many research papers deal with PD and PID parameters optimisation with fuzzy logic such as in [11–13], but not a lot use neural networks approach.

The aim of parameters optimization is to achieve the best control effect by making the controller and the controlled systems characteristics well-coordinated. If the selected parameters of the PD controller are inopportune, its control effect will be very modest. However, there are all kinds of uncertainties and nonlinearities in the quad-rotor control system, so it is hard to establish the precise traditional math model. Moreover, the traditional parameter optimization methods of the PD controller cannot promise normal work and it is difficult to realize perfect control effect. For this reason, recently, neural networks have demonstrated their growth in PD parameters optimization. In fact, the neural network can learn by itself and simulate the system parameters without knowing about the structure of the system so as to get the system rule. Currently, PID controller parameters optimized by neural network are becoming a promising topic [14–16]. In fact in [14], a robust PID controller based artificial neural network is presented for quad-rotor control. The proposed PD tuning algorithm adjusts continuously the PD parameters with tracking error minimization.

The objective of this work is using artificial intelligence permitting to conceptualize an intelligent tracking control to a quad-rotor that is exposed to wind disturbances. In this way, neural networks are used to adjust the parameters of the PD controller for the attitude control in an on line manner. This attitude control concerns the roll pitch and yaw angles. Thus, there are three neural networks for each angle, which structures are so special and contain at least one hidden layer of two neurons that are the Proportional and the Derivative functions.

Basically, the system may meet some wind disturbances in its fly, that depend on its environment, and that can affect its trajectory following. In this case, the quad-rotor must compensate these disturbances and continue its navigation without changing its trajectory.

Accordingly, the principal objective is the design and implementation of PD classical controllers and PD-NN controllers for controlling the attitude angles, based on neural networks in order to best allow the robot following a desired behavior while tracking a desired trajectory despite of wind disturbances. The quad-rotor must be robust to sudden environment change and must react quickly.

This paper is composed of seven sections. The first section contains introduction. The second one deals with dynamics modeling. The third section accounts for the model of wind gust. In the forth the PD classical control strategy and the PD-NN control strategy optimized by neural networks are detailed. The fifth section deals with both simulations and experimental results. The sixth section is dedicated to analysis. The seventh section presents conclusion.

2 Dynamic model of the quad-rotor

Modeling of a quad-rotor is based on the overall model which is built with the dynamic models of the quad-rotor in addition to the DC motor dynamics that must be taken into account. A basic model of an unmanned quad-rotor [17–20] is shown in Fig. 1.

Fig. 1.
Fig. 1.

Model of quad-rotor

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

It is assumed that the front and the rear motors rotate counter clockwise when the others rotate clockwise. The sum of the thrusts of each motors is the throttle input. If the speed of the rear and the front motors is increased (decreased), the movement of the pitch is attained. If the lateral motors are used, the roll movement is achieved similarly. If the speed of the front and rear motors is increased (decreased) and the speed of the lateral motors is decreased (increased), the yaw movement is activated [18].

2.1 Newton-Euler model

In this section, the Newton-Euler formalism is used to build the specific model information of the quad-rotor architecture based on the rigid-body [21].

Two frames have to be considered such as in Fig. 1

The inertial frame of the earth (E-frame)

The vehicle body-fixed frame (B-frame)

These frames are linked over three successive rotations:

Rotation around the x-axis: Roll;

Rotation around the y-axis: Pitch;

Rotation around the z-axis: Yaw.

The following suppositions have been made in this approach:

The starting point of the body-fixed frame corresponds to the vehicle body center of mass.

The body principal axes of inertia matches the axes of the B-frame.

In the body-fixed frame, the motions equations are suitably formulated based on the following reasons [21]:

The time-invariant inertia matrix.

To simplify the equations, the benefit of body symmetry is considered.

Measurements taken on-board are easily converted to body-fixed frame.

In body-fixed frame, the control forces are always given.

The generalized coordinates of the quad-rotor are:

q = ( x ,   y ,   z ,   ϕ ,   θ ,   ψ ) where ( x ,   y ,   z ) represents the quad-rotor center of mass relative position with regards to an inertial frame E and ( ϕ , θ , ψ ) are the three angles of Euler expressing the quad-rotor orientation namely the roll, the pitch and the yaw of the vehicle.

Suppose that the transitional and rotational coordinates are in the form: ξ = ( x ,   y ,   z ) ) ∈ ℜ 3 and η = ( ϕ ,   θ ,   ψ ) ∈ ℜ 3 .

The total transitional kinetic energy of the quad-rotor is:
T t r a n s = 1 2 m ξ ˙ T ξ ˙
where m is the mass of the quad-rotor.
The rotational kinetic energy is described as:
T r o t = 1 2 J η ˙ T η ˙ = 1 2 ω T I ω
where matrix J = J ( η ) is the auxiliary matrix, I is the body inertia matrix and ω is the angular speed.
The potential energy in the system is described as:
U = m . g . z
where z is the quad-rotor altitude and g is the acceleration due to gravity.
The Lagrangian is defined from (1)–(3) as:
L = T t r a n s + T r o t − U
Then the full quad-rotor dynamics is obtained as a function of the external generalized forces F = ( F ξ , τ ) from:
F = d d t ∂ L ∂ q − ∂ L ∂ q = ( m x ¨ m y ¨ m z ¨ I x ϕ ¨ + I x ϕ ˙ I y θ ¨ + I y θ ˙ I z ψ ¨ + I z ψ ˙ ) − ( 0 0 − m g 0 0 0 )

F ξ is the translational force applied to the quad-rotor due to the throttle control input, τ represents the pitch, roll, and yaw moments.

The principal control inputs are defined as follows:
F r = ( 0   0   u ) T
where the main thrust is:
u = f 1 + f 2 + f 3 + f 4
where f i = b . ω i 2 , b is a positive constant and ω i are the angular speed of the motor i.
Then F ξ can be written as:
F ξ = R . F r
where R is the transformation matrix representing the orientation of the quad-rotor as:
R = [ c θ c ψ s θ s ψ − s θ c ψ s θ s φ − s ψ s φ s ψ s θ s φ + c ψ c φ c θ s φ c ψ s θ c φ + s ψ s φ s ψ s θ c φ − c ψ s φ c θ c φ ]

With: c = cos ,   s = sin

The generalized torques for the η variables are:
τ = ( τ φ   τ θ   τ ψ ) T
where:
τ φ = l ( f 3 − f 1 ) = b l ( − ω 1 2 + ω 3 2 )
τ θ = l ( f 2 − f 4 ) = b l ( − ω 2 2 + ω 4 2 )
τ ψ = ∑ i = 1 ' τ M i = d ( − ω 1 2 + ω 2 2 − ω 3 2 + ω 4 2 )
Thus the control distribution from the four actuator motors of the quad-rotor is given by:
[ u τ φ τ θ τ ψ ] = [ b b b b 0 − b l 0 b l − b l 0 b l 0 − d d − d d ] [ ω 1 2 ω 2 2 ω 3 2 ω 4 2 ]
where l is the distance from the motors to the centre of gravity, τ M i is the torque produced by motor M i   and d and b are constants known as force-to-moment scaling factor.
The final dynamic model of the quad-rotor looks as:
m ξ ¨ + ( 0 0 m g ) = F ξ
J ( η ) η ¨ + C ( η ,   η ⋅ ) = τ
where,
F ξ = ( c ψ s θ c φ + s ψ s φ s ψ s θ c φ − c ψ s φ c θ c φ ) u
And auxiliary Matrix ( J ( η ) ) = J = T η T I T η
With :   T η = ( − s θ 0 1 c θ s ψ c ψ 0 c θ c ψ − s ψ 0 )
Thus the system has the form of an under-actuated system with six outputs ( x , y , z , φ , θ , ψ ) and four inputs ( u , τ φ , τ θ , τ ψ ) , and the dynamic model of the quad-rotor is written as:
{ x ¨ = ( c ψ s θ c φ + s ψ s φ ) u m y ¨ = ( s ψ s θ c φ − C ψ s φ ) u m z ¨ = − g + ( c θ c φ ) u m φ ¨ = θ ⋅ ψ ⋅ ( I y − I z I x ) − J p I x θ ⋅ Ω + τ φ I x θ ¨ = ψ ⋅ φ ⋅ ( I z − I x I y ) + J p I y φ ⋅ Ω + τ θ I y ψ ¨ = θ ⋅ φ ⋅ ( I x − I y I z ) + τ ψ I z

I x , I y , I z are body inertia, J p is propeller/rotor inertia, and Ω = ( ω 1 , ω 2 , ω 3 , ω 4 )

2.2 Actuators dynamic modeling: DC-motor

In general cases, the driving system of quad-rotors is based on an armature-controlled DC motors which are considered as servo actuators. These actuators train the system and drive it by providing torque control inputs. The architecture of the DC motor is given in Fig. 2.

Fig. 2.
Fig. 2.

DC motor architecture

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

Kirchhoff's voltage law is applied giving:
v ( t ) = V R ( t ) + V L ( t ) + e ( t ) = R i ( t ) + L d i ( t ) d t + K E ω M ( t )
where V R ( t ) is the voltage through the resistor R and V L ( t ) is the voltage through the inductor L, i ( t ) is the current of the motor, K E is the electrical constant of the motor and ω M is the motor angular speed.
Thanks to construction optimization, most of the motors used in robotics show small inductance. For this reason the inductor effect is neglected. Therefore the above equation is simplified according to this one:
v ( t ) = R i ( t ) + K E ω M ( t )
The dynamics of the motor is described by:
J T M ω ⋅ M = T M − T L
where J T M is the total motor moment of inertia, ω ˙ M is the motor angular acceleration, T M is the motor torque and T L is the load torque.
The motor torque T M is proportional to the electrical current i, consequently we find:
J T M ω ⋅ M = − K E K M R ω M − T L + K M R v

The two constants K E and K M have the same value even if the units of measurement differ.

The real motor system is composed of three units which are the motor itself, the propeller and the gear box.

To take the relations between these elements into consideration, we have:
ω M T M P η = ω P T M P
where: T M P is the motor torque in the propeller axis.
η is the conversion efficiency of the gear box which attaches the mechanical power of the motor axis P M to the propeller axis one P P
J M ω ⋅ M = T M − T P M
J P ω ⋅ P = T M P − T P
where: ω P is the propeller angular speed and ω ˙ P is the propeller angular acceleration.

J M is the rotor moment of inertia around the motor axis, J P is the rotor moment of inertia around the propeller axis, T M is the propeller torque in the motor axis and T P is the propeller torque.

To calculate the dynamics of the gear box system, this equation is derived:
( J M + J P η N 2 ) ω ⋅ M = T M − T P η N
where N is the reduction ratio of the gear box and is equal to the motor speed ω M divided by the propeller speed ω P .
According to Eq. (23), the motor system can be modeled with the following differential equation.
( J p + η N 2 J M ) ω ⋅ P = − K E K M R η N 2 ω P − d ω P 2 + K M R η N v
where d is the aerodynamic drag factor
Where the ω ˙ P coefficient is the total rotational moment of inertia around the propeller axis J T P with:
J T P = J P + η N 2 J M
Since the motor differential equation is non-linear, the first order Taylor series method has been adopted to linearize it around its working point as:
ω ⋅ P = A P ω P + B P v + C P

A P is the linearized propeller's speed coefficient, B P is the linearized input voltage coefficient and C P is the linearized constant coefficient.

The matrix form of the differential equation is given by:
Ω ⋅ P = A P Ω P + B P v + C P
where Ω ˙ P is the propellers acceleration vector, Ω P is the propellers speed vector, and v is the inputs voltage vector.

3 Wind gust modeling

If a quad-rotor undergoes a crosswind, it may be pushed far downwind or knocked over. Basically, this leads to forces f v i , acting on every rotor. These forces are expected in the air flow generated by the wind gust [22–26]. This means that the degree of these forces is a function of the additional lateral air flow coming from the wind gust and acting on the propeller as shown in Fig. 3.

Fig. 3.
Fig. 3.

Aerodynamic analysis of rotor subjected to wind disturbance

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

Where:

f m i = b ω i 2 : represents the thrust of the propellers i = 1,…, 4.

f v i : designates the additional thrust of the side wind.

α: symbolizes the angle between the axis of the propeller and the gust of side wind.

V v : is the speed of the side wind gust.

V h : is the speed of the wind produced by the propeller

V ˆ : is the total wind speed.

Therefore, downwind, the total thrust is given by the following expression:
f T i = f m i + f v i = 2. ρ . A . V ˆ . V h

  • ρ : is the air density.

  • A: is the area of the propeller.

The relation describing the total wind speed is given by:
V ˆ = [ ( V v ⁡ cos ⁡ α + V h ) 2 + ( V v ⁡ sin ⁡ α ) 2 ] 1 / 2
When the wind comes from the right of the x-axis, then the angle α = 90°, and this relation becomes:
V ˆ = [ ( V h ) 2 + ( V v ) 2 ] 1 / 2
The wind speed V h induced by the propellers is defined as in [24, 26] by:
V ˆ = [ ( V v ⁡ cos ⁡ α + V h ) 2 + ( V v ⁡ sin ⁡ α ) 2 ] 1 / 2
The thrust produced by the wind will therefore be expressed by:
f v i = 2. ρ . A . ( d . ω i 2 2. ρ . A + V v 2 ) 1 / 2 − f m i
In addition, an aerodynamic drag τ d r a g opposes the engine torque. This aerodynamic drag is given by:
τ d r a g = ρ . A 2 V v 2
In the case of the quad-rotor is troubled by wind gusts, the induced forces f v i in each rotor produce additional aerodynamic wind torques acting on the propellers. These torques could be expressed by:
[ τ v φ τ v θ τ v ψ ] = [ ( f v 4 − f v 2 ) l ( f v 3 − f v 1 ) l ∑ i = 1 4 τ t r a î n é i ]
where l   is the distance between the center of the quad-rotor and the center of the propellers.
Basically, the applied gravitational force to the machine is given by:
f g = − m . g . k ˆ
where k ˆ refers to the unit vector coinciding with the z axis and g denotes the acceleration of gravity.
Consequently, we have:
{ F = R ( ∑ i = 1 4 f M i + ∑ i = 1 4 f v i ) τ = τ A + τ v A + f g
where:

τ A = [ τ φ ,   τ θ ,   τ ψ ] T and τ v A = [ τ v φ ,   τ v θ ,   τ v ψ ] T

From Eqs (15) and (16), we have:
{ m ξ = R ( ∑ i = 1 4 f M i + ∑ i = 1 4 f v i ) + f g J Ω ⋅ = − Ω ∧ J Ω + τ A + τ v A − τ f a − τ g h
This leads to:
{ x ¨ = − K t x m x ⋅ + ( c ψ s θ c φ + s ψ s φ ) U 1 m + W 1 y ¨ = − K t y m y ⋅ + ( s ψ s θ c φ − c ψ s φ ) U 1 m + W 1 z ¨ = − K t z m z ⋅ − g + ( c θ c φ + s ψ s φ ) U 1 m + W 1 φ ¨ = − θ ⋅ ψ ⋅ ( I z − I y I x ) − J r I x Ω r θ ⋅ − K f a x I x φ ⋅ 2 + U 2 I x + W 2 θ ¨ = − φ ⋅ ψ ⋅ ( I z − I x I y ) + J r I y Ω r φ ⋅ − K f a y I x θ ⋅ 2 + U 3 I y + W 3 ψ ¨ = − θ ⋅ φ ⋅ ( I y − I x I z ) − K f a z I z ψ ⋅ 2 + U 4 I z + W 4
where:
U = [ U 1 ,   U 2 ,   U 3 ,   U 4 ] = [ b ( ω 1 2 + ω 2 2 + ω 3 2 + ω 4 2 ) b l ( ω 4 2 − ω 2 2 ) b l ( ω 3 2 − ω 1 2 ) d ( ω 1 2 − ω 2 2 + ω 3 2 − ω 4 2 ) ] = [ u τ φ τ θ τ ψ ]
W = [ W 1 ,   W 2 ,   W 3 ,   W 4 ] is the vector disturbances produced by the wind and is defined as:
W = [ ∑ i = 1 4 f v i m ( f v 4 − f v 2 )   l I x ( f v 3 − f v 1 )   l I y ∑ i = 1 4 τ t r a î n é i I z ]

These disturbances are applied to the quad-rotor in order to check the performances of the system control.

The main problem is that the quad-rotor should overcome these disturbances and must not be blown by the wind whatever its strength. Evidently, the relation between the weight of the quad-rotor and the speed wind must be taken into account and respected.

4 Control strategies

In this section, a trajectory tracking hindrance and a position control problems are presented when the quad-rotor is evolving in a hostile environment.

The aim of the work is founded on two control techniques: a PD conventional control strategy and a PD-NN intelligent control strategy, a comparative study will be done based on the robustness of these controllers to the disturbances caused by the wind.

4.1 PD control strategies

The PD control strategy is presented in Fig. 4. Two types of PD controllers are adopted: the first one concerns positions and altitude control, the second one is opted for attitude angles control, and the PID controller is devoted to the motors control.

Fig. 4.
Fig. 4.

PD and PD control strategies

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

The classical PID controller is represented with its continuous transfer function as follows:
C ( p ) = K P + K I p + K D p
where: K P is the proportional coefficient, K I is integral coefficient and K D is the derivative coefficient.
The control law expression is based on the error between the desired variable and the process variable and is given by:
u ( t ) = K P e ( t ) + K I ∫ e ( t ) d t + K D d e ( t ) d t
The PD controllers for positions: x, y and z respectively are described as:
u x = K P x ( x d e s − x ) + K D x ( x ⋅ d e s − x ⋅ )
u y = K P y ( y d e s − y ) + K D y ( y ⋅ d e s − y ⋅ )
u z = K P z ( z d e s − z ) + K D z ( z ⋅ d e s − z ⋅ )

The PD controllers for angles (Altitude and Attitude):

Roll ‘ φ ' , pitch ‘ θ ' and yaw ‘ ψ ' respectively are described as:
u φ = K P φ ( φ d e s − φ ) + K D φ ( φ ⋅ d e s − φ ⋅ )
u θ = K P θ ( θ d e s − θ ) + K D θ ( θ ⋅ d e s − θ ⋅ )
u ψ = K P ψ ( ψ d e s − ψ ) + K D ψ ( ψ ⋅ d e s − ψ ⋅ )
The PID controllers for motors speeds are respectively described as:
u ω 1 = K P ω 1 ( ω 1 d e s − ω 1 ) + K I ω 1 ∫ ( ω 1 d e s − ω 1 ) d t + K D ω 1 ( ω ⋅ 1 d e s − ω ⋅ 1 )
u ω 2 = K P ω 2 ( ω 2 d e s − ω 2 ) + K I ω 2 ∫ ( ω 2 d e s − ω 2 ) d t + K D ω 2 ( ω ˙ 2 d e s − ω ˙ 2 )
u ω 3 = K P ω 3 ( ω 3 d e s − ω 3 ) + K I ω 3 ∫ ( ω 3 d e s − ω 3 ) d t + K D ω 3 ( ω ⋅ 3 d e s − ω ⋅ 3 )
u ω 4 = K P ω 4 ( ω 4 d e s − ω 4 ) + K I ω 4 ∫ ( ω 4 d e s − ω 4 ) d t + K D ω 4 ( ω ⋅ 4 d e s − ω ⋅ 4 )

The tuning of the PID coefficients is based on the closed loop scheme with the use of the Ziegler and Nichols approach. The principle benefit of this method is its simplicity. It consists on setting the integral K I gain to the extreme, and derivative K D gain to zero.

Though, till it reaches the critical gain K osc , the proportional K P gain is increased, and the system oscillates continuously with T osc period among constant amplitude oscillations. Formerly, the PID gains are set based on the gains K osc and T osc with mathematical approximations [27, 28].

The numerical values of all PD and PID controllers are given in the next Table 1.

Table 1.

Numerical values of all PD and PID controllers
K P K I K D
Positions 5 0 8
Angles 9 0 14
Motors speeds 1 8 1

4.2 PID optimized neural networks approach: PID-NN control strategy

4.2.1 Neural network controller scheme

The main idea is the parameters optimization of the PD controller dedicated for the attitude angles, with the use of the famous feed-forward neural network. The methodology principle is to dynamically and on line adjust these parameters in order to reach the optimal PD-NN controller performances, according to the system running state.

The control strategy is based on three groups of controllers, one PD controllers group for the positions and the altitude, one PD-NN controllers group for the attitude angles and one PID controllers group for the speed of the quad-rotor.

The principle of the PD optimized neural networks approach for the attitude angles is shown in Fig. 5.

Fig. 5.
Fig. 5.

Principle of PD optimized neural networks approach

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

In this figure, the back propagation training algorithm is used to adjust the “P” and “D” gains related to the attitude angles. This method is based on the errors between the desired and the actual positions, angles and speeds.

The block diagram of the neural network is given in Fig. 6.

Fig. 6.
Fig. 6.

Block diagram of the neural network approach

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

4.2.2 Neural network architecture

The neural networks used are multi-layer networks with the back-propagation training method. In this work, three neural networks where designed for attitude angles: Roll angle, Pitch angle and Yaw angle.

For each angle, as seen in Fig. 7, the structure of the neural network is composed of three layers. The input layer contains the actual and the desired angles, the hidden layer is composed of two hidden neurons that are the proportional function “P” and the derivative function “D” and the third layer deals with the torques corresponding to each angle [22].

Fig. 7.
Fig. 7.

Neural network structure for attitude angles control

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

The mathematical equations that govern the principle of these three similar neural networks are described in layers as follows:
  1. ✓ The input layer with two input neurons:
{ e 1 ( φ , θ , ψ ) ( k ) = ( φ ,   θ ,   ψ ) ( k ) e 2 ( φ , θ , ψ ) ( k ) = ( φ ,   θ ,   ψ ) d ( k )
With k represents the iterations.
  1. ✓ The hidden layer composed of two hidden neurons and whose inputs are described by:
u j ( φ , θ , ψ ) ( k ) = ∑ i = 1 2 ω i j ( φ , θ , ψ ) ( k ) e i ( φ , θ , ψ ) ( k ) ,   j = 1 ,   2
where ω i j ( k ) are the weights between the hidden and the input layers.
So as:
{ u 1 ( φ , θ , ψ ) ( k ) = ω 11 ( φ , θ , ψ ) ( k ) . e 1 ( φ , θ , ψ ) ( k ) + ω 21 ( φ , θ , ψ ) ( k ) . e 2 ( φ , θ , ψ ) ( k ) u 2 ( φ , θ , ψ ) ( k ) = ω 12 ( φ , θ , ψ ) ( k ) . e 1 ( φ , θ , ψ ) ( k ) + ω 22 ( φ , θ , ψ ) ( k ) . e 2 ( φ , θ , ψ ) ( k )
  1. ✓ The outputs of the hidden layer are described with:
{ s 1 ( φ , θ , ψ ) ( k ) = u 1 ( φ , θ , ψ ) ( k ) = ω 11 ( φ , θ , ψ ) ( k ) e 1 ( φ , θ , ψ ) ( k ) + ω 21 ( φ , θ , ψ ) ( k ) e 2 ( φ , θ , ψ ) ( k ) s 2 ( φ , θ , ψ ) ( k ) = ∑ i = 1 2 ω i 2 ( φ , θ , ψ ) k ) e i ( φ , θ , ψ ) ( k ) − ∑ i = 1 2 ω i 2 ( φ , θ , ψ ) ( k − 1 ) e i ( φ , θ , ψ ) ( k − 1 )
  1. ✓ The output layer has a single neuron whose main function is to provide the control signal. This neuron is expressed by:
( U 2 , U 3 , U 4 ) ( k ) = ω 1 ( φ , θ , ψ ) ' ( k ) . s 1 ( φ , θ , ψ ) ( k ) + ω 2 ( φ , θ , ψ ) ' ( k ) . s 2 ( φ , θ , ψ ) ( k )

With ω j ′ are the weights between the output and the hidden layers.

This gives:
( U 2 ,   U 3 ,   U 4 ) ( k ) = ω 1 ( φ , θ , ψ ) ′ ( k ) u 1 ( φ , θ , ψ ) ( k ) + ω 2 ( φ , θ , ψ ) ′ ( k ) ( u 2 ( φ , θ , ψ ) ( k ) − u 2 ( φ , θ , ψ ) ( k − 1 ) )
Finally:
( U 2 ,   U 3 ,   U 4 ) ( k ) = K P ( ω 11 ( φ , θ , ψ ) ( k ) e 1 ( φ , θ , ψ ) ( k ) + ω 21 ( φ , θ , ψ ) ( k ) e 2 ( φ , θ , ψ ) ( k ) ) + K D ( ∑ i = 1 2 ω i 2 ( φ , θ , ψ ) ( k ) e i ( φ , θ , ψ ) ( k ) − ∑ i = 1 2 ω i 2 ( φ , θ , ψ ) ( k − 1 ) e i ( φ , θ , ψ ) ( k − 1 )
Initially, the weights between the input layer and the hidden layer are chosen as such:
{ ω 1 j ( φ , θ , ψ ) = + 1 ω 2 j ( φ , θ , ψ ) = − 1   j = 1,2
And the weights between the hidden layer and the output layer are defined, through the principle of the classical PD controller, by:
{ ω 1 ( φ , θ , ψ ) ' = K P ω 2 ( φ , θ , ψ ) ' = K D
The auto-tuning algorithm is the back-propagation training algorithm, because of its aptitude to adapt to changing environments. The back-propagation algorithm trains the neural network and updates the PD constants online. This algorithm to minimize the cost function E (k) by modifying the weights based on the gradient descent method. This cost function is expressed as the square of the difference between the input to the network and the desired input.
E ( k ) = 1 2 e ( φ , θ , ψ ) 2 ( k )
where e ( φ , θ , ψ ) are the errors between the attitude angles and their desired values, and can be described as:
e ( φ , θ , ψ ) ( k + 1 ) = e ( φ , θ , ψ ) ( k ) + Δ e ( φ , θ , ψ ) ( k )

At first, the entries should be applied to the network; it propagates from the first layer to the hidden layers, to output the angles of attitude. These angles are then compared to the desired values and a corresponding error vector is calculated. These errors propagate back, from the output layer, to all the neurons of the hidden layer so that all the neurons in the network have received an error signal thus involving it in its contribution to the total error.

The weights between the hidden layer and the output layer, which are the K P and K D coefficients of the PD controller, are updated by the following equation:
ω j ′ ( k + 1 ) = ω j ′ ( k ) − η j . Δ ω j ′ ( k )
With: η j is the learning rate and Δ ω j ′ ( k ) is the error gradient at unit j .
The variable quantity Δ e ( φ , θ , ψ ) ( k ) is defined as:
Δ e ( φ , θ , ψ ) ( k ) = ∂ e ( φ , θ , ψ ) ( k ) ∂ ω j ′ ( k ) . Δ ω j ′ ( k )
With this algorithm, the gradient is updated by the following expression:
Δ ω j ′ ( k ) = − η ∂ E ( k ) ∂ ω j ′ ( k ) = − η ∂ E ( k ) ∂ U 2,3,4 ( k ) . ∂ U 2,3,4 ( k ) ∂ ω j ′ ( k )
Giving:
Δ ω j ′ ( k ) = − e ( φ , θ , ψ ) ( k ) . s j ( k ) . δ ( k )
where:
δ ( k ) = sgn ( φ ,   θ ,   ψ ) ( k ) − ( φ ,   θ ,   ψ ) ( k − 1 ) U 2,3,4 ( k ) − U 2,3,4 ( k − 1 )
From the input layer to the hidden layer, the weights between the input layer and the hidden layer are updated by the following equation:
ω i j ( k + 1 ) = ω i j ( k ) − η j . Δ ω i j ( k )

With: η j is the learning rate and Δ ω i j ( k ) is the error gradient at unit j.

Where:
Δ ω i j ( k ) = − e ( φ , θ , ψ ) ( k ) . ω j ' ( k ) . e i ( k ) . δ ( k )

After the training algorithm, the optimized resultant numerical values of the PD-NN controller for the attitude angles are given in Table 2 and are compared with those of the classical PD.

Table 2.

Numerical optimized values of the PD-NN and the classical PD controllers for the attitude angles
Angles K P K D
Classical PD 10 20
PD-NN 12.5031 8.2124

5 Simulation results

5.1 Simulation results

  • Controlled quad-rotor parameters responses with PD and PD-NN controllers

The training design of the PD and PD-NN controllers is established with the Matlab/Simulink environment, and simulation results are carried out with considering wind disturbances applied in all three directions. The control strategy consists of a desired trajectory which is founded on x d , y d and z d desired positions and also on desired yaw angle ψ d = pi / 6 . They are presented in Fig. 8.

Fig. 8.
Fig. 8.

x, y and z positions and ψ angle references

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

The following Figs 9 –12 represent results of all controlled quad-rotor parameters compared to references for both training control strategies PD and PD-NN controllers:

Fig. 9.
Fig. 9.

Controlled x, y and z positions

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

Fig. 10.
Fig. 10.

Controlled roll, pitch and yaw angles

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

Fig. 11.
Fig. 11.

Controlled motors speeds

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

Fig. 12.
Fig. 12.

Spiral trajectory of quad-rotor

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

The trajectory tracking is given by:

  • PD and PD-NN controllers comparative study with wind disturbances

The goal is to compare PD and PD-NN control strategies facing different levels of wind disturbances to test the robustness and the stability of both approaches against these troubles. Some wind velocities V v were applied increasingly and two different stability thresholds were obtained for both control strategies. In fact, a comparative study is conducted and simulations results were obtained at what times several wind acceleration values were applied. The stability test is verified on the trajectory tracking and how the control strategy is able to let the quad-rotor following the reference trajectory.

Some simulations results are exposed for selected wind disturbances:

  • V v = 3.24   k n o t s

The trajectory tracking is represented by (Fig. 13):

Fig. 13.
Fig. 13.

Spiral trajectory of quad-rotor

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

V v = 9.18    k n o t s

The trajectory tracking is represented by (Fig. 14): Vv = 10:25 knots

Fig. 14.
Fig. 14.

Spiral trajectory of quad-rotor

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

The trajectory tracking is represented by (Fig. 15): Vv = 21:06 knots

Fig. 15.
Fig. 15.

Spiral trajectory of quad-rotor

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

The trajectory tracking is represented by (Fig. 16):

Fig. 16.
Fig. 16.

Spiral trajectory of quad-rotor

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

To represent the variations of the quad-rotor positions with regards to the disturbances caused by the wind velocities, Fig. 17 highlights the stability thresholds of both control strategies.

  • PD and PD-NN strategies for trajectories tracking

Fig. 17.
Fig. 17.

Quad-rotor trajectory variations against wind disturbances

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

It is a task of varying the trajectories types in order to check the efficiency of both strategies to follow desired ones. A spiral trajectory is kept with rise and fall protocols.

Figure 18 shows the behavior of each control strategy:

Fig. 18.
Fig. 18.

(a) Quad-rotor medium fall from 20 m to 16 m, (b) quad-rotor very high rise from 10 m to 20 m

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

5.2 Experimental results with V-REP

The experimental results for the PD-NN controller are obtained based on the use of the V-REP environment with which some trajectories were considered and tested such as: circular, rectangular, eight and diamond shapes. These trajectories are represented in Fig. 19.

Fig. 19.
Fig. 19.

(a) Circular shape, (b) rectangular shape, (c) eight shape and (d) diamond shape

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

5.3 Experimental results with the BLADE Inductrix FPV+

The experimental results are applied on a quad-rotor BLADE Inductrix FPV+ described in Fig. 20.

Fig. 20.
Fig. 20.

Quad-rotor BLADE Inductrix FPV+

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

The wind disturbances acting on the quad-rotor are applied with a fan and the trajectory to track is fixed as a rectangular shape.

Figure 21 shows the experimental result of trajectory tracking and it is observed that the quad-rotor manages to reach its trajectory.

Fig. 21.
Fig. 21.

Experimental results with rectangular trajectory

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

6 Discussion and analyses

In the previous section, desired performances were acted to on the quad-rotor and the controlled parameters responses were presented with regards to the variation of wind acceleration disturbances. Evidently, in all the previous cited cases, the quad-rotor should behave exactly like the references with both control strategies.

In fact, from Figs. 9 –11, the quad-rotor follows the desired positions, angles and motors speeds with both controllers without adding wind disturbance.

In Fig. 12, the quad-rotor follows the desired trajectory. It is to confirm that the trajectory selected is very hard to track especially when the system is highly instable. In fact, this trajectory is composed of straight sections along z direction and compound alternations along x and y which lead to a circular and spiral trajectory.

In addition, it should be mentioned that the PD-NN controller offers faster and quick responses as represented in Fig. 22:

Fig. 22.
Fig. 22.

PD and PD-NN controllers times responses at 5%

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

According to this figure, time responses at 5% are as follows:

For PID-NN controller τ r 5 % = 1.8 s

For PID controller τ r 5 % = 5.8 s

However, quad-rotor tests show fairly acceptable errors. Table 3 shows the maximum values of the errors reached for positions and angles for both strategies the classical one and the intelligent one.

Table 3.

Errors values for positions and angles for both strategies
Strategy x pos y pos z pos φ θ ψ
PID 0.2596 0.2597 0.0580 0.1287 0.0279 0.0096
PID-NN 0.2048 0.2047 0.0451 0.0569 0.0145 0.0014

The RMSE for the attitude angles between PD-NN and classical PD is given by Fig. 23:

Fig. 23.
Fig. 23.

RMSE for the attitude angles between PD-NN and classical PD

Citation: International Review of Applied Sciences and Engineering 13, 2; 10.1556/1848.2021.00325

When applying wind disturbances, the stability and the robustness of both control strategies were tested. Figures 13 –16 shows the behavior of the proposed controllers facing wind disturbances. Effectively, when increasing disturbances, the controlled quad-rotor with PD and PD-NN controllers loses stability, however the second controller proposes better responses and the stability threshold is higher if compared with the PD controller.

Figure 17 shows the trajectory variation against disturbance caused by the wind acceleration. It should be noticed that the controlled PD quad-rotor reaches instability from wind acceleration of 10.92   k n o t s , but with the PD-NN, it reaches instability from wind acceleration of 19.65   k n o t s . This value is considered to be acceptable and is tested in reality with the drone the BLADE Inductrix FPV+.

Concerning trajectory tracking, it is observed in Fig. 18, that the controlled PD quad-rotor cannot follow all types of trajectories in cases of falling down. Nevertheless, the controlled PD-NN quad-rotor can track all types of trajectories particularly with the fall and the rise.

Figure 19 shows that for the experimental results reached with the V-REP environment, the controlled PD-NN can follow all types of trajectories. Especially for the eight and diamond shapes that are more complicated than the others.

Figure 21 shows that for the experimental results reached with the BLADE Inductrix FPV+, the controlled PD-NN follows successfully the rectangular trajectories, mainly in presence of wind gust created through a fan with an air outlet speed of 17.49   k n o t s .

Figure 23 represents the RMSE for the attitude angles between the classical PD and the PD-NN controllers and demonstrates the effectiveness of the PD-NN strategy over the classical one. The results of this test seems to be satisfactory in terms of difference between the two control strategies and demonstrates that the PD-NN controller is the best.

Basically, the PD-NN controller allows improved responses whether in the case of applying wind disturbances with different degrees: it seems to have a large margin of stability against these disturbances. Or in the case of trajectory tracking: it follows all the trajectories without any constraint. It might also be noted that in hover state and in the presence of wind disturbances, the quad-rotor can maintain its attitude. This case demonstrates its stability and robustness.

These results are compared with the work presented in [22], in which a linear active disturbance rejection control (LADRC) is proposed for stability control of an aerial robot quad-rotor under wind gusts. It is noticed that the controlled PID quad-rotor reaches instability from wind acceleration of 7,77538  knots , but with the LADRC, it reaches instability from wind acceleration of 19,4384  knots . . Basically, the LADRC and the PD-NN control strategies have strong ability of wind disturbance compensation and have comparable stability thresholds to wind gust disturbances.

7 Conclusion

In this paper, a PD and a PD-NN control schemes were proposed for a quad-rotor that is progressing in an environment with outdoor influences. The work treats the problem of wind turbulences and proposes a solution to this problem based on the PD-NN controller.

Moreover, the used trajectory is very difficult to follow, but the PD-NN controller optimized by neural networks leads to excellent results in terms of trajectory following and insensitivity to strong wind disturbances either with simulation or with experimentation.

In fact, it was revealed that this controller is robust beside different rigorous wind accelerations. It also promises stability and precision for static error performances. Simulation and experimental results of the PD-NN for the quad-rotor control strategy were given to verify and ensure the effectiveness of the controlled system in terms of quick and accurate responses.

Finally, it is to guarantee that the objective of this work was reached. Effectively, when progressing in a hostile environment with wind disturbances, the controlled quad-rotor is able to defend itself against these troubles without disturbing its trajectory following, its stability and its accuracy.

Basically, some other optimization algorithms are considered to be used in future works such as the Particle Swarm Optimization (PSO) algorithm, the Social Spider Optimization (SSO) algorithm and the Grey Wolf Optimization (GWO) algorithm which are useful tools to tune the parameters of proportional-derivative (PD) versions.

References

  • [1]↑

    G. Singhal , B. Bansod , and L. Mathew , “Unmanned aerial vehicle classification, applications and challenges: A review,” Preprints, p. 19, 2018. Available: https://doi.org/10.20944/preprints201811.0601.v1. Accessed: Nov. 27, 2018.

    • Search Google Scholar
    • Export Citation
  • [2]↑

    J. Ajmera and V. Sankaranarayanan , “Trajectory tracking control of a quad-rotor,” in International Conference on Control Communication & Computing India (ICCC), Trivandrum, 2015, pp. 48–53.

    • Search Google Scholar
    • Export Citation
  • [3]↑

    C. Wang , W. Liu , and M. Q. Meng , “Obstacle avoidance for quad-rotor using improved method based on optical flow,” in IEEE International Conference on Information and Automation, Lijiang, 2015, pp. 1674–1679.

    • Search Google Scholar
    • Export Citation
  • [4]↑

    T. Ustunkok and M. Karakaya , “Effect of PSO tuned P, PD, and PID controllers on the stability of a quad-rotor,” in 1st International Informatics and Software Engineering Conference (UBMYK), Ankara, Turkey, 2019, pp. 1–6.

    • Search Google Scholar
    • Export Citation
  • [5]

    J. J. Castillo-Zamora , K. A. Camarillo-GóMez , G. I. PéRez-Soto , and J. RodríGuez-ReséNdiz , “Comparison of PD, PID and sliding-mode position controllers for V–tail quadcopter stability,” IEEE Access, vol. 6, pp. 38086–38096, 2018. Available: https://doi.org/10.1109/ACCESS.2018.2851223. Accessed: Jun. 28, 2018.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [6]

    H. S. Khan and M. B. Kadri , “Attitude and altitude control of quad-rotor by discrete PID control and non-linear model predictive control,” in Paper presented at the International Conference on Information and Communication Technologies (ICICT), Karachi, 2015, pp. 1–11.

    • Search Google Scholar
    • Export Citation
  • [7]

    H. Liu and G. Gao , “Dynamic modeling and analyzing for a novel X-quad-rotor,” in Paper presented at the 3rd International Conference on Computational Intelligence & Communication Technology (CICT), Ghaziabad, 2017, pp. 1–4.

    • Search Google Scholar
    • Export Citation
  • [8]↑

    K. El Hamid , M. Mjahed , A. El Kari , and H. Ayad , “Neural and fuzzy based nonlinear flight control for an unmanned quad-rotor,” Paper Presented Int. Rev. Automatic Control (IREACO), vol. 11, no. 3, 2018.

    • Search Google Scholar
    • Export Citation
  • [9]↑

    O. Doukhi , A. Fayjie , and D. Lee , “Intelligent controller design for quad-rotor stabilization in presence of parameter variations,” J. Adv. Transport., vol. 2017, p. 10, 2017.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [10]↑

    M. Algabri , H. Mathkour , M. A. Mekhtiche , M. A. Bencherif , M. Alsulaiman , M. A. Arafah , and H. Ghaleb , “Wireless vision-based fuzzy controllers for moving object tracking using a quad-rotor,” Int. J. Distributed Sensor Networks, vol. 13, no. 4, 2017.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [11]↑

    H. Housny , E. Chater , and H. ElFadil , “Fuzzy PID control tuning design using Particle Swarm optimization algorithm for a quad-rotor,” in Paper presented at the IEEE 5th International Conference on Optimization and Applications (ICOA), 2019.

    • Search Google Scholar
    • Export Citation
  • [12]

    J. Xu , Y. Ma , and J. Huang , “3D path tracking controller based on fuzzy PID optimized by PSO for quad-rotor,” in Chinese Automation Congress (CAC), 2019, pp. 3522–3527.

    • Search Google Scholar
    • Export Citation
  • [13]

    T. Liu , Y. Chen , Z. Chen , H. Wu , and L. Cheng , “Adaptive fuzzy fractional order PID control for 6-DOF quad-rotor,” in 39th Chinese Control Conference (CCC), 2020, pp. 2158–2163.

    • Search Google Scholar
    • Export Citation
  • [14]↑

    S. Bari , S. S. Zehra Hamdani , H. U. Khan , M. U. Rehman , and H. Khan , “Artificial neural network based self-tuned PID controller for flight control of quadcopter,” in International Conference on Engineering and Emerging Technologies (ICEET), 2019, pp. 1–5.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [15]

    M. Fatan , B. L. Sefidgari , and A. V. Barenji , “An adaptive neuro PID for controlling the altitude of quadcopter robot,” in 18th International Conference on Methods & Models in Automation & Robotics (MMAR), 2013, pp. 662–665.

    • Search Google Scholar
    • Export Citation
  • [16]

    S. Furukawa , S. Kondo , A. Takanishi , and H. Lim , “Radial basis function neural network based PID control for quad-rotor flying robot,” in 17th International Conference on Control, Automation Systems (ICCAS), 2017, pp. 580–584.

    • Search Google Scholar
    • Export Citation
  • [17]↑

    H. C. T. E. Fernando , A. T. A. De Silva , M. D. C. De Zoysa , K. A. D. C. Dilshan , and S. R. Munasinghe , “Modelling, simulation and implementation of a quad-rotor UAV,” in IEEE 8th International Conference on Industrial and Information Systems, 2013, pp. 207–212.

    • Search Google Scholar
    • Export Citation
  • [18]↑

    G. Jithu and P. R. Jayasree , “Quad-rotor modelling and control,” in International Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT), 2016, pp. 1167–1172.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [19]

    M. Walid , N. Slaheddine , A. Mohamed , and B. Lamjed , “Modelling, identification and control of a quad-rotor UAV,” in 15th International Multi-Conference on Systems, Signals & Devices (SSD), 2018, pp. 1017–1022.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [20]

    T. A. Ahmad , E. S. Fernando , A. K. Nashwa , K. Anis , A. Adel , J. H. Amjad , and K. I. Ibraheem , “Lagrangian dynamic model derivation and energy shaping control of non-holonomic unmanned aerial vehicles,” in Proceedings of the International Conference on Artificial Intelligence and Computer Vision (AICV2021), vol. 1377, 2021, pp. 483–493.

    • Search Google Scholar
    • Export Citation
  • [21]↑

    M. Ardema , Newton-Euler Dynamics. Springer Science and Business Media, Inc, 2005.

  • [22]↑

    Y. Chen , Y. He , and M. Zhou , “Decentralized PID neural network control for a quad-rotor helicopter subjected to wind disturbance,” J. Cent. South Univ., vol. 22, no. 1, pp. 168–179, 2015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [23]

    L. Ding and Z. Wang , “A robust control for an aerial robot quad-rotor under wind gusts,” J. Robotics, pp. 1–8, 2018.

  • [24]↑

    G. Perozzi , D. Efimov , J. Biannic , L. Planckaert , and P. Coton , “Wind estimation algorithm for quad-rotors using detailed aerodynamic coefficients,” in Annual American Control Conference (ACC), 2018, pp. 1921–1926.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [25]

    Y. Guo , B. Jiang , and Y. Zhang , “A novel robust attitude control for quad-rotor aircraft subject to actuator faults and wind gusts,” IEEE/CAA J. Automatica Sinica, vol. 5, no. 1, pp. 292–300, 2018.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [26]↑

    R. T. Palomaki , N. T. Rose , M. Van Den Bossche , T. J. Sherman , and S. F. J. De Wekker , “Wind estimation in the lower atmosphere using multirotor aircraft,” J. Atmos. Oceanic Technol., vol. 34, no. 5, pp. 1183–1191, 2017.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [27]↑

    Z. He and L. Zhao , “A simple attitude control of quad-rotor helicopter based on Ziegler-ichols rules for tuning PD parameters,” Sci. World J., vol. 2014, p. 13, 2014.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [28]↑

    K. J. Astrom and T. Hagglund , “Revisiting the Ziegler–Nichols step response method for PID control. Elsevier,” J. Process Control, vol. 14, pp. 635–650, 2004.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [1]

    G. Singhal , B. Bansod , and L. Mathew , “Unmanned aerial vehicle classification, applications and challenges: A review,” Preprints, p. 19, 2018. Available: https://doi.org/10.20944/preprints201811.0601.v1. Accessed: Nov. 27, 2018.

    • Search Google Scholar
    • Export Citation
  • [2]

    J. Ajmera and V. Sankaranarayanan , “Trajectory tracking control of a quad-rotor,” in International Conference on Control Communication & Computing India (ICCC), Trivandrum, 2015, pp. 48–53.

    • Search Google Scholar
    • Export Citation
  • [3]

    C. Wang , W. Liu , and M. Q. Meng , “Obstacle avoidance for quad-rotor using improved method based on optical flow,” in IEEE International Conference on Information and Automation, Lijiang, 2015, pp. 1674–1679.

    • Search Google Scholar
    • Export Citation
  • [4]

    T. Ustunkok and M. Karakaya , “Effect of PSO tuned P, PD, and PID controllers on the stability of a quad-rotor,” in 1st International Informatics and Software Engineering Conference (UBMYK), Ankara, Turkey, 2019, pp. 1–6.

    • Search Google Scholar
    • Export Citation
  • [5]

    J. J. Castillo-Zamora , K. A. Camarillo-GóMez , G. I. PéRez-Soto , and J. RodríGuez-ReséNdiz , “Comparison of PD, PID and sliding-mode position controllers for V–tail quadcopter stability,” IEEE Access, vol. 6, pp. 38086–38096, 2018. Available: https://doi.org/10.1109/ACCESS.2018.2851223. Accessed: Jun. 28, 2018.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [6]

    H. S. Khan and M. B. Kadri , “Attitude and altitude control of quad-rotor by discrete PID control and non-linear model predictive control,” in Paper presented at the International Conference on Information and Communication Technologies (ICICT), Karachi, 2015, pp. 1–11.

    • Search Google Scholar
    • Export Citation
  • [7]

    H. Liu and G. Gao , “Dynamic modeling and analyzing for a novel X-quad-rotor,” in Paper presented at the 3rd International Conference on Computational Intelligence & Communication Technology (CICT), Ghaziabad, 2017, pp. 1–4.

    • Search Google Scholar
    • Export Citation
  • [8]

    K. El Hamid , M. Mjahed , A. El Kari , and H. Ayad , “Neural and fuzzy based nonlinear flight control for an unmanned quad-rotor,” Paper Presented Int. Rev. Automatic Control (IREACO), vol. 11, no. 3, 2018.

    • Search Google Scholar
    • Export Citation
  • [9]

    O. Doukhi , A. Fayjie , and D. Lee , “Intelligent controller design for quad-rotor stabilization in presence of parameter variations,” J. Adv. Transport., vol. 2017, p. 10, 2017.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [10]

    M. Algabri , H. Mathkour , M. A. Mekhtiche , M. A. Bencherif , M. Alsulaiman , M. A. Arafah , and H. Ghaleb , “Wireless vision-based fuzzy controllers for moving object tracking using a quad-rotor,” Int. J. Distributed Sensor Networks, vol. 13, no. 4, 2017.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [11]

    H. Housny , E. Chater , and H. ElFadil , “Fuzzy PID control tuning design using Particle Swarm optimization algorithm for a quad-rotor,” in Paper presented at the IEEE 5th International Conference on Optimization and Applications (ICOA), 2019.

    • Search Google Scholar
    • Export Citation
  • [12]

    J. Xu , Y. Ma , and J. Huang , “3D path tracking controller based on fuzzy PID optimized by PSO for quad-rotor,” in Chinese Automation Congress (CAC), 2019, pp. 3522–3527.

    • Search Google Scholar
    • Export Citation
  • [13]

    T. Liu , Y. Chen , Z. Chen , H. Wu , and L. Cheng , “Adaptive fuzzy fractional order PID control for 6-DOF quad-rotor,” in 39th Chinese Control Conference (CCC), 2020, pp. 2158–2163.

    • Search Google Scholar
    • Export Citation
  • [14]

    S. Bari , S. S. Zehra Hamdani , H. U. Khan , M. U. Rehman , and H. Khan , “Artificial neural network based self-tuned PID controller for flight control of quadcopter,” in International Conference on Engineering and Emerging Technologies (ICEET), 2019, pp. 1–5.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [15]

    M. Fatan , B. L. Sefidgari , and A. V. Barenji , “An adaptive neuro PID for controlling the altitude of quadcopter robot,” in 18th International Conference on Methods & Models in Automation & Robotics (MMAR), 2013, pp. 662–665.

    • Search Google Scholar
    • Export Citation
  • [16]

    S. Furukawa , S. Kondo , A. Takanishi , and H. Lim , “Radial basis function neural network based PID control for quad-rotor flying robot,” in 17th International Conference on Control, Automation Systems (ICCAS), 2017, pp. 580–584.

    • Search Google Scholar
    • Export Citation
  • [17]

    H. C. T. E. Fernando , A. T. A. De Silva , M. D. C. De Zoysa , K. A. D. C. Dilshan , and S. R. Munasinghe , “Modelling, simulation and implementation of a quad-rotor UAV,” in IEEE 8th International Conference on Industrial and Information Systems, 2013, pp. 207–212.

    • Search Google Scholar
    • Export Citation
  • [18]

    G. Jithu and P. R. Jayasree , “Quad-rotor modelling and control,” in International Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT), 2016, pp. 1167–1172.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [19]

    M. Walid , N. Slaheddine , A. Mohamed , and B. Lamjed , “Modelling, identification and control of a quad-rotor UAV,” in 15th International Multi-Conference on Systems, Signals & Devices (SSD), 2018, pp. 1017–1022.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [20]

    T. A. Ahmad , E. S. Fernando , A. K. Nashwa , K. Anis , A. Adel , J. H. Amjad , and K. I. Ibraheem , “Lagrangian dynamic model derivation and energy shaping control of non-holonomic unmanned aerial vehicles,” in Proceedings of the International Conference on Artificial Intelligence and Computer Vision (AICV2021), vol. 1377, 2021, pp. 483–493.

    • Search Google Scholar
    • Export Citation
  • [21]

    M. Ardema , Newton-Euler Dynamics. Springer Science and Business Media, Inc, 2005.

  • [22]

    Y. Chen , Y. He , and M. Zhou , “Decentralized PID neural network control for a quad-rotor helicopter subjected to wind disturbance,” J. Cent. South Univ., vol. 22, no. 1, pp. 168–179, 2015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [23]

    L. Ding and Z. Wang , “A robust control for an aerial robot quad-rotor under wind gusts,” J. Robotics, pp. 1–8, 2018.

  • [24]

    G. Perozzi , D. Efimov , J. Biannic , L. Planckaert , and P. Coton , “Wind estimation algorithm for quad-rotors using detailed aerodynamic coefficients,” in Annual American Control Conference (ACC), 2018, pp. 1921–1926.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [25]

    Y. Guo , B. Jiang , and Y. Zhang , “A novel robust attitude control for quad-rotor aircraft subject to actuator faults and wind gusts,” IEEE/CAA J. Automatica Sinica, vol. 5, no. 1, pp. 292–300, 2018.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [26]

    R. T. Palomaki , N. T. Rose , M. Van Den Bossche , T. J. Sherman , and S. F. J. De Wekker , “Wind estimation in the lower atmosphere using multirotor aircraft,” J. Atmos. Oceanic Technol., vol. 34, no. 5, pp. 1183–1191, 2017.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [27]

    Z. He and L. Zhao , “A simple attitude control of quad-rotor helicopter based on Ziegler-ichols rules for tuning PD parameters,” Sci. World J., vol. 2014, p. 13, 2014.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [28]

    K. J. Astrom and T. Hagglund , “Revisiting the Ziegler–Nichols step response method for PID control. Elsevier,” J. Process Control, vol. 14, pp. 635–650, 2004.

    • Crossref
    • Search Google Scholar
    • Export Citation
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Cover International Review of Applied Sciences and Engineering
International Review of Applied Sciences and Engineering
Print ISSN:
2062-0810
Online ISSN:
2063-4269

Senior editors

Editor-in-Chief: Ákos, Lakatos, University of Debrecen, Hungary

Founder, former Editor-in-Chief (2011-2020): Ferenc Kalmár, University of Debrecen, Hungary

Founding Editor: György Csomós, University of Debrecen, Hungary

Associate Editor: Derek Clements Croome, University of Reading, UK

Associate Editor: Dezső Beke, University of Debrecen, Hungary

Editorial Board

  • Mohammad Nazir AHMAD, Institute of Visual Informatics, Universiti Kebangsaan Malaysia, Malaysia

    Murat BAKIROV, Center for Materials and Lifetime Management Ltd., Moscow, Russia

    Nicolae BALC, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

    Umberto BERARDI, Toronto Metropolitan University, Toronto, Canada

    Ildikó BODNÁR, University of Debrecen, Debrecen, Hungary

    Sándor BODZÁS, University of Debrecen, Debrecen, Hungary

    Fatih Mehmet BOTSALI, Selçuk University, Konya, Turkey

    Samuel BRUNNER, Empa Swiss Federal Laboratories for Materials Science and Technology, Dübendorf, Switzerland

    István BUDAI, University of Debrecen, Debrecen, Hungary

    Constantin BUNGAU, University of Oradea, Oradea, Romania

    Shanshan CAI, Huazhong University of Science and Technology, Wuhan, China

    Michele De CARLI, University of Padua, Padua, Italy

    Robert CERNY, Czech Technical University in Prague, Prague, Czech Republic

    Erdem CUCE, Recep Tayyip Erdogan University, Rize, Turkey

    György CSOMÓS, University of Debrecen, Debrecen, Hungary

    Tamás CSOKNYAI, Budapest University of Technology and Economics, Budapest, Hungary

    Anna FORMICA, IASI National Research Council, Rome, Italy

    Alexandru GACSADI, University of Oradea, Oradea, Romania

    Eugen Ioan GERGELY, University of Oradea, Oradea, Romania

    Janez GRUM, University of Ljubljana, Ljubljana, Slovenia

    Géza HUSI, University of Debrecen, Debrecen, Hungary

    Ghaleb A. HUSSEINI, American University of Sharjah, Sharjah, United Arab Emirates

    Nikolay IVANOV, Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia

    Antal JÁRAI, Eötvös Loránd University, Budapest, Hungary

    Gudni JÓHANNESSON, The National Energy Authority of Iceland, Reykjavik, Iceland

    László KAJTÁR, Budapest University of Technology and Economics, Budapest, Hungary

    Ferenc KALMÁR, University of Debrecen, Debrecen, Hungary

    Tünde KALMÁR, University of Debrecen, Debrecen, Hungary

    Milos KALOUSEK, Brno University of Technology, Brno, Czech Republik

    Jan KOCI, Czech Technical University in Prague, Prague, Czech Republic

    Vaclav KOCI, Czech Technical University in Prague, Prague, Czech Republic

    Imre KOCSIS, University of Debrecen, Debrecen, Hungary

    Imre KOVÁCS, University of Debrecen, Debrecen, Hungary

    Angela Daniela LA ROSA, Norwegian University of Science and Technology, Trondheim, Norway

    Éva LOVRA, Univeqrsity of Debrecen, Debrecen, Hungary

    Elena LUCCHI, Eurac Research, Institute for Renewable Energy, Bolzano, Italy

    Tamás MANKOVITS, University of Debrecen, Debrecen, Hungary

    Igor MEDVED, Slovak Technical University in Bratislava, Bratislava, Slovakia

    Ligia MOGA, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

    Marco MOLINARI, Royal Institute of Technology, Stockholm, Sweden

    Henrieta MORAVCIKOVA, Slovak Academy of Sciences, Bratislava, Slovakia

    Phalguni MUKHOPHADYAYA, University of Victoria, Victoria, Canada

    Balázs NAGY, Budapest University of Technology and Economics, Budapest, Hungary

    Husam S. NAJM, Rutgers University, New Brunswick, USA

    Jozsef NYERS, Subotica Tech College of Applied Sciences, Subotica, Serbia

    Bjarne W. OLESEN, Technical University of Denmark, Lyngby, Denmark

    Stefan ONIGA, North University of Baia Mare, Baia Mare, Romania

    Joaquim Norberto PIRES, Universidade de Coimbra, Coimbra, Portugal

    László POKORÁDI, Óbuda University, Budapest, Hungary

    Roman RABENSEIFER, Slovak University of Technology in Bratislava, Bratislava, Slovak Republik

    Mohammad H. A. SALAH, Hashemite University, Zarqua, Jordan

    Dietrich SCHMIDT, Fraunhofer Institute for Wind Energy and Energy System Technology IWES, Kassel, Germany

    Lorand SZABÓ, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

    Csaba SZÁSZ, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

    Ioan SZÁVA, Transylvania University of Brasov, Brasov, Romania

    Péter SZEMES, University of Debrecen, Debrecen, Hungary

    Edit SZŰCS, University of Debrecen, Debrecen, Hungary

    Radu TARCA, University of Oradea, Oradea, Romania

    Zsolt TIBA, University of Debrecen, Debrecen, Hungary

    László TÓTH, University of Debrecen, Debrecen, Hungary

    László TÖRÖK, University of Debrecen, Debrecen, Hungary

    Anton TRNIK, Constantine the Philosopher University in Nitra, Nitra, Slovakia

    Ibrahim UZMAY, Erciyes University, Kayseri, Turkey

    Andrea VALLATI, Sapienza University, Rome, Italy

    Tibor VESSELÉNYI, University of Oradea, Oradea, Romania

    Nalinaksh S. VYAS, Indian Institute of Technology, Kanpur, India

    Deborah WHITE, The University of Adelaide, Adelaide, Australia

International Review of Applied Sciences and Engineering
Address of the institute: Faculty of Engineering, University of Debrecen
H-4028 Debrecen, Ótemető u. 2-4. Hungary
Email: irase@eng.unideb.hu

Indexing and Abstracting Services:

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2023  
Scimago  
Scimago
H-index		 11
Scimago
Journal Rank		 0.249
Scimago Quartile Score Architecture (Q2)
Engineering (miscellaneous) (Q3)
Environmental Engineering (Q3)
Information Systems (Q4)
Management Science and Operations Research (Q4)
Materials Science (miscellaneous) (Q3)
Scopus  
Scopus
Cite Score		 2.3
Scopus
CIte Score Rank		 Architecture (Q1)
General Engineering (Q2)
Materials Science (miscellaneous) (Q3)
Environmental Engineering (Q3)
Management Science and Operations Research (Q3)
Information Systems (Q3)		  
Scopus
SNIP		 0.751


International Review of Applied Sciences and Engineering
Publication Model Gold Open Access
Online only
Submission Fee none
Article Processing Charge 1100 EUR/article
Regional discounts on country of the funding agency World Bank Lower-middle-income economies: 50%
World Bank Low-income economies: 100%
Further Discounts Limited number of full waivers available. Editorial Board / Advisory Board members: 50%
Corresponding authors, affiliated to an EISZ member institution subscribing to the journal package of Akadémiai Kiadó: 100%
Subscription Information Gold Open Access

International Review of Applied Sciences and Engineering
Language English
Size A4
Year of
Foundation		 2010
Volumes
per Year		 1
Issues
per Year		 3
Founder Debreceni Egyetem
Founder's
Address		 H-4032 Debrecen, Hungary Egyetem tér 1
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 2062-0810 (Print)
ISSN 2063-4269 (Online)

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Oct 2024 0 249 10
Nov 2024 0 319 11
Dec 2024 0 292 7
Jan 2025 0 85 6
Feb 2025 0 165 5
Mar 2025 0 155 5
Apr 2025 0 0 0