International Journal of Electrical and Computer Engineering (IJECE) Vol.
No.
June 2025, pp.
ISSN: 2088-8708.
DOI: 10.
11591/ijece.
Enhancing linear quadratic regulator and proportional-integral linear quadratic regulator controllers for photovoltaic systems Mohamed Assabaa1,3.
Adel Bouchahed2,3.
Abdellah Draidi3.
Boudjemaa Mehimmedetsi4.
Ahmed Belhani2 Laboratoire de Traitement de Signal.
Department of Electronics.
Faculty of Science and Technology.
University of Constantine 1.
Constantine.
Algeria Laboratoire Satellites Intelligence Artificielle Cryptographie et Internet des Objets.
Department of Electronics.
Faculty of Science and Technology.
University of Constantine 1.
Constantine.
Algeria Electromechanical Department.
Institute of Science and Applied Techniques.
University of Constantine 1.
Constantine.
Algeria Electromechanical Department.
Institute of Science and Technology.
Abdelhafid Boussouf University Center.
Mila.
Algeria
Article Info
ABSTRACT
Article history:
This article introduces the linear quadratic regulator (LQR) control and the hybrid linear quadratic regulator proportional-integral (LQR-PI) control, both applied to a photovoltaic system coupled with a DC-DC boost The converter outputs direct current electrical energy to power direct loads.
Two robust control correctors, based on the LQR and LQR-PI methods, are designed to enhance the static and dynamic performance of the PV DC-DC boost system.
These controllers aim to minimize oscillations and overshoots while ensuring stability across varying solar conditions, thereby optimizing operation around the maximum power point.
The disturb and observe maximum power point tracking (MPPT) technique, integrated with the LQR and LQR-PI controllers, ensures system functionality under The novelty of this work lies in the development of a MATLAB control block diagram capable of regulating the reference voltage provided by the perturb and observe (P&O) MPPT algorithm.
MATLAB
simulations demonstrate the robustness and high performance of the LQR and LQR-PI controllers, validating the efficacy of this boost converter control strategy.
Received Sep 4, 2024 Revised Dec 15, 2024 Accepted Jan 16, 2025 Keywords:
DC-DC boost converter LQR and LQR-PI corrector
P&O MPPT
Photovoltaic panel PV PWM control This is an open access article under the CC BY-SA license.
Corresponding Author:
Mohamed Assabaa Laboratoire de Traitement de Signal.
Department of Electronics.
Faculty of Science and Technology.
University of Constantine 1 Constantine.
Algeria Electromechanical Department.
Institute of Science and Applied Techniques.
University of Constantine 1 Constantine.
Algeria Email: mohamed.
assabaa@umc.
INTRODUCTION
Photovoltaic (PV) systems are increasingly being adopted as a viable solution for harnessing solar energy, especially in isolated areas where access to centralized electricity networks is unavailable.
However, these systems encounter notable challenges due to the irregular availability of sunlight, resulting in variations in voltage, current, and power output.
To mitigate these issues, maximum power point tracking (MPPT) techniques are commonly employed to optimize energy capture under fluctuating conditions.
Furthermore, advanced control strategies, such as proportional-integral (PI), linear quadratic regulator (LQR), and model predictive control, have been explored to enhance operational stability and overall system performance.
Journal homepage: http://ijece.
ISSN: 2088-8708
Despite these advancements.
PV systems often struggle with inefficiencies, including power oscillations, slow response times, and diminished performance under dynamic environmental factors.
This study aims to address these challenges by enhancing the performance of PV-DC-to-DC boostconverter systems through the implementation of advanced control techniques.
A hybrid control approach is developed, combining LQR and proportional-integral (LQR-PI) methods with the perturb and observe (P&O) MPPT algorithm, to achieve improved static and dynamic responses.
This approach focuses on minimizing power fluctuations and improving stability during variations in solar irradiance, ensuring efficient and reliable operation.
These improvements are particularly vital for regions like the southern Mediterranean, including Algeria, where dependable solar energy solutions are critical for supporting applications such as agriculture and irrigation.
The outcomes of this research contribute to advancing PV system control methodologies, fostering greater adoption and optimized use of solar power in practical applications.
In the subsequent paragraphs, a compilation of pertinent literature highlighting these research efforts will be The study presents an analysis, design, and implementation of nonlinear controllers tailored for the fundamental negative super lift Luo-converter, a direct current-direct current (DC-to-DC) converter featuring advanced topology.
To enhance dynamic load voltage analysis and current control within the coil of the fundamental negative super lift Luo-converter (FNSLLC), a linear quadratic regulator (LQR) and a fuzzy logic controller are devised.
The LQR controller governs the current passing through the coil within the inner servo loop, while the FLC controller controls the load voltage in the outer voltage loop.
The efficacy of employing LQR alongside FLC in optimizing FNSLLC performance is validated through various run tests conducted using MATLAB/Simulink and a programmable prototype on board (FPGA) .
An LQR is employed to control a hybrid power system comprising an ultracapacitor for energy storage and a wind power system.
The primary objective of this control scheme is to regulate the direct current bus voltage to a predefined level while maximizing the extraction of available wind energy.
Through extensive testing across various scenarios, encompassing both simulations and experiments, the efficacy of the proposed LQR controllers is demonstrated.
They exhibit robustness by accurately tracking voltage and current references, swiftly restoring the system to its nominal operating state under diverse conditions, including fluctuations in wind speed and load demand .
A combination of a LQR and a Kalman filter (KF) is employed to regulate the output parameters of a buck-boost converter and mitigate disturbances.
This control methodology is applied in conjunction with a solar panel system.
The outcomes of the study indicate that the proposed controller effectively manages the adjustment of output quantities of the DC-to-DC converter and facilitates accurate tracking of the maximum power point .
The study introduces a novel control technique utilizing the LQR method in single-phase grid-connected photovoltaic systems.
Compared to the backstepping method, the LQR technique demonstrates greater resilience to sudden changes and disturbances, resulting in reduced overshoot.
Simulation outcomes underscore the robustness of the LQR control across diverse weather conditions, affirming its effectiveness in photovoltaic system regulation .
A design of X DC-to-DC converter incorporating an optimal LQR controller along with integrated gain action results in high stability across different output characteristics of the DC-DC converter .
A robust control strategy for a DC-DC boost converter, utilizing a LQR and leveraging the potential of linear matrix inequalities (LMI.
, guarantees high stability across various simulation results .
In the system, a P&O algorithm-based MPPT technique serves as an external loop controller, managing the reference voltage required by the LQR controller.
This setup, compared to the PI controller, demonstrates superior performance and robustness.
Overall, the system effectively tracks the maximum power point, yielding satisfactory results .
To reach average power and stand-alone operation through the integration of a DC-to-DC boostconverter into fuel cells (FC), a LQR is developed for controlling the power converter's parameters.
However, in practical applications, the classic LQR may introduce an offset in the output voltage due to the effective series resistance (ESR) of the output capacitor.
To address this issue and enhance system performance, two modifications are proposed: the m-LQR controller, which minimizes the impact of ESR, and the M-LQR controller, which regulates the inductor current.
Both modifications yield superior results compared to the classic LQR controller .
In another application aimed at enhancing power supply quality and controlling power flow between a PV system and a non-linear load, a LQR is employed to mitigate power quality degradation in the grid, especially during climate variations.
The effectiveness of this approach is validated using the MATLAB/Simulink environment .
In a PV-wind hybrid water pumping system, the energy sources are linked via a multi-input DC-toDC converter, with its output directly connected to a DC motor pump, bypassing the need for a battery bank.
To enhance system performance, a linear quadratic Gaussian (LQG) controller with loop transfer recover regulator (LQG/LTR), in combination with a regulator LQR, is implemented.
This configuration enables the Int J Elec & Comp Eng.
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system to achieve high static and dynamic performance.
Simulation results demonstrate the robustness of the controller when applied to the system .
In a separate study, a nonlinear observer is developed based on both sliding mode controller (SMC) and extended Kalman filter (EKF).
These observers utilize a process model to facilitate the operation of a system comprising a DC-to-DC boost-converter integrated with a fuel cell system.
The integrated controlled system operates without voltage drop, maintaining stability compared to a traditional PI controller.
The Findings are validated using the MATLAB/Simulink simulations .
This article explores two distinct control techniques utilized for a DC-to-DC boost photovoltaicconverter system.
The first technique combines a P&O-MPPT with linear quadratic regulator control.
The second technique integrates the P&O-MPPT technique with proportional-integral linear quadratic regulator Both approaches aim to regulate the voltage and current output of the converter directly.
However, the performance of these output characteristics varies between the two methods.
Our contribution involves the design of an MPPT approach using the P&O method, combined with LQR-PI control.
We achieve this by integrating a proportional integral (PI) corrector into a voltage servo loop, where the reference voltage is derived from a mathematical equation.
This enhancement enables the system to operate with reduced oscillations and disturbances during changes in illumination compared to conventional LQR control methods.
We conducted simulations of these control techniques using the MATLAB environment, varying irradiances applied to the DC-to-DC boost photovoltaic system to assess their performance.
Table 1 is a nomenclature table that defines the various acronyms and abbreviations used throughout this article.
It ensures clarity by providing concise explanations of key terms and symbols.
This reference aids in understanding the concepts and control strategies discussed.
Table 1.
Nomenclature Abbreviation FNSLLC
FLC
FPGA
LMIs
MPPT
P&O
ESR
m-LQR
M-LQR
MIC
LQG/LTR
SMC
EKF
P&O MPPT
LQR-PI
LQR
DC-DC
PWM
ycyecye yeOyecye yc Meaning Solar panel Fundamental negative super lift Luo-converter Fuzzy logic controller Electronic programming card Continuous-continuous Direct current Kalman filter Linear matrix inequalities Maximum power point tracking Fuel cell Perturb and observe Effective series resistance Modifications-linear quadratic regulator Modifications-linear quadratic regulator Multi-input DC-DC converter Linear quadratic Gaussian control improved with loop transfer recovery Sliding mode controller Extended Kalman filter Proportional integral controller Perturb and observe maximum power point tracking Linear quadratic regulatorAeproportional integral Linear quadratic regulator Direct current-direct current Pulse width modulation Photovoltaic panel output voltage (V) Photovoltaic panel output current (A) Diode Abbreviation Meaning PV power .
ycEycyyc MOSFET switch ycIycO Parallels modules ycAycy yaycycayc Saturation of solar cells in dark current (A) Resistance in series () ycIycyce Parallel resistance () ycIycyyce ycAyc Series modules ya0yc The current of reverse saturation Actual temperature ycN CellAos reference temperature (C) ycN0 yc Electron charge (C) yaya Tape space (W/m.
ya BoltzmannAos constant (J/K) yca Ideality factor Temperature coefficient yaycn short circuit current yaycayca ya, yayc yaycyEa ya yaycnycu yc yaycE yaya ycOyccyca yayccyca ycI yaycuycyc Solar and reference radiation (W/m.
Photocurrent (A) Inductor (H) Capacitor at boost input (F) switch control signal Proportional Gain integral gain DC bus voltage (V) DC bus current .
Load resistance .
boost output capacitor .
uNy.
SYSTEM DESCRIPTION The system presented in this work is comprised of a photovoltaic panel connected to a DC-to-DC boost converter, supplying power to a resistive load, as illustrated in Figure 1.
The photovoltaic generator produces voltage and current, which are fed into the terminals of the DC-to-DC boost-converter.
The converter then elevates the voltage from the photovoltaic generator to an suitable level based on the input supply voltage's amplitude.
The controllers utilized in this study are designed to operate the PV-boost system at its MPPT, thereby enhancing the static performance of the photovoltaic system coupled with a boost DC-to-DC converter.
Enhancing linear quadratic regulator and proportional-integral linear A (Mohamed Assaba.
A ISSN: 2088-8708 yeo Irradiance ( y.
Boost yea Panel Temperature (Deg.
ycOycuycyc
Converter ycOycyyc
Gate pulse ycnycyyc
PWM
MPPT
ycyeeyeIyeN
ycOycyyc
LQR-PI
LQR
yce Figure 1.
Photovoltaic system connected to a DC-to-DC boost-converter Mathematical model of photovoltaic system and boost-converter Figure 2 presents the application of two different control strategies for a DC-DC boost converter.
These techniques are implemented within a photovoltaic system.
The figure highlights the distinct approaches and their integration into the system.
Figure 2.
Structural diagram of the LQR and LQR-PI control utilized for the boost converter associated with a PV panel From the diagram in Figure 2, the equations governing the behavior of the photovoltaic (PV) panel and boost converter are derived.
These equations capture the system's dynamics and interactions.
They form the basis for analyzing the performance of the system as follow: The mathematical model governing the operation of the photovoltaic system, as proposed by several researchers .
Ae.
, can be expressed as .
yaycyyc( = ycAycy yaycyEa Oe ycAycy yaycycayc .
ceycuycy ( ycA ycy yc.
cOycyyc ycA yc yaycyyc ycIycyce ) yca ya ycN ycuyc ) Oe .
Oe ycA ycy ycAyc ycI ycAycEa ycyyce ycOycyyc ycA yc yaycyyc ycIycyce .
ycN 3 ycyaya ycN0 ya yca .
yaycycayc = yaycycaycyc ( ) yceycuycy [ Oe ]] ycN Int J Elec & Comp Eng.
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yaycyEa = .
aycayca yaycn .
cN Oe .
] ya yayc The mathematical expressions that describe the functioning of the boost-converter are detailed below .
Ae.
when the ycIyc is in the closed position and the diode D is reverse-biased, during the interval yc OO .
0 , t 0 dT ], the following equations apply:
ya ya yccycnyco = ycOycEycO = Oe yccyca ycI when the ycIyc is in the open state and the diode D is forward-biased, during the interval yc OO .
0 dT, t 0 T ], the following equations are obtained:
ya ya yccycnyco = ycOycEycO Oe ycOyccyca = ycnyco Oe yccyca ycI The dynamic model of the boost-converter under continuous conduction operation are presented as .
ya ya yccycnya = ycOycEycO Oe ycOyccyca .
Oe y.
yccycOyccyca = ycnya .
Oe y.
Oe yccyca with u define the control signal of IGBT.
We set: ycu1 = ycnya and ycu2 = ycOyccyca then .
ycuN1 = ycuN 2 = ycOycEycO ya Oe Oey.
Oey.
ya Oe ycIya The complete system parameters consist of the coil inductance L [H], the capacitor capacitance C [F] and the load resistance R [].
The state variables are defined by the coil current and the capacitor voltage.
The control signal u takes values from the set .
, representing the state of the switch Sw: 0 for open and 1 for closed.
This control signal can be replaced by its average value over a chopping period, denoted as d, which represents the duty cycle ycc = ycNycuycu /ycNyc , where Ton is the conduction time and Ts is the chopping period.
The set of equations given by .
can be expressed in a state-space representation as .
Oeyc.
ya ya ] ycOycyyc [ 1 ] = [.
Oeyc.
ycuN 2 ya yc = .
ycIya cO ] yccyca The system is linearized around an equilibrium point with .
ycuN = 0 0 = yaycU yaAycO ycU = OeyaOe1 yaAycO ycu = ycU ycuE ycc = ya yccE { ycnya = yaya ycnEya Enhancing linear quadratic regulator and proportional-integral linear A (Mohamed Assaba.
A ISSN: 2088-8708 From .
, we can derive the linear model of the system .
, .
, .
ycnENya [ N ] = [.
Oey.
ycOEyccyca ya ycE = [ .
Oey.
ya ycIya ycOyccyca ycnEya ] [ E ] [ ya .
yccE [ ya ] ycOE
ycOyccyca
ya 1 ycnEya
][ ]
0 ycOEyccyca Constitution of the MPPT perturb and observe algorithm The P&O method for MPPT is analyzed in numerous studies, such as those cited in .
Ae.
This technique uses the voltage and current outputs from the PV system as key variables.
By utilizing these variables, the power at the current time ycy.
and at the previous time step ycy.
c Oe .
can be computed.
Figure 3 illustrates the P&O technique, which is designed to identify the maximum power point.
Figure 3 depicts a PV system connected to a boost converter, which is regulated using the P&O MPPT algorithm.
This method is compared against a ramp-shaped carrier signal to produce pulse-width modulation (PWM).
The PV panelAos behavior is modeled in MATLAB Simulink using .
, which account for parameters such as variable irradiance, temperature, and the arrangement of cells in series and These factors collectively enhance the voltage and current output of the PV module.
The boost converterAos output voltage is subsequently supplied to a resistive load.
Figure 3.
P&O algorithm
DESIGN OF THE LQR AND LQR-PI CONTROL LAW
Using the equations governing the boost-converter, we can develop a control law utilizing the LQR method and a hybrid LQR-PI control, expressed through state equations:
ycuN = yaycu.
yaAyc.
yc = yaycu.
with: x, u, y.
B and C are respectively: state vector, input vector, output vector, state matrix, control matrix, and the output matrix.
To achieve high static and dynamic performance in controlling the boost converter, we represent the system described by state .
in the configuration of a closed-loop system as showed in Figure 4:
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Figure 4.
The main configuration of the LQR corrector In which K represent the gain matrix, and control vector is given by .
= Oeya.
To enhance the efficiency of the boost-converter control, we employ the infinite horizon L-Q-R theory, using the following criterion .
Ae.
ya= O O .
cu ycN .
ycEycu.
ycycN .
ycIyc.
)yccyc .
when the control is time-invariant and linear, the control law simplifies to a constant state feedback, where K is derived from .
, and ycE is defined in the Riccati equation in algebraic form:
ya yaycN ycE.
Oe ycE.
yaAycIOe1 yaAycN ycE.
ycE = 0 with Q Ou 0 and R > 0 exhibit symmetry in their matrix form.
For the stabilization of our system, state feedback control theory is applied with an optimal control approach, which induces a closed-loop system:
= OeycI Oe1 yaAycN ycEycu.
where The matrix ycE, satisfying the Riccati algebraic equation, remains asymptotically stable under the following conditions: the pair .
a, yaA} satisfies the controllability condition, while the pair .
OoycE} is Additionally.
P is positive if and only if the pair .
OoycE} is fully visible.
Accordingly, full set of eigenvalues associated with the matrix .
a Oe yaAycIOe1 yaAycN ycE] will have negative real parts.
Figure 5 illustrates the L-Q-R and L-Q-R-PI control laws, with the PI corrector expressed as .
yc yc.
= yaycy yce.
yaya O0 yce.
where yaycy is the proportional gain and yaya is the integral gain.
Figure 5.
Block diagram of the LQR and LQR-PI control Enhancing linear quadratic regulator and proportional-integral linear A (Mohamed Assaba.
A ISSN: 2088-8708
RESULTS AND DISCUSSION
The mathematical models for the PV system and DC-to-DC boost-converter are presented in a block diagram format.
The PV system operates under variable illumination of .
W/m 2 and a temperature of 25 AC.
These models capture the system's behavior and performance under these conditions.
To generate different results, the DC-to-DC boost-converter parameters are specified in Table 2.
The study highlights the benefits of LQR and LQR-PI control strategies in improving the performance of a PVpowered DC-to-DC boost-converter.
These techniques are shown to enhance system operation under changing illumination levels.
The results demonstrate significant performance improvements in such dynamic conditions.
Figure 6 illustrates how the voltage, current, and power at the output of the PV panel vary with changes in illumination and temperature.
Specifically, at an illumination level of 1000 W/mA, the PV power Ppv is 147 Watts.
This power decreases as illumination drops, reaching 35 Watts at 200 W/mA.
The voltage characteristic, as a function of time, ranges between 34.
5 and 38.
3 Volts, depending on the applied Additionally, the shape of the Ipv current waveform changes with variations in illumination.
G = 1000 W/mA, the Ipv current is 4.
2 Amperes.
Figure 7 shows the Vdc voltages applied across the resistive load, controlled by two different The blue curve represents the Vdc voltage achieved with the LQR-PI control method, while the red curve corresponds to the LQR technique.
The LQR-PI method demonstrates superior response time and reduced overshoot compared to the LQR method.
The Vdc voltage using the L-Q-R-PI technique effectively tracks changes in illumination, reaching up to 55 Volts for an illumination of 1000 W/mA.
Figure 8 presents the current characteristics.
The Idc current controlled by the LQR-PI technique exhibits better response time, stability, and minimal overshoot compared to the LQR method.
The Idc current also accurately follows changes in illumination, reaching up to 7.
8 Amperes for an illumination of 1000 W/mA.
Figure 9 illustrates the variation in power delivered at the output of the DC-to-DC boost-converter.
The power closely follows changes in illumination applied to the PV system.
The blue curve represents the power achieved using the LQR-PI method, which demonstrates superior response time and reduced overshoot compared to the LQR method.
With the LQR-PI technique, the maximum direct current power Pdc reaches 430 W for an illumination of 1000 W/mA, whereas the LQR method achieves a maximum of 400 W.
Figure 10 displays the pulses generated by the PWM technique applied to the MOSFET.
The MATLAB simulation results across the various figures indicate the robustness and stability of the L-Q-R-PI control compared to the LQR control technique.
The LQR-PI method delivers more stable performance with fewer oscillations, overshoots, and disturbances across the illumination range from 200 to 1000 W/mA.
Table 2.
Estimated specifications of the DC-to-DC boost converter Parameters DC voltage at the input ycycyc Frequency of switching yeNyei Load resistor yc Boost converter Inductor yc Boost converter Capacitor ycyeOyea = ycyeayenyei Output DC voltage ycyeIyeE ycyec ycyc Estimated parameters .
5 Oe 38.
ycO 20 ycoyayc 01ya 0000299 ya .
Oe .
ycO Ppv Power (Wat.
Vpv Voltage (V) Ipv Current (A) Ppv (Wat.
Ipv (A) Vpv (V) 200 W/m2 800 W/m2 400 W/m2 1000 W/m2 600 W/m2 Time .
Figure 6.
Photovoltaic panel characteristics when changing illumination Int J Elec & Comp Eng.
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Vdc P&O MPPT LQR-PI (V) Vdc P&O MPPT LQR (V) Vdc Voltage (V) 200 w/m2 600 w/m2 400 w/m2 800 w/m2 1000 w/m2 Time.
Figure 7.
Voltage characteristics for different control techniques when changing illumination Idc Current (A) 200 w/m2 400 w/m2 600 w/m2 800 w/m2 1000 w/m2 Idc P&O MPPT LQR (A) Idc P&O MPPT LQR-PI Time .
Figure 8.
Current characteristics for different control techniques when changing illumination Pdc Power .
200 w/m2 400 w/m2 800w/m2 600 w/m2 1000 w/m2 Pdc P&O MPPT LQR .
Pdc P&O MPPT LQR-PI .
Time .
Figure 9.
Boost converter output power characteristics for different control techniques when changing Pulse Signal Time .
Figure 10.
PWM control signal Enhancing linear quadratic regulator and proportional-integral linear A (Mohamed Assaba.
A ISSN: 2088-8708 The results confirm that the LQR-PI control technique significantly outperforms the conventional LQR method in enhancing dynamic performance, power conversion efficiency, and system stability.
Specifically.
LQR-PI achieves faster response times and minimizes overshoot, ensuring stable and efficient operation under varying illumination conditions.
Additionally, the higher output power achieved with LQRPI control demonstrates its effectiveness in maximizing energy extraction from the PV system.
Furthermore, the reduced oscillations and improved tracking of voltage and current highlight the ability of LQR-PI to better handle the nonlinear and dynamic behavior of PV systems, making it a robust solution for improving overall system performance.
CONCLUSION
The study highlights the advantages of LQR-PI control in improving the performance of PV-powered DC-to-DC boost-converters, particularly in terms of response time, stability, and power output.
In order to improve the static and dynamic performances of the PV-DC-to-DC boost-converter system, the LQR-PI control and the LQR control play a significant role in removing oscillations and fluctuations in the system's various properties of the system especially when changing the illumination.
These two previously mentioned techniques are associated with the P&O-MPPT technique.
The LQR-PI control algorithm combined with the P&O-MPPT algorithm provides robust and highperformance operation for the PV-boost system in response to changes in irradiance.
It outperforms the LQR control strategy, which experiences some oscillations and overshoots during illumination changes.
Simulation results obtained in the MATLAB environment validate the effectiveness and robustness of both control techniques when applied to the photovoltaic system DC-to-DC boost-converter.
While the findings confirm the robustness and efficacy of the proposed method, further experimental validation and broader comparisons are necessary to generalize these results to real-world systems.
FUNDING INFORMATION
Authors state no funding involved.
AUTHOR CONTRIBUTIONS STATEMENT
This journal uses the Contributor Roles Taxonomy (CRediT) to recognize individual author contributions, reduce authorship disputes, and facilitate collaboration.
Name of Author Mohamed Assabaa Adel Bouchahed Abdellah Draidi Boudjemaa Mehimmedetsi Ahmed Belhani C : Conceptualization M : Methodology So : Software Va : Validation Fo : Formal analysis ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue I : Investigation R : Resources D : Data Curation O : Writing - Original Draft E : Writing - Review & Editing ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue ue Vi : Visualization Su : Supervision P : Project administration Fu : Funding acquisition CONFLICT OF INTEREST STATEMENT Authors state no conflict of interest.
DATA AVAILABILITY
The authors confirm that the data supporting the findings of this study are available within the Int J Elec & Comp Eng.
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REFERENCES