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Fractal Fract
Volume 10
Issue 2
10.3390/fractalfract10020084
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Article

HIL Implementation of Proposed Fractional-Order Linear-Quadratic-Integral Controller for PV-Module Voltage Regulation to Enhance the Classical Perturb and Observe Algorithm

by
Noureddine Bouarroudj
1,
Abdelkader Lakhdari
1,
Djamel Boucherma
2,
Abdelhamid Djari
3,
Yehya Houam
1,
Vicente Feliu-Batlle
4,
Maamar Bettayeb
5,
Boualam Benlahbib
1,
Rasheed Abdulkader
6,*,
Walied Alfraidi
6 and
Hassan M. Hussein Farh
6,*
1
Unité de Recherche Appliquée en Energies Renouvelables (URAER), Centre de Développement Des Energies Renouvelables (CDER), Ghardaia 47133, Algeria
2
Research Center in Industrial Technologies (CRTI), Cheraga 16014, Algeria
3
Electrical Engineering Department, Echahid Cheikh Larbi Tebessi University, Tebessa 12022, Algeria
4
School of Industrial Engineering, Instituto de Investigaciones Energéticas y Aplicaciones Industriales, University of Castilla-La Mancha, Av. Camilo Jose Cela, S/N, 13001 Ciudad Real, Spain
5
Electrical Engineering Department, College of Engineering, University of Sharjah, Sharjah 27272, United Arab Emirates
6
Department of Electrical Engineering, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
*
Authors to whom correspondence should be addressed.
Fractal Fract. 2026, 10(2), 84; https://doi.org/10.3390/fractalfract10020084
Submission received: 18 November 2025 / Revised: 20 January 2026 / Accepted: 21 January 2026 / Published: 26 January 2026
(This article belongs to the Special Issue Fractional-Order Dynamics and Control in Green Energy Systems)
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Abstract

This paper addresses the limitations of conventional single-stage direct-control maximum power point tracking (MPPT) methods, such as the Perturb and Observe (P&O) algorithm. Fixed-step-size duty-cycle perturbations cause a trade-off between slow tracking with small oscillations and fast tracking with large oscillations, along with poor responsiveness to rapid weather variations and output voltage fluctuations. Two main contributions are presented. First, a fractional-order DC–DC boost converter (FOBC) is introduced, incorporating fractional-order dynamics to enhance system performance beyond improvements in control algorithms alone. Second, a novel indirect-control MPPT strategy based on a two-stage architecture is developed, where the P&O algorithm generates the optimal voltage reference and a fractional-order linear-quadratic-integral (FOLQI) controller—designed using a fractional-order small-signal model—regulates the PV module voltage to generate the FOBC duty cycle. Hardware-in-the-loop simulations confirm substantial performance improvements. The proposed FOLQI-based indirect-control approach with FOBC achieves a maximum MPPT efficiency of 99.26%. An alternative indirect method using a classical linear-quadratic-integral (LQI) controller with an integer-order boost converter reaches 98.38%, while the conventional direct-control P&O method achieves only 94.21%, demonstrating the superiority of the proposed fractional-order framework.
Keywords: PV-module; MPPT; FOBC; P&O algorithm; LQI controller; FOLQI controller; HIL validation PV-module; MPPT; FOBC; P&O algorithm; LQI controller; FOLQI controller; HIL validation

Share and Cite

MDPI and ACS Style

Bouarroudj, N.; Lakhdari, A.; Boucherma, D.; Djari, A.; Houam, Y.; Feliu-Batlle, V.; Bettayeb, M.; Benlahbib, B.; Abdulkader, R.; Alfraidi, W.; et al. HIL Implementation of Proposed Fractional-Order Linear-Quadratic-Integral Controller for PV-Module Voltage Regulation to Enhance the Classical Perturb and Observe Algorithm. Fractal Fract. 2026, 10, 84. https://doi.org/10.3390/fractalfract10020084

AMA Style

Bouarroudj N, Lakhdari A, Boucherma D, Djari A, Houam Y, Feliu-Batlle V, Bettayeb M, Benlahbib B, Abdulkader R, Alfraidi W, et al. HIL Implementation of Proposed Fractional-Order Linear-Quadratic-Integral Controller for PV-Module Voltage Regulation to Enhance the Classical Perturb and Observe Algorithm. Fractal and Fractional. 2026; 10(2):84. https://doi.org/10.3390/fractalfract10020084

Chicago/Turabian Style

Bouarroudj, Noureddine, Abdelkader Lakhdari, Djamel Boucherma, Abdelhamid Djari, Yehya Houam, Vicente Feliu-Batlle, Maamar Bettayeb, Boualam Benlahbib, Rasheed Abdulkader, Walied Alfraidi, and et al. 2026. "HIL Implementation of Proposed Fractional-Order Linear-Quadratic-Integral Controller for PV-Module Voltage Regulation to Enhance the Classical Perturb and Observe Algorithm" Fractal and Fractional 10, no. 2: 84. https://doi.org/10.3390/fractalfract10020084

APA Style

Bouarroudj, N., Lakhdari, A., Boucherma, D., Djari, A., Houam, Y., Feliu-Batlle, V., Bettayeb, M., Benlahbib, B., Abdulkader, R., Alfraidi, W., & Hussein Farh, H. M. (2026). HIL Implementation of Proposed Fractional-Order Linear-Quadratic-Integral Controller for PV-Module Voltage Regulation to Enhance the Classical Perturb and Observe Algorithm. Fractal and Fractional, 10(2), 84. https://doi.org/10.3390/fractalfract10020084

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