Enhanced general conformable controller based on Lyapunov technique for DC-DC static converters: Application to a solar system

Omar kahouli; Mourad Elloumi; Omar Naifar; Abdellatif Ben Makhlouf; Yassine Bouteraa; Sarra Elgharbi; Omar kahouli; Mourad Elloumi; Omar Naifar; Abdellatif Ben Makhlouf; Yassine Bouteraa; Sarra Elgharbi

doi:10.3934/math.2024522

AIMS Mathematics

2024, Volume 9, Issue 5: 10698-10716. doi: 10.3934/math.2024522

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Enhanced general conformable controller based on Lyapunov technique for DC-DC static converters: Application to a solar system

1.
Department of Electronics Engineering, Applied College, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Control and Energy Management Laboratory, National School of Engineering, Sfax University, BP 1173, Sfax 3038, Tunisia
3.
Laboratory of Sciences and Technology of Automatic Control and Computer Engineering, National School of Engineering of Sfax, University of Sfax, P.O. Box 1173, 3038 Sfax, Tunisia
4.
Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Sfax, Tunisia
5.
Department of Computer Engineering, College of Computer Engineering and sciences, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
6.
Chemistry Department, College of science, University of Ha'il, Ha'il 2440, Saudi Arabia

Received: 20 November 2023 Revised: 20 February 2024 Accepted: 27 February 2024 Published: 18 March 2024
MSC : 34H05, 81T80, 93A30

To synthesize the proper control signal while guaranteeing the necessary performance indices (speed, resilience, accuracy, etc.), mathematical models were frequently used to represent physical systems. These descriptions were utilized for control, monitoring, and detection in these kinds of systems. Quality and performance of the process may suffer if the model is inaccurate or incomplete. As a result, conformable systems (CS) may be used to make these mathematical models more near to the real world. However, non-power-electronics experts who need to model and simulate complex systems may find the task of modeling static converters to be rather challenging. Researchers have just recently outlined the properties of the general conformable systems (GCS). This innovative approach built upon the principle of the classical integer order systems, employing the same mathematical foundations for its derivation. With the introduction of this novel description of systems, a fresh array of differential equations emerged, specifically tailored for the realm of direct current to direct current (DC-DC) static converters. GCS has been proved to be more flexible and profitable than the traditional integer-order one for representing DC-DC static converters. This advancement paved the way for more effective control techniques based on the Lyapunov method, with practical applications in photovoltaic (PV) systems and beyond.
- general conformable systems,
- Lyapunov technique,
- DC-DC static converters,
- modelling and control
Citation: Omar kahouli, Mourad Elloumi, Omar Naifar, Abdellatif Ben Makhlouf, Yassine Bouteraa, Sarra Elgharbi. Enhanced general conformable controller based on Lyapunov technique for DC-DC static converters: Application to a solar system[J]. AIMS Mathematics, 2024, 9(5): 10698-10716. doi: 10.3934/math.2024522

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Abstract

To synthesize the proper control signal while guaranteeing the necessary performance indices (speed, resilience, accuracy, etc.), mathematical models were frequently used to represent physical systems. These descriptions were utilized for control, monitoring, and detection in these kinds of systems. Quality and performance of the process may suffer if the model is inaccurate or incomplete. As a result, conformable systems (CS) may be used to make these mathematical models more near to the real world. However, non-power-electronics experts who need to model and simulate complex systems may find the task of modeling static converters to be rather challenging. Researchers have just recently outlined the properties of the general conformable systems (GCS). This innovative approach built upon the principle of the classical integer order systems, employing the same mathematical foundations for its derivation. With the introduction of this novel description of systems, a fresh array of differential equations emerged, specifically tailored for the realm of direct current to direct current (DC-DC) static converters. GCS has been proved to be more flexible and profitable than the traditional integer-order one for representing DC-DC static converters. This advancement paved the way for more effective control techniques based on the Lyapunov method, with practical applications in photovoltaic (PV) systems and beyond.

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