**1. Introduction**

Energy production is one of the most important development priorities. On the one hand, it has been observed that the world's electrical energy consumption is rapidly increasing [1–9]. On the other hand, energy production uses fossil fuels [10–13] such as oil, coal, and natural gas. They are all burnt and used as energy sources for production. The use of fossil fuels can help to offset the energy demand. However, there is too much carbon dioxide (CO2) in the atmosphere, which can lead to big problems both for people and the earth. This forces humans to seek out alternative energy sources that may be capable of saving both people and the planet.

Many alternative sources are suggested. Among these sources, renewable energy is the most commonly used one. Nowadays, photovoltaic solar energy [14–16] and wind energy have become the most used alternative energy sources. The operating power of both the photovoltaic generator and the wind energy sources depends on metrological conditions such as temperature, irradiation, wind speed, etc. [17–21]. The optimal use of the produced energy can be assumed only if the produced wind and photovoltaic sources' maximum power are extracted and tracked for any change in the metrological conditions. Tools to track these specific points are required [22–27].

Most of the proposed power point tracking algorithms are based on varying the generator characteristics in such a way as to be adapted to the latter of the load. The generator characteristic changes are assumed by using a DC-DC converter and a maximum power point tracking (MPPT) algorithm [28–30]. Different DC-DC converters are used as buck converters, boost converters, buck–boost converters, etc. [31–34]. The boost and buck converters are the most commonly used. The buck DC-DC converter is used especially in DC link control, as the DC voltage of the photovoltaic/wind conversion system output depends on the metrological conditions. DC-DC converters are naturally classified as nonlinear systems due to their commuting properties. They are the most commonly used circuits in power electronics, especially in DC link voltage stabilization.

**Citation:** Hamed, S.B.; Hamed, M.B.; Sbita, L. Robust Voltage Control of a Buck DC-DC Converter: A Sliding Mode Approach. *Energies* **2022**, *15*, 6128. https://doi.org/10.3390/ en15176128

Academic Editors: Saad Motahhir, Najib El Ouanjli and Mustapha Errouha

Received: 15 June 2022 Accepted: 28 July 2022 Published: 24 August 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

In general, the DC link voltage must be fixed at a desired value despite input voltage and load variations [35]. To regulate the DC voltage magnitude, and obtain a constant and stable output voltage and fast response, many types of controllers are used [27], such as fuzzy logic, PI controllers, PID controllers, sliding mode control, etc. Conventional controllers are in general conceived by using small signal state equations obtained at a specific operation point. The conceived control algorithm remains efficient only around the specified operating point. To avoid the drawbacks of conventional controllers, nonlinear control approaches are investigated and used in the control voltage loop of the buck DC-DC converter. Among these nonlinear control algorithms, the sliding mode approach is the most used. Different sliding mode algorithms, both for continuous and discrete times, are proposed in the literature [36–43]. In [36], a cascade loop control is proposed. The voltage control loop is based on a classical PID controller, and the current loop control is based on zero order sliding mode control over a continuous time. The validity of the conceived algorithm is confirmed under different working conditions, including target voltage variation, load variation and input voltage variations. In [37], a sliding mode controlled pole is conceived both in voltage and current control loops. An integral switching surface is used here. Simulation results are given under target voltage variation and load variation. The fractional order sliding mode is also used in the literature [38]. Different sliding mode approaches for discrete time are used. In fact, in [39], discrete time sliding mode control is investigated for the output voltage control. The performance of the used algorithm is tested only for a fixed target output voltage. Discrete time fast terminal sliding mode control with mismatched disturbance is conceived for DC-DC buck converters, and the control strategy is investigated in [40]. The validity of the proposed algorithm, both in simulation and experimentation, is assessed under both load variations and fluctuations in the input voltage. A discrete repetitive adaptive sliding mode control for the DC-DC buck converter under only variable target output voltage perturbed with a Gaussian noise is conceived in [41]. Simulation results under fixed target voltage and load variations are given. An Adaptive Global Sliding Mode Controller based on the Lyapunov approach is designed for perturbed DC-DC buck converters [42]. In this work, the external disturbances and dynamic uncertainties are modeled with a sinusoidal function. In [43,44], to cope with the chattering problem, a high-order sliding mode control of the DC-DC buck converter is conceived. Practical results under target output voltage variation are presented. In most of the mentioned studies, the performance of the conceived algorithms is validated against external disturbances as input voltage and load variations. The internal disturbances in terms of DC-DC buck converter parameter variations are omitted. Thus, in this paper, we are interested in the performance of the first-order sliding mode in DC-DC buck output voltage control with both external and internal disturbances. Besides this, to highlight the good performance of the investigated control algorithm, a comparison study with four control algorithms is carried out.

The paper is organized as follows. Section 2 presents the modeling of the buck DC-DC converter feeding a resistive load. Section 3 describes the sliding mode controller principle and its application in buck DC-DC converter output voltage control. Section 4 presents the internal model controller. The fuzzy logic controller is given in Section 5. Section 6 illustrates the obtained results in simulation, both for internal and external disturbances. Section 5 concludes the work and presents some suggested prospects.
