This work addresses the stabilization problem for a pair of linear Korteweg–de Vries (KdV) equations coupled through dispersive effects on a bounded domain. The model is motivated by a physical phenomenon in which two long internal waves, having nearly equal phase speeds but corresponding to different modes, interact. Control inputs are applied at the left (Dirichlet) boundaries, while the right boundaries remain uncontrolled. Our goal is to design a feedback control law based on the backstepping method to achieve stabilization for any domain length. Finally, numerical simulations are provided to illustrate the theoretical results.

Control barrier functions (CBFs) provide a systematic framework for enforcing safety constraints in nonlinear control systems. However, their implementation typically relies on accurate system models, which can limit their applicability in the presence of significant modeling uncertainties or unknown dynamics. This paper proposes a model-free framework for the computation of recursive control barrier functions based on the ultra-local model approach that leverages online estimation of the unknown system dynamics to construct CBF constraints. This approach does not require an explicit model of the system dynamics and enhances robustness with respect to disturbances and model mismatch. The resulting control architecture enables the enforcement as well as the anticipation of safety constraints for systems with higher relative degree. The effectiveness of the proposed approach is illustrated on the adaptive cruise control benchmark.

This paper presents an optimized control structure for a PV microgrid based on a three-phase quasi-Z source inverter (qZSI) ensuring enhanced power quality in the stand-alone mode of operation. The control strategy adopted consists of three control stages. The first control stage is used to optimize the energy efficiency of the photovoltaic (PV) generator under various irradiation conditions. An indirect control-based maximum power point tracking (MPPT) procedure is implemented. The second controller stabilizes DC-bus voltage to maintain the power balance between the PV energy source and a nonlinear (NL) load demand through a battery connected to the qZSI capacitor via a bidirectional DC/DC converter. The third control stage regulates the output AC voltage and current of the qZSI to their references. A fractional-order PID controller (FOPID) is adopted for all control stages to ensure good tracking under various scenarios: changing irradiation conditions, non-linearity of the load, and its variation. The yellow saddle goatfish algorithm (YSGA) is used to calculate the control parameters. Simulation results are performed to highlight the presented approach performance.

In this letter, we propose a Power Tower Function (PTF) truncated at order 2, to design control laws in continuous time and under sampling. The contributions are twofold. The first one aims to demonstrate the usefulness of the PTF in the synthesis of control laws when the latter are recursive and applied to a system subject to non-matching perturbations. As a result, with one term in the control (instead of using two separate terms), a fixed-finite time convergence is ensured and an overestimation of the fixed-time is provided. Furthermore, a new sliding-mode control is obtained because the PTF is equivalent to the sign function on the sliding manifold. Filippov solutions are then invoked to avoid differentiating directly the sign function. Consequently, the second contribution aims to highlight that an implicit or semi-implicit Euler discretization can best approximate solutions in the Filippov's meaning. Simulation results are given to show the well founded of the proposed control.

In this paper, a decentralized control scheme based on the universal droop controller (UDC) is proposed for the flexible operation of the microgrid. This new control approach can share load power among parallel distributed generation (DG) inverters in microgrids with a restored voltage magnitude and frequency in islanded operating mode. Based on a fuzzy logic controller, the same decentralized control scheme can also synchronize the microgrid voltage with the main grid to ensure a seamless transition to the grid-connected mode. Multiple inverters with different functionalities, operating as voltage-controlled voltage source inverter (VC-VSI) and current-controlled voltage source inverter (CC-VSI) are considered in this work for an overall assessment of the proposed control structure. The CC-VSI is used to supply the maximum power of a photovoltaic (PV) generator via a quasi-Z-source inverter (qZSI) where a new fractional-order proportional-integral-derivative (FOPID) regulator-based incremental conductance (IC) method is adopted. The control parameters set is optimized using the new chaotic yellow saddle goatfish algorithm (C-YSGA). Simulation results are performed to highlight the proposed control strategy performance.

A flat control law is based on the structural analysis of a controlled system, allowing optimal placement of sensors and actuators. Once designed, any desired dynamics can be imposed onto the system. When the target dynamics comes from a system structurally different from the controlled one, generalized synchronization can be achieved, provided the control gain is sufficiently large. As the gain increases, various relationships emerge between the drive and response systems, depending on differences in their dimensions and dissipation rates. The principal contribution of this work lies in the exploration of drive-response system pairs with varying dimensions (ranging from 2 to 4) and dissipation levels, including combinations of dissipative and conservative systems. We identify several types of generalized synchronization, using a classification based on the thickness of the resulting Lissajous curves and the lack of conjugacy between the first-return maps of the drive and response systems.

This article presents a hybrid controller developed for a Shunt Active Filter (SAF) with Photovoltaic (PV) generation Structure. This structure, referred to as (PV-SAF/CHB-PN), uses a Multi-Level Inverter (MLI)-type-Cascaded H-Bridge (CHB) to realize several aspects: i- Increase the apparent switching frequency. ii- Generate approximately sinusoidal output voltage. iii- Minimize the output filter size. The hybrid controller, implemented via Petri Nets (PNs), optimizes the dispatch commitment among the H-Bridge modules and the arms of each modules. Thus, to compensate for perturbations, while generating the MPPT pf the PV panels, a PN current controller combined with a new analytical Hysteresis control approach, is employed. Meanwhile, a PN voltage controller balances the DC voltages across of the MLI-CHB inputs and achieves a practical stability using the Lyapunov method. The PV generators are integrated, via DC/DC converters, into the DC side of the SAF. Hence, Model Predictive Controller based Perturb and Observe (MPC-Based P&O-MPPT) algorithm optimizes the MPPT extraction without drift phenomena.Finally, a case study for textile factory using real measurements via power quality analyzers, demonstrates the effectiveness of 3 CHB modules structure in mitigating harmonic impacts of the main textile machine of (SL-50 kVA), validating the hybrid controller, and integrating green energy.

Controlling dynamical systems, specially high dimensional dynamical networks, is of primary interest. Such a problem is intrinsically related to analyzing the observability of the corresponding state space from measurements, as well as its dual aspect of controllability. An additional constraint can be added by requiring the system to be flat, meaning that its state and actuating signal can be expressed in terms of the measurements and a finite number of its derivatives. Starting from the placement of sensors providing global observability, we address the dual problem of placing the actuators allowing global controllability, and of designing a flat input. Since global observability of a network of y-coupled Rössler systems can be reduced to the observability of each pair of nodes, a step before controlling a network is to design a flat control law for a pair of diffusively y-coupled Rössler systems. It is shown that such a system is flat when a differential delay is inserted.

In this paper, we propose an active fault-tolerant control law, based on a fault estimation method and differential flatness, for a three-phase inverter, connected to the grid by LCL filters. The system is vulnerable multiple faults, therefore an active fault-tolerant control is required to preserve the electrical power conversion between renewable resources and the grid. First, the fault estimation is achieved using our recent algorithm (Laaziz et al., 2024), based on a left inversion technique and on the super-twisting differentiator, and then, active fault-tolerant control law based on a differential flatness approach is applied. In the paper, we provide flatness analysis of the inverter and its LCL filters in healthy and faulty conditions. In particular, we show the flat output is the same for both healthy and faulty systems, which is crucial for the active fault-tolerant control law design. This common flat output is computed thanks to a new model of the inverter and its output LCL filters. Several simulation results demonstrate the effectiveness of the proposed method under both healthy and faulty conditions, including symmetric and asymmetric faults.

The present paper proposes a comparison of three well-established controllers: a robust proportional–integral–derivative (PID) controller (Conord and Peaucelle, 2021), a model-free control (Fliess and Join, 2013, 2022) and an adaptive sliding-mode control based on the super-twisting algorithm (Shtessel et al., 2023). The benchmark considered is an airfoil section equipped with trailing edge jets, load sensors and a perturbation system. The objective is to track the lift command under external wind perturbations. The outcome of this work is the comparison of performances for three control laws that are suitable when little knowledge is known from the physics. This study quantifies performance not only in terms of load control, but also in the needed implementation effort.

This work is dedicated to the application of a semi-implicit homogeneous differentiator to estimate the angular velocity and the angular acceleration of each of the eight electric motors of the CRAFT cable-driven parallel robot from the recording of the angular position of their respective output shaft. These motors drive the winding or unwinding of eight cables to move the robot moving-platform. The results show that this differentiator, whose the definition is respectively based on two projectors, is an extremely efficient tool for estimating the angular velocities and accelerations of the eight motors. These estimated velocities and accelerations are much less noisy than their reference signals obtained by backward difference. Moreover, the estimated quantities obtained with this differentiator are successfully compared to those obtained by a non-linear observer based on the interpolation and numerical difference of the measured position variable. Those promising results will definitely contribute to a better control of the CRAFT robot.

This paper investigates modern control approaches to improve the energy fineness of grid-connected PV systems. From a two-stage command structure, the first controller regulates the boost converter-based DC side to maintain fast and accurate maximum power point tracking (MPPT) of the photovoltaic (PV) generator under varying climatic circumstances. At this level, a novel nonlinear control approach, called fractional-order terminal super-twisting algorithm (FOTSTA) is introduced for the PV boost converter. The FOTSTA approach is a hybrid strategy characterized by simplicity, high robustness, great efficiency, ease of implementation, does not require knowledge of the mathematical model of the studied system, low cost, and fast dynamic response. A comparative study is conducted with the well-known versions of nonlinear command: sliding mode control and super-twisting algorithm to evaluate the performance of the proposed FOTSTA approach. In the second stage, the model predictive command is applied to regulate the active and reactive power of the three-phase grid-connected inverter-based AC side to their reference values that are generated by the outer loop of the DC link voltage via an anti-windup proportional-integral controller. The simulation was performed in MATLAB using a BM SX150S solar panel. The results demonstrate the competence and moderation of the proposed FOTSTA approach in terms of tracking performance, feasibility, less energy ripples, and robustness against varying solar irradiance conditions. Furthermore, the comparison test reveals a better reflection on the inversion stage, which improves various functionalities assigned to the grid-connected inverter side, namely harmonic pollution compensation and power flow quality from the solar PV power generation source to the grid.

In this note, we discuss a generalization of the well-known implicit function theorem to the time-delay case. We show that the latter problem is closely related to the bicausal changes of coordinates of time-delay systems. An iterative algorithm is proposed to check the conditions and to construct the desired bicausal change of coordinates for the proposed implicit function theorem. Moreover, we show that our results can be applied to delayed differential-algebraic equations (DDAEs) to reduce their indices and to get their solutions. Some numerical examples are given to illustrate our results.

This study is dedicated to the design of a digital differentiator for a triple integrator. A cascade of two interconnected semi-implicit Euler double differentiators approach is proposed. This allows the digital differentiator to benefit from similar structure of second order discrete-time homogeneous differentiators, such as modularity and more degree of freedom regarding the parameter settings. Numerical results are presented to support the rightness of the proposed method.

In this paper, we consider two boost choppers connected in parallel, with two different sources, and a load with low power demand. The two boost choppers can enter in a discontinuous mode of operation by providing a small current that approaches zero. To prevent this, we propose a new strategy for power distribution based on the value of the current at the limit between continuous and discontinuous modes. In the case of a very low power demand, one boost chopper can be disconnected, ensuring a continuous mode operation for the remaining boost chopper.

In this article, a recently developed adaptive version of super-twisting is applied to the control of the aerodynamic lift on a wind turbine blade section, while considering local disturbances in the airflow. The proposed control law serves as a model-free control strategy, relying on only two parameters. This strategy reduces the need for tuning and modeling efforts: the first parameter governs the speed of gain variation, while the second parameter is associated with the desired accuracy, enabling control of unknown dynamics. We discuss the capability of the proposed model to track the lift reference of a wind turbine blade in the presence of external perturbations and actuator saturation. Experimental results demonstrate the feasibility of such control.

In this paper, we show that a flatness-based approach can control each subsystem while allowing global system supervision. To illustrate this capability we propose a power flow management strategy based on a Petri net methodology for the supervision. The microgrid is composed of two boost and one buck-boost choppers connected in parallel through a common bus voltage. The two boost choppers are supplied by two different constant voltage sources while the buck-boost is fed by a battery. The main contributions of this article are twofold: first, we generate the power references from the power demand and the battery state of charge; and second, we design a control law based on the differential flatness of the model and on a specific choice of flat outputs.

This work addresses the problem of controlling the local aerodynamic lift of a wind turbine blade taking into account disturbances caused by turbulent perturbations at the blade scale. This work deals with the study of a model-free based control algorithm implemented in the high fidelity simulated environment ISIS-CFD, where the controller acts at the level of the blade section to track the lift to a desired reference. Numerical experiments have been conducted in order to highlight some properties of the aerodynamic closed-loop system under several operating conditions.

This paper presents a diagnosis method to detect, isolate and estimate faults occurring in permanent magnet synchronous generator (PMSG). This method is based on a dynamical sparse recovery (SR) algorithm that is able to reconstruct online and with finite-time convergence a sparse vector of numerous faults from few system measurements. The faulty PMSG system is affected by a partial inter-turn short circuit and voltage dip faults. Using Matlab/Simulink environment, some scenarios are presented to present the efficiency of SR method for diagnostic of PMSG system.