In this paper, we present the design of a fractional-order sliding mode observer (FO-SMO) for actuator fault estimation in a quadrotor unmanned aerial vehicle (QUAV) system. Actuator faults can significantly compromise the stability and performance of QUAV systems; therefore, early detection and compensation are crucial. Sliding mode observers (SMOs) have recently demonstrated their accuracy in estimating faults in QUAV systems under matched uncertainties. However, existing SMOs encounter difficulties associated with chattering and sensitivity to initial conditions and noise. These challenges significantly impact the precision of fault estimation and may even render fault estimation impossible depending on the magnitude of the fault. To address these challenges, we propose a new fractional-order SMO structure based on the Caputo derivative definition. To demonstrate the effectiveness of the proposed FO-SMO in overcoming the limitations associated with classical SMOs, we assess the robustness of the FO-SMO under three distinct scenarios. First, we examined its performance in estimating actuator faults under varying initial conditions. Second, we evaluated its ability to handle significant chattering phenomena during fault estimation. Finally, we analyzed its performance in fault estimation under noisy conditions. For comparison purposes, we assess the performance of both observers using the Normalized Root-Mean-Square Error (NRMSE) criterion. The results demonstrate that our approach enables more accurate actuator fault estimation, particularly in scenarios involving chattering phenomena and noise. In contrast, the performance of classical (non-fractional) SMO suffers significantly under these conditions. We concluded that our FO-SMO is more robust to initial conditions, chattering phenomena, and noise than the classical SMO.

A fault detection and isolation (FDI) approach based on nonlinear sliding mode observers for a wind turbine model is presented. Problems surrounding pitch and drive train system FDI are addressed. This topic has generated great interest because the early detection of faults in these components allows avoiding irreparable damage in wind turbines. A fault diagnosis strategy using nonlinear sliding mode observer banks is proposed due to its ability to handle model uncertainties and external disturbances. Unlike the reported solutions, the solution approach does not need a priori knowledge of the faults and considers system uncertainty. The robustness to disturbances, uncertainties, and measurement noise is shown in the dynamic of the generated residuals, which is sensible to only one kind of fault. To show the effectiveness of the proposed FDI approach, numerical examples based on a wind turbine benchmark model, considering closed loop applications, are presented.

Fractional-order calculus (FOC) has gained significant attention in electric vehicle (EV) energy storage and management systems, as it provides enhanced modeling and analysis capabilities compared to traditional integer-order approaches. This review presents a comprehensive survey of recent advancements in the application of FOC to EV energy storage systems, including lithium-ion batteries (LIBs), supercapacitors (SCs), and fuel cells (FCs), as well as their integration within energy management systems (EMS). The review focuses on developments in electrochemical, equivalent circuit, and data-driven models formulated in the fractional-order domain, which improve the representation of nonlinear, memory-dependent, and multi-scale dynamics of energy storage devices. It also discusses the benefits and limitations of current FOC-based models, identifies open challenges such as computational feasibility and parameter identification, and outlines future research directions. Overall, the findings indicate that FOC offers a robust framework with significant potential to advance next-generation EV energy storage and management systems.

Quadrotor unmanned aerial vehicles (QUAVs) are widely used in civil and defense applications, yet reliable trajectory tracking remains challenging under external disturbances and limited sensing. Conventional backstepping–sliding mode controllers ensure robustness only by selecting discontinuous gains larger than the disturbance bound, which increases chattering and limits the use of smooth switching functions. This paper addresses these limitations by integrating explicit disturbance compensation into a backstepping–sliding framework through a super-twisting observer (STO). The STO reconstructs matched disturbances acting on the translational and rotational dynamics in real time, and the estimated signals are directly injected into the control law. This approach enables effective disturbance rejection beyond the nominal sliding gain while preserving robustness under smooth control actions. Simulation results under single- and multi-frequency perturbations demonstrate accurate disturbance reconstruction (FIT indices above 95%), improved tracking performance, and a significant reduction in chattering. The proposed strategy provides a robust control solution for QUAVs operating in uncertain environments.

This study addresses robust trajectory tracking for quadrotor unmanned aerial vehicles (QUAVs) under partial state measurements and bounded external disturbances. To this end, a control framework is introduced that integrates backstepping sliding mode control (BSMC) with a super-twisting observer (STO). In this scheme, only position and attitude are directly measured while the STO reconstructs the linear and angular velocities in real time. The estimated states are then fed into the control law, enabling accurate trajectory tracking and robust performance without full-state feedback or explicit disturbance compensation. The approach is validated through three simulation scenarios: nominal full-state feedback, observer-based control without disturbances, and observer-based control under bounded time-varying perturbations. Quantitative metrics confirm consistent tracking accuracy and closed-loop stability across all scenarios. These results demonstrate the effectiveness of the integrated BSMC–STO framework for QUAV operations in sensor-limited and disturbance-prone environments.

This paper proposes a modification of a Sliding Mode Classical Observer (SMCO) to adapt it to the fractional approach. This adaptation involves using a set of definitions based on fractional calculus theory, particularly the approach developed by Riemann–Liouville, resulting in a Sliding Mode Fractional Observer (SMFO). Both observers are used to perform disturbance reconstruction considered additive in a Quadrotor Unmanned Aerial Vehicle (UAV) model. Then, this work presents the fractional-order sliding mode observer’s mathematical formulation and integration into the Quadrotor UAV model. To validate the quality of the disturbance reconstruction process of the proposed SMFO observer scheme, numerical simulations are carried out, where a reconstruction quality indicator (BQR) is proposed based on the analysis of performance indices such as the Mean Square Error (MSE), the First Probability Moment (FPM), and Second Probability Moment (SPM), which were obtained for both the SMCO and the SMFO. The simulation results demonstrate the efficacy of the proposed observer in accurately reconstructing disturbances under various environmental conditions. Comparative analyses with SMCO highlight the advantages of the fractional-order approach in terms of reconstruction accuracy and improvement of its transitory performance. Finally, the presented SMFO offers a promising avenue for enhancing the reliability and precision of disturbance estimation, ultimately contributing to the advancement of robust control strategies for Quadrotor UAV systems.