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.

The hovering flight of a quadrotor Unmanned Aerial Vehicle (UAV) refers to maintaining the aircraft in a fixed position in the air, without lateral, vertical, or rotational movements, using only the vehicle’s control systems to maintain proper balance in all spatial dimensions. Algorithms and control systems have been developed to continuously adjust motor speeds to counteract deviations from the desired position and achieve effective hovering flight. This paper proposes a set of PID controllers with an integral effect based on the Riemann–Liouville fractional-order approach to improve the hovering flight of a quadrotor UAV. This research innovates by introducing a set of fractional-order PID controllers for UAV hover stability, which offer better adaptability to non-linear dynamics and robustness than traditional PID controllers. Also presented is the development of new performance metrics (MSE, BQC-LR), which allow for more comprehensive control system evaluations. A thorough comparative analysis with conventional control methods demonstrates the superior performance of fractional-order control in real-world simulations. The numerical simulation results show the effectiveness of the proposed Fractional Integral Action PID Controller in the control of UAV hovering flight, while comparative analyses against a classical controller emphasize the benefits of the fractional-order approach in terms of control accuracy.

The interaction of digital systems with dynamic systems requires synchrony and the accomplishment of time constrains, so the simulation of physical processes needs an implementation by means of real-time systems (RTS). However, as it can be expected, every simulation and/or implementation might demand too many computational resources, surpassing the capacity of the processor used by computational systems. This is the reason for the need to perform a temporary computational complexity analysis based on the study of the behavior of the execution times of the implemented simulation. In this regard, the Real-Time Operating Systems (RTOS) feature time managing tools, which allow their precise measurement and the establishment of scheduling criteria in process execution. Therefore, this research proposes accomplishing a temporary computational complexity analysis of the real-time simulation by an embedded system (ES) of an unmanned aerial vehicle (UAV) propelled by four rotors. Derived from this analysis, formal definitions are elaborated and proposed, which establish a close relationship between the temporary computational complexity and typical real-time temporary constraints. To the best of the author’s knowledge, the definitions presented in this article have not been reported in the literature. Furthermore, to perform the temporary computational complexity analysis of the UAV, the mathematical modeling based on the Euler–Lagrange approach is presented in detail. Finally, simulations were performed using a real-time system implemented on the Embedded Computer System (ECS) Raspberry Pi 2 Model B+, in order to validate the suggested definitions.