An Adaptation of a Sliding Mode Classical Observer to a Fractional-Order Observer for Disturbance Reconstruction of a UAV Model: A Riemann–Liouville Fractional Calculus Approach

Miguel Angel Hernández-Pérez, Gustavo Delgado-Reyes (), Vicente Borja-Jaimes, Jorge Salvador Valdez-Martínez () and Marisol Cervantes-Bobadilla
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Miguel Angel Hernández-Pérez: Instituto de Ingeniería, Universidad Veracruzana, Juan Pablo II, Boca del Río 94294, Veracruz, Mexico
Gustavo Delgado-Reyes: Instituto de Ingeniería, Universidad Veracruzana, Juan Pablo II, Boca del Río 94294, Veracruz, Mexico
Vicente Borja-Jaimes: Departamento de Ingeniería Electrónica, TecNM/Centro Nacional de Investigación y Desarrollo Tecnológico (CENIDET) Interior Internado Palmira s/n Col. Palmira, Cuernavaca 62490, Morelos, Mexico
Jorge Salvador Valdez-Martínez: Industrial Mechanics Academic Division, Universidad Tecnológica Emiliano Zapata del Estado de Morelos, Av. Universidad Tecnológica No. 1, Emiliano Zapata 62760, Morelos, Mexico
Marisol Cervantes-Bobadilla: Centro de Investigación en Ingeniería y Ciencias Aplicadas, (CIICAp-IICBA), UAEM, Av. Universidad 1001, Chamilpa, Cuernavaca 62209, Morelos, Mexico

Mathematics, 2023, vol. 11, issue 24, 1-23

Abstract: 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.

Keywords: sliding mode observer; disturbance reconstruction; fractional-order observer; UAV quadrotor mathematical model; reconstruction quality indicator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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