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
Abstract
:1. Introduction
2. UAV Mathematical Modeling
2.1. UAV Kinematics
2.2. UAV State-Space Model
2.3. UAV Mathematical Model Linearization
3. Main Results
3.1. Sliding Mode Classical-Observer (SMCO) Desing
3.2. Sliding Mode Fractional-Observer (SMFO) Design
4. Results Validation and Discussion
4.1. Comparison of the Disturbance Reconstruction SMFO vs. SMCO
- : bounded-magnitude sinusoidal signal.
- : bounded-magnitude square signal.
- : bounded-magnitude sawtooth signal.
4.2. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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State-Space Variables | State-Space Variables |
---|---|
Description | Parameter Value |
---|---|
UAV mass | kg |
UAV rotor mass | 0.088 kg |
UAV arms length | m |
x-axis inertia | |
y-axis inertia | |
z-axis inertia z |
MSE | FPM | SPM | |||||
---|---|---|---|---|---|---|---|
Disturbance | SMCO | SMFO | SMCO | SMFO | SMCO | SMFO | BQR |
SMFO | |||||||
SMFO | |||||||
SMFO |
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Hernández-Pérez, M.A.; Delgado-Reyes, G.; Borja-Jaimes, V.; Valdez-Martínez, J.S.; Cervantes-Bobadilla, M. 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. Mathematics 2023, 11, 4876. https://doi.org/10.3390/math11244876
Hernández-Pérez MA, Delgado-Reyes G, Borja-Jaimes V, Valdez-Martínez JS, Cervantes-Bobadilla M. 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. Mathematics. 2023; 11(24):4876. https://doi.org/10.3390/math11244876
Chicago/Turabian StyleHernández-Pérez, Miguel Angel, Gustavo Delgado-Reyes, Vicente Borja-Jaimes, Jorge Salvador Valdez-Martínez, and Marisol Cervantes-Bobadilla. 2023. "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" Mathematics 11, no. 24: 4876. https://doi.org/10.3390/math11244876