Abstract
This article presents a fuzzy adaptive control law (FACL) designed for tracking the trajectory of a low-scale unmanned aerial vehicle (UAV), based on a new fuzzy adaptive neural proportional integral derivative (FANPID) controller. FACL estimates the angles of rotation, if the reference trajectory is proposed, applying the adaptivity of the new FANPID-Lyapunov controller. UAV parameters were previously identified using the fuzzy adaptive neurons (FAN) method and experimental aerodynamic data. FANPID-Lyapunov controller optimizes trajectory tracking and stability analysis is performed. The FACL simulation results obtained in Matlab®/Simulink show the effectiveness, adaptivity and optimization of the flight control system, because it self-tunes the angles satisfactorily, adapts the gains and parameter for the FANPID-Lyapunov-Fuzzy controller, and reduces the error considerably compared to the controllers PID-Fixed gains, PID-Fuzzy adaptive gains, PID-Lyapunov-Fixed gains, and FOPID-Lyapunov-Fuzzy adaptive gains and parameters.
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Abbreviations
- a :
-
real number 0 < a
- b :
-
real number 0 < b
- c :
-
real number 0 < c
- c 1 :
-
constant
- Dderivative:
-
constant
- d(k):
-
unmodeled dynamic
- e(k):
-
error
- F x, F y, F z :
-
forces on x, y, z axis
- F z modeι :
-
thrust force on the z axis
- g :
-
acceleration of gravity
- g 1, g 2, g 3 :
-
constant gains
- I :
-
integration constant
- I x, I y, I z :
-
moments of inertia on x, y, z axis
- k :
-
time variable
- k l, k p, k q, k r :
-
parameters identified in [17]
- k v1, k v2, k v3, k v4 :
-
angular velocities of the propellers [rad/second], estimated in [17]
- m :
-
UAV mass
- M p model, M q model :
-
moments with respect to the x, y, z
- M r model :
-
axes
- N :
-
filter coefficient
- p, q, r :
-
UAV angles for the u, v, w axis
- P :
-
proportionality constant
- s :
-
complex Laplace variable
- U 1, U 2, U 3, U 4 :
-
modulation index, pulse width modulation (PWM) signal at [0, 1]
- v in j (k):
-
dendrite inputs
- V threshol d (k):
-
threshold
- w in j(k):
-
synaptic weights
- W c :
-
adaptive weight
- u, v, w :
-
displacement of the UAV on u, v, w axis of the body axes
- x, y, z :
-
UAV displacement on x, y, z axis
- ỹ(k):
-
sigmoid activation function (SAF)
- φ, θ, ψ :
-
angles for rolling, pitching and yaw maneuver, at x, y, z axis
- γ(k):
-
learning factor for unipolar systems, 0 < γ ≤ 1, and for bipolar systems, −1 < γ ≤ 1
- Φ(·):
-
a function
- ∥·∥:
-
Euclidean norm
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This work was supported by the Department of Automatic Control and LAFMIA UMI of CINVESTAV-IPN, CONACYT and ITSOEH. We appreciate the support of the National Council for Science and Technology (CONACYT for its acronym in Spanish), Postdoctoral Scholarship Program, together with the Department of Automatic Control and Department of Autonomous Air and Underwater Navigation Systems of the French Mexican Laboratory of Informatics and Automatic Control, Mixed International Unit (LAFMIA UMI for its acronym in Spanish), Center for Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV-IPN for its acronym in Spanish), and Electromechanical Engineering Division, Higher Technological Institute of the West of the State of Hidalgo (ITSOEH for its acronym in Spanish).
Abigail María Elena Ramírez Mendoza received her B.S. degree in mechanical electrical engineering from National Autonomous University of Mexico (UNAM for its acronym in Spanish) in 1996, master and Ph.D. degrees in Engineering degrees, from UNAM, Mexico, in 1998 and 2013, respectively. From 2015–2018, she was a distinguished researcher with a CONACYT Research Fellowship — Autonomous University of Nuevo León (UANL for its acronym in Spanish), Mexico. From 2013–2014 and 2019–2020, she obtained a Postdoctoral Stay at the Department of Automatic Control at CINVESTAV-IPN, Mexico. Professor at Department of Electromechanical Engineering, ITSOEH, Mexico, 2021–2022. She is currently doing a Postdoctoral stay at the Department of Autonomous Air and Submarine Navigation Systems, LAFMIA UMI, CINVESTAV-IPN. Her research interests include fuzzy neurons, fuzzy adaptive control, and system identification.
Wen Yu received his B.S. degree in automatic control from Tsinghua University, Beijing, China in 1990 and his M.S. and Ph.D. degrees, both in electrical engineering, from Northeastern University, Shenyang, China, in 1992 and 1995, respectively. Since 1996, he has been at CINVESTAV-IPN, Mexico City, Mexico, where he is currently a Professor at Department of Automatic Control. Dr. Wen Yu serves as Associate Editor of IEEE Transactions on Cybernetics, Neurocomputing, and Journal of Intelligent and Fuzzy Systems. He is a member of the Mexican Academy of Sciences.
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Mendoza, A.M.E.R., Yu, W. Fuzzy Adaptive Control Law for Trajectory Tracking Based on a Fuzzy Adaptive Neural PID Controller of a Multi-rotor Unmanned Aerial Vehicle. Int. J. Control Autom. Syst. 21, 658–670 (2023). https://doi.org/10.1007/s12555-021-0299-2
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DOI: https://doi.org/10.1007/s12555-021-0299-2