Abstract
The quadrotor system’s nonlinear behaviour, uncertain modelling parameters and the presence of exogenous disturbances in the surrounding environment make its flight control a critical and challenging job. Several linear and nonlinear control methodologies have been proposed so far for this purpose during the past few decades which still need improvements. In this paper, variable exponential sliding mode control (ESMC) is proposed for the attitude stabilization and altitude tracking of a quadrotor having parametric uncertainties and being exposed to exogenous disturbances. The multi-layer perceptron (MLP) neural network is incorporated with the ESMC to accommodate adaptively the effect of parametric uncertainties. The conventional weight update law of the neural network is replaced by the sliding mode effect, thereby enhancing the learning efficiency of the network without computational complexities. A finite-time disturbance observer (FTDO) is integrated with the control law to make the controller robust to exogenous disturbances and minimize the chattering issue as well. The stability of the proposed control scheme is checked and verified by the Lyapunov theory. Numerous simulations of the proposed control algorithm are carried out on a quadrotor model suffering from exogenous disturbances and parametric uncertainties in MATLAB SIMULINK and the results are compared with the SMC. The remarkable performance of the proposed control strategy demonstrates and substantiates its validity.
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References
Ahmed, N., Abid, R., & Rameez, K. (2021b). Part 1: Robust adaptive control of quadrotor with disturbance observer. Aircraft Engineering and Aerospace Technology, 93(4), 544–552. https://doi.org/10.1108/AEAT-07-2020-0151
Ahmed, N., Abid, R., Syed, S., & Rameez, K. (2021a). Robust composite-disturbance observer based flight control of quadrotor attitude. Journal of Intelligent & Robotic Systems. https://doi.org/10.1007/s10846-021-01463-6
Ailon, A., & Arogeti, S. (2015). Closed-form nonlinear tracking controllers for quadrotors with model and input generator uncertainties. Automatica, 54, 317–324. https://doi.org/10.1016/j.automatica.2015.02.020
Alexis, K., Nikolakopoulos, G., & Tzes, A. (2011). Switching model predictive attitude control for a quadrotor helicopter subject to atmospheric disturbances. Control Engineering Practice, 19(10), 1195–1207. https://doi.org/10.1016/j.conengprac.2011.06.010
Ali, N., Tawiah, I., & Zhang, W. (2020). Finite-time extended state observer based nonsingular fast terminal sliding mode control of autonomous underwater vehicles. Ocean Engineering. https://doi.org/10.1016/j.oceaneng.2020.108179
Barghandan, S., Badamchizadeh, M. A., & Jahed-Motlagh, M. R. (2017). Improved adaptive fuzzy sliding mode controller for robust fault tolerant of a Quadrotor. International Journal of Control, Automation and Systems, 15, 427–441. https://doi.org/10.1007/s12555-015-0313-7
Basri, M. A. M. (2018). Trajectory tracking control of autonomous quadrotor helicopter using robust neural adaptive backstepping approach. Journal of Aerospace Engineering. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000804
Bouzid, Y., Siguerdidjane, H., & Bestaoui, Y. (2017). Nonlinear internal model control applied to VTOL multi-rotors UAV. Mechatronics, 47, 49–66. https://doi.org/10.1016/j.mechatronics.2017.08.002
Chen, F., Lei, W., Zhang, K., Tao, G., & Jiang, B. (2016). A novel nonlinear resilient control for a quadrotor UAV via backstepping control and nonlinear disturbance observer. Nonlinear Dynamics, 85(2), 1281–1295. https://doi.org/10.1007/s11071-016-2760-y
Faraji, A., Nejati, Z., & Abedi, M. (2020). Actuator faults estimation for a helicopter UAV in the presence of disturbances. Journal of Control, Automation and Electrical Systems, 31, 1153–1164. https://doi.org/10.1007/s40313-020-00621-9
Guerrero-Sánchez, M. E., Mercado-Ravell, D. A., Rogelio, L., & García-Beltrán, C. D. (2017). Swing-attenuation for a quadrotor transporting a cable-suspended payload. ISA Transactions, 68, 433–449. https://doi.org/10.1016/j.isatra.2017.01.027
Huang, T., Huang, D., Wang, Z., & Shah, A. (2019). Robust tracking control of a quadrotor UAV based on adaptive sliding mode controller. Complexity. https://doi.org/10.1155/2019/7931632
Huang, Y., Zheng, Z., Sun, L., & Zhu, M. (2018). Saturated adaptive sliding mode control for autonomous vessel landing of a quadrotor. IET Control Theory and Applications, 12(13), 1830–1842. https://doi.org/10.1049/iet-cta.2017.0998
Hussain, S., & Malik, F. M. (2020). Extended-order high- gain observer based feedback control law for tracking the longitudinal dynamics of mini UAV. Journal of Control, Automation and Electrical Systems, 31, 10–20. https://doi.org/10.1007/s40313-019-00535-1
Jia, Z., Yu, J., Mei, Y., Chen, Y., Shen, Y., & Ai, X. (2017). Integral backstepping sliding mode control for quadrotor helicopter under external uncertain disturbances. Aerospace Science and Technology, 68, 299–307. https://doi.org/10.1016/j.ast.2017.05.022
Kim, H. S., Park, J. B., & Joo, Y. H. (2017). A systematic approach to fuzzy-model-based robust control design for a quadrotor UAV under imperfect premise matching. International Journal of Fuzzy Systems, 19(4), 1227–1237. https://doi.org/10.1007/s40815-016-0233-6
Labbadi, M., & Cherkaoui, M. (2019a). Robust adaptive nonsingular fast terminal sliding-mode tracking control for an uncertain quadrotor UAV subjected to disturbances. ISA Transactions, 99, 290–304. https://doi.org/10.1016/j.isatra.2019.10.012
Labbadi, M., & Cherkaoui, M. (2019b). Robust adaptive backstepping fast terminal sliding mode controller for uncertain quadrotor UAV. Aerospace Science and Technology, 93, 105306. https://doi.org/10.1016/j.ast.2019.105306
Lee, T. (2013). Robust adaptive attitude tracking on SO(3) with an application to a quadrotor UAV. IEEE Transactions on Control Systems Technology, 21(5), 1924–1930. https://doi.org/10.1109/TCST.2012.2209887
Li, S., Wang, Y., & Tan, J. (2017). Adaptive and robust control of quadrotor aircrafts with input saturation. Nonlinear Dynamics, 89(1), 255–265. https://doi.org/10.1007/s11071-017-3451-z
Liu, H., Xi, J., & Zhong, Y. (2017a). Robust attitude stabilization for nonlinear quadrotor systems with uncertainties and delays. IEEE Transactions on Industrial Electronics, 64(7), 5585–5594. https://doi.org/10.1109/TIE.2017.2674634
Liu, Y., Rajappa, S., Montenbruck, J. M., Stegagno, P., Bülthoff, H., Allgöwer, F., & Zell, A. (2017b). Robust nonlinear control approach to nontrivial maneuvers and obstacle avoidance for quadrotor UAV under disturbances. Robotics and Autonomous Systems, 98, 317–332. https://doi.org/10.1016/j.robot.2017.08.011
Maqsood, H., Qu, Y., Taimoor, M. and Yang, B. (2020). Robust control design with novel extended disturbance observer for quadrotor vehicle. In 2020 Chinese control and decision conference (CCDC), pp. 2715–2720. Doi: https://doi.org/10.1109/CCDC49329.2020.9164157.
Maqsood, H., & Qu, Y. (2020). Nonlinear disturbance observer based sliding mode control of quadrotor helicopter. Journal of Electrical Engineering & Technology. https://doi.org/10.1007/s42835-020-00421-w
Mofid, O., & Mobayen, S. (2018). Adaptive sliding mode control for finite-time stability of quad-rotor UAVs with parametric uncertainties. ISA Transactions, 72, 1–14. https://doi.org/10.1016/j.isatra.2017.11.010
Muñoz, F., González-Hernández, I., Salazar, S., Espinoza, E. S., & Lozano, R. (2017). Second order sliding mode controllers for altitude control of a quadrotor UAS: Real-time implementation in outdoor environments. Neurocomputing, 233, 61–71. https://doi.org/10.1016/j.neucom.2016.08.111
Nguyen, N. P., Mung, N. X., Thanh, H. L. N. N., Huynh, T. T., Lam, N. T., & Hong, S. K. (2021). Adaptive sliding mode control for attitude and altitude system of a quadcopter UAV via neural network. IEEE Access, 9, 40076–40085. https://doi.org/10.1109/ACCESS.2021.3064883
Poutney, A., Kennedy, C., Clayton, G., & Ashrafiuon, H. (2018). Robust tracking control of quadrotors based on differential flatness: Simulations and experiments. IEEE/ASME Transactions on Mechatronics, 23(3), 1126–1137. https://doi.org/10.1109/TMECH.2018.2820426
Raffo, G. V., Ortega, M. G., & Rubio, F. R. (2010). An integral predictive/nonlinear control structure for a quadrotor helicopter. Automatica, 46(1), 29–39. https://doi.org/10.1016/j.automatica.2009.10.018
Razmi, H., & Afshinfar, S. (2019). Neural network-based adaptive sliding mode control design for position and attitude control of a quadrotor UAV. Aerospace Science and Technology, 91, 12–27. https://doi.org/10.1016/j.ast.2019.04.055
Ríos, H., Falcón, R., González, O. A., & Dzul, A. (2019). Continuous sliding-mode control strategies for quadrotor robust tracking: Real-time application. IEEE Transactions on Industrial Electronics, 66(2), 1264–1272. https://doi.org/10.1109/TIE.2018.2831191
Ríos, H., González-Sierra, J., & Dzul, A. (2017). Robust tracking output-control for a quad-rotor: A continuous sliding-mode approach. Journal of the Franklin Institute, 354(15), 6672–6691. https://doi.org/10.1016/j.jfranklin.2017.08.024
Shao, X., Liu, J., Cao, H., Shen, C., & Wang, H. (2018). Robust dynamic surface trajectory tracking control for a quadrotor UAV via extended state observer. International Journal of Robust and Nonlinear Control, 28(7), 2700–2719. https://doi.org/10.1002/rnc.4044
Tang, Y. R., Xiao, X., & Li, Y. (2017). Nonlinear dynamic modeling and hybrid control design with dynamic compensator for a small-scale UAV quadrotor. Measurement, 109, 51–64. https://doi.org/10.1016/j.measurement.2017.05.036
Tian, B., Liu, L., Lu, H., Zuo, Z., Zong, Q., & Zhang, Y. (2018). Multivariable finite time attitude control for quadrotor UAV: Theory and experimentation”. IEEE Transactions on Industrial Electronics, 65(3), 2567–2577. https://doi.org/10.1109/TIE.2017.2739700
Ullah, M., Zhao, C. and Maqsood, H. (2021b). Fixed-time extended disturbance observer-based robust control for quadrotor vehicle. In 2021b Chinese control and decision conference (CCDC), pp. 6127–6132. Doi: https://doi.org/10.1109/CCDC52312.2021b.9601923
Ullah, M., Zhao, C., Maqsood, H., Ul Hassan, M., & Humayun, M. (2021a). Improved neural network-based sensor fault detection and estimation strategy for an autonomous aerial vehicle. International Journal of Intelligent Unmanned Systems. https://doi.org/10.1108/IJIUS-09-2021-0109
Walid, M., Slaheddine, N., Mohamed, A. and Lamjed, B. (2014). Modeling and control of a quadrotor UAV. In Proceedings of the 15th international conference on sciences and techniques of automatic control and computer engineering, pp. 343–348. Doi: https://doi.org/10.1109/STA.2014.7086762
Xiao, B., & Yin, S. (2017). A new disturbance attenuation control scheme for quadrotor unmanned aerial vehicles. IEEE Transactions on Industrial Informatics, 13(6), 2922–2932. https://doi.org/10.1109/TII.2017.2682900
Yin, Y., Niu, H., & Liu, X. (2017). Adaptive neural network sliding mode control for quad tilt rotor aircraft. Complexity, 2017, 1–13. https://doi.org/10.1155/2017/7104708
Zou, Y., & Zhu, B. (2017). Adaptive trajectory tracking controller for quadrotor systems subject to parametric uncertainties. Journal of the Franklin Institute, 354(15), 6724–6746. https://doi.org/10.1016/j.jfranklin.2017.08.027
Funding
National Natural Science Foundation of China, grant number: 62073264, Key Research and Development Project of Shaanxi Province, 2021, grant number: ZDLGY01-01.
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Ullah, M., Zhao, C., Maqsood, H. et al. Exponential Sliding Mode Control Based on a Neural Network and Finite-Time Disturbance Observer for an Autonomous Aerial Vehicle Exposed to Environmental Disturbances and Parametric Uncertainties. J Control Autom Electr Syst 33, 1659–1670 (2022). https://doi.org/10.1007/s40313-022-00955-6
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DOI: https://doi.org/10.1007/s40313-022-00955-6