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Image of Vibration Testing and System Dynamics
ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

ADRC-Backstepping with Sliding Mode Observer for Reconfigurable Quadrotor: Design and Optimization

Journal of Vibration Testing and System Dynamics 10(1) (2026) 13--33 | DOI:10.5890/JVTSD.2026.03.002

Kamel Kadri$^{1}$, Farès Boudjema$^{2}$, Yasser Bouzid$^{1}$, Saddam Hocine Derrouaoui$^{3}$, Imad Eddine Tibermacine$^{4}$

$^{1}$ Complex Systems Control and Simulators (CSCS) Laboratory, Ecole Militaire Polytechnique, Bordj el Bahri, 16046, Algires, Algeria

$^{2}$ Process Control Laboratory (PCL), National Polytechnic School (ENP), 10, Av. Hassen Badi, 182, Algeria

$^{3}$ Ecole supérieure Ali Chabati, Algires, Algeria

$^{4}$ Department of Computer, Automation and Management Engineering, Sapienza University of Rome, Italy

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Abstract

Transformable autonomous aerial systems possess intricate dynamics as a result of inherent nonlinearities and control uncertainties, which are frequently worsened by unmeasured disturbances caused by structural reconfiguration, such as spinning body components. To tackle these issues, it is essential to have a software sensor (observer) that can estimate non-measurable states and a sophisticated method to reject disturbances. This work presents a novel cascade scheme controller that utilizes the Active Disturbance Rejection Control (ADRC) in the internal loop to address unforeseeable disturbances in nonlinear systems. At the same time, a separate loop employs a Backstepping controller based on the state variables Sliding Mode Observer (SMO), guaranteeing global stability for the entire system. We utilize these methodologies on a Reconfigurable Quadrotor, which serves as a Transformable Unmanned Aerial System. The Multiobjective Particle Swarm Optimization (MPSO) algorithm is utilized to achieve parameter synthesis for the entire system. Numerical simulations provide evidence of the system's exceptional performance in terms of robustness, energy optimization, and perturbation rejection.

References

  1. [1]  Zhang, C., Hu, H., Wang, J., and Zhang, X. (2021), A review of unmanned aerial vehicle low-altitude remote sensing (UAV-LARS) use in agricultural monitoring in China, Remote Sensing, 13(6), 1221.
  2. [2]  Saeed, A.S., Younes, A.B., Cai, C., and Cai, G. (2018), A survey of hybrid unmanned aerial vehicles, Progress in Aerospace Sciences, 98, 91–105.
  3. [3]  Mei, C., Guo, D., Chen, G., Cai, J., and Li, J. (2024), Event-triggered adaptive control for a class of nonlinear systems with dead-zone input, Electronics, 13(1), 210.
  4. [4]  Yu, X., Zhou, S., Guo, K., Zhang, Y., and Guo, L. (2023), Integrated reconfiguration mechanism for quadrotors with capability analysis against rotor failure, Journal of Guidance, Control, and Dynamics, 46(2), 401–409.
  5. [5]  Sun, Y., Liu, X., Cao, K., Shen, H., Li, Q., Chen, G., Xu, J., and Ji, A. (2023), Design and theoretical research on aerial-aquatic vehicles: a review, Journal of Bionic Engineering, 20(6), 2512-2541.
  6. [6]  Wang, J., Zhu, B., and Zheng, Z. (2023), Robust adaptive control for a quadrotor UAV with uncertain aerodynamic parameters, IEEE Transactions on Aerospace and Electronic Systems, 59(6), 8313-8326.
  7. [7]  Salmi, A., Guiatni, M., Bouzid, Y., Derrouaoui, S.H., and Boudjema, F. (2024), Fault tolerant control based on thau observer of a reconfigurable quadrotor with total loss of actuator, Unmanned Systems, 12(4), 667–683.
  8. [8]  Yu, Z., Qu, Y., and Zhang, Y. (2019), Fault-tolerant containment control of multiple unmanned aerial vehicles based on distributed sliding-mode observer, Journal of Intelligent $\&$ Robotic Systems, 93, 163–177.
  9. [9]  Messaoud, S.B., Belkhiri, M., Belkhiri, A., and Rabhi, A. (2024), Active disturbance rejection control of flexible industrial manipulator: a MIMO benchmark problem, European Journal of Control, 77, 100965.
  10. [10]  Zhong, H., Li, S., Wang, Y., and Liu, H. (2016), Adaptive robust RBFNNs-based model estimator for a small quadrotor aircraft robot, in 2016 12th IEEE/ASME International Conference on Mechatronic and Embedded Systems and Applications (MESA), pp. 1–6.
  11. [11]  Huang, T., Huang, D., Wang, Z., Dai, X., and Shah, A. (2021), Generic adaptive sliding mode control for a quadrotor UAV system subject to severe parametric uncertainties and fully unknown external disturbance, International Journal of Control, Automation and Systems, 19(2), 698–711.
  12. [12]  Gambhire, S.J., Kishore, D.R., Londhe, P.S., and Pawar, S.N. (2021), Review of sliding mode based control techniques for control system applications, International Journal of Dynamics and Control, 9(1), 363–378.
  13. [13]  Amer, T.S., Elhagary, M.A., Hassan, S.S., and Galal, A.A. (2024), Examining the behavior of a two-connected-spring pendulum according to non-resonance and resonance conditions, Journal of Low Frequency Noise, Vibration and Active Control, 14613484241302267.
  14. [14]  Amer, A., Zhang, W., Amer, T.S., and Li, H. (2025), Nonlinear vibration analysis of a 3DOF double pendulum system near resonance, Alexandria Engineering Journal, 113, 262–286.
  15. [15]  Amer, T.S., Abdelhfeez, S.A., Elbaz, R.F., and Abohamer, M.K. (2024), Exploring dynamics, stability, and bifurcation in a coupled damped oscillator with piezoelectric energy harvester, Journal of Low Frequency Noise, Vibration and Active Control, 113(2025), 262-286.
  16. [16]  Bahnasy, T.A., Amer, T.S., Abohamer, M.K., Abosheiaha, H.F., Elameer, A.S., and Almahalawy, A. (2024), Stability and bifurcation analysis of a 2DOF dynamical system with piezoelectric device and feedback control, Scientific Reports, 14(1), 26477.
  17. [17]  Abohamer, M.K., Amer, T.S., Arab, A., and Galal, A.A. (2024), Analyzing the chaotic and stability behavior of a Duffing oscillator excited by a sinusoidal external force, Journal of Low Frequency Noise, Vibration and Active Control, 44(2), 969-986.
  18. [18]  Derrouaoui, S.H., Bouzid, Y., Guiatni, M., Dib, I., and Moudjari, N. (2020), Design and modeling of unconventional quadrotors, in 2020 28th Mediterranean Conference on Control and Automation (MED), pp. 721–726.
  19. [19]  Harvey, C., Gamble, L.L., Bolander, C.R., Hunsaker, D.F., Joo, J.J., and Inman, D.J. (2022), A review of avian-inspired morphing for UAV flight control, Progress in Aerospace Sciences, 132, 100825.
  20. [20]  Han, J. (2009), From PID to active disturbance rejection control, IEEE Transactions on Industrial Electronics, 56(3), 900–906.
  21. [21]  Guo, B.Z. and Zhao, Z.L. (2017), Active Disturbance Rejection Control for Nonlinear Systems: An Introduction, John Wiley \& Sons.
  22. [22]  Kadri, K., Boudjema, F., Bouzid, Y., Ghazali, M., and Sahouli, H. (2023), Active disturbance rejection control of unconventional quadrotor based on grey wolf optimization algorithm, in 2023 International Conference on Advances in Electronics, Control and Communication Systems (ICAECCS), pp. 1–7.
  23. [23]  Herbst, G. and Madonski, R. (2025), Active Disturbance Rejection Control: From Principles to Practice, Springer Nature.
  24. [24]  Su, Z., Sun, L., Xue, W., and Lee, K.Y. (2023), A review on active disturbance rejection control of power generation systems: fundamentals, tunings and practices, Control Engineering Practice, 141, 105716.
  25. [25]  Cao, Y., Cao, Z., Feng, F., and Xie, L. (2023), ADRC-based trajectory tracking control for a planar continuum robot, Journal of Intelligent $\&$ Robotic Systems, 108(1), 1.
  26. [26]  Derrouaoui, S.H., Bouzid, Y., and Guiatni, M. (2021), Nonlinear robust control of a new reconfigurable unmanned aerial vehicle, Robotics, 10(2), 76.
  27. [27]  Lv, W., Park, J.H., Lu, J., and Guo, R. (2023), Adaptive fuzzy output feedback control for a class of uncertain nonlinear systems in the presence of sensor attacks, Journal of the Franklin Institute, 360(3), 2326–2343.
  28. [28]  Derrouaoui, S.H., Bouzid, Y., and Guiatni, M. (2022), Adaptive integral backstepping control of a reconfigurable quadrotor with variable parameters’ estimation, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 236(7), 1294-1309.
  29. [29]  Fu, B., Che, W., Liu, Y., Wang, Q., and Yu, H. (2024), Novel sliding-mode control for a class of second-order systems with mismatched disturbances, International Journal of Robust and Nonlinear Control, 34(2), 1277–1291.
  30. [30]  Jing, Y., Wang, X., Heredia-Juesas, J., Fortner, C., Giacomo, C., Sipahi, R., and Martinez-Lorenzo, J. (2022), PX4 simulation results of a quadcopter with a disturbance-observer-based and PSO-optimized sliding mode surface controller, Drones, 6(9), 261.
  31. [31]  Derrouaoui, S.H., Bouzid, Y., and Guiatni, M. (2021), PSO-based optimal gain scheduling backstepping flight controller design for a transformable quadrotor, Journal of Intelligent $\&$ Robotic Systems, 102(3), 1–25.
  32. [32]  Zhong, S., Huang, Y., and Guo, L. (2021), An ADRC-based PID tuning rule, International Journal of Robust and Nonlinear Control, 32(18), 9542-9555.
  33. [33]  Xie, J., Wei, W., Liao, P., and Liu, J. (2022), Design of ADRC controller for induction motor based on improved fal function, in 2022 14th International Conference on Advanced Computational Intelligence (ICACI), pp. 216–220.
  34. [34]  Xue, W. and Huang, Y. (2016), Tuning of sampled-data ADRC for nonlinear uncertain systems, Journal of Systems Science and Complexity, 29, 1187–1211.
  35. [35]  Hou, Z., Tian, J., Yang, J., Wang, S., and Chao, T. (2022), An ADRC attitude control algorithm of quadrotor for wind interference, in International Conference on Guidance, Navigation and Control, pp. 5617–5628.
  36. [36]  Xia, Y. and Fu, M. (2013), Compound Control Methodology for Flight Vehicles, vol. 438, Springer.
  37. [37]  Hermann, R. and Krener, A. (1977), Nonlinear controllability and observability, IEEE Transactions on Automatic Control, 22(5), 728–740.
  38. [38]  Guo, J., Xue, W., and Hu, T. (2016), Active disturbance rejection control for PMLM servo system in CNC machining, Journal of Systems Science and Complexity, 29, 74–98.
  39. [39]  Kennedy, J. and Eberhart, R. (1995), Particle swarm optimization, in Proceedings of ICNN'95—International Conference on Neural Networks, 4, 1942–1948.
  40. [40]  Bouzid, Y., Derrouaoui, S.H., and Guiatni, M. (2021), PID gain scheduling for 3D trajectory tracking of a quadrotor with rotating and extendable arms, in 2021 International Conference on Recent Advances in Mathematics and Informatics (ICRAMI), 1–4.
  41. [41]  Derrouaoui, S.H., Bouzid, Y., Guiatni, M., and Belmouhoub, A. (2022), Trajectory tracking of a reconfigurable multirotor using optimal robust sliding mode controller, University of El Oued.
  42. [42]  Belmouhoub, A., Medjmadj, S., Bouzid, Y., Derrouaoui, S.H., and Guiatni, M. (2022), Enhanced backstepping control for an unconventional quadrotor under external disturbances, The Aeronautical Journal, 127(1310), 627-650.

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