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An Observer-based Backstepping Integral Nonsingular Fast Terminal Sliding Mode Fault Tolerant Control Design for Quadrotors Under Different Types of Actuator Faults

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  • Robot and Applications
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Abstract

This paper develops a fault tolerant control (FTC) approach for quadrotor aerial vehicles under different types of actuator faults. An observer-based fault detection and diagnosis mechanism is devised to estimate the faults. A robust finite-time convergent controller which merges the features of Backstepping, and Integral Nonsingular Fast Terminal Sliding surface is proposed to ensure the finite time stability of the states in nominal conditions and their asymptotic stability in faulty conditions. A control redistribution method is formulated to maintain the quadrotor in flight, in the case of complete actuator failure and lock in place (LIP) faults. The proposed controller was assessed in the presence of loss of actuator effectiveness (LOE) faults, complete damage of one rotor and LIP faults. The obtained results confirmed the ability of the proposed approach to enable the quadrotor to track the commanded trajectory precisely under partial LOE faults and continue tracking with an expected performance degradation under the effect of complete motor failure and LIP faults.

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References

  1. N. Mohamed, J. Al-Jaroodi, I. Jawhar, A. Idries, and F. Mohammed, “Unmanned aerial vehicles applications in future smart cities,” Technological Forecasting and Social Change, vol. 153, 119293, 2020.

    Article  Google Scholar 

  2. K. Valavanis, “Special issue on unmanned aerial vehicles (UAVs),” Control Theory and Technology, vol. 16, no. 2, pp. 81–81, 2018.

    Article  MathSciNet  Google Scholar 

  3. F. Nan, S. Sun, P. Foehn and D. Scaramuzza, “Nonlinear MPC for quadrotor fault-tolerant control,” IEEE Robotics and Automation Letters, vol. 7, no. 2, pp. 5047–5054, April 2022.

    Article  Google Scholar 

  4. B. Wang and Y. Zhang, “An adaptive fault-tolerant sliding mode control allocation scheme for multirotor helicopter subject to simultaneous actuator faults,” IEEE Transactions on Industrial Electronics, vol. 65, no. 5, pp. 4227–4236, May 2018.

    Article  Google Scholar 

  5. H. Yang, Y. Jiang, and S. Yin, “Fault-tolerant control of time-delay Markov jump systems with Itô stochastic process and output disturbance Based on sliding mode observer,” IEEE Transactions on Industrial Informatics, vol. 14, no. 12, pp. 5299–5307, December 2018.

    Article  Google Scholar 

  6. B. Xiao, S. Yin, and H. Gao, “Reconfigurable tolerant control of uncertain mechanical systems with actuator faults: A sliding mode observer-based approach,” IEEE Transactions on Control Systems Technology, vol. 26, no. 4, pp. 1249–1258, July 2018.

    Article  Google Scholar 

  7. B. Li, W. Gong, Y. Yang, B. Xiao, and D. Ran, “Appointed fixed time observer-based sliding mode control for a quadrotor UAV under external disturbances,” IEEE Transactions on Aerospace and Electronic Systems, vol. 58, no. 1, pp. 290–303, February 2022

    Article  Google Scholar 

  8. K. Liu and R. Wang, “Antisaturation Adaptive Fixed-Time Sliding Mode Controller Design to Achieve Faster Convergence Rate and Its Application,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 69, no. 8, pp. 3555–3559, August 2022.

    Google Scholar 

  9. J. Xiong, J. Pan, G. Chen, X. Zhang, and F. Ding, “Sliding mode dual-channel disturbance rejection attitude control for a quadrotor,” IEEE Transactions on Industrial Electronics, vol. 69, no. 10, pp. 10489–10499, October 2022.

    Article  Google Scholar 

  10. M. Labbadi, Y. Boukal, and M. Cherkaoui, “Advanced robust nonlinear control approaches for quadrotor unmanned aerial vehicle: Roadmap to improve tracking-trajectory performance in the presence of external disturbances,” Springer Nature, vol. 384, 2021.

  11. G. Xu, Y. Xia, D. Zhai, and B. Cui, “Adaptive sliding mode disturbance observer-based funnel trajectory tracking control of quadrotor with external disturbances,” IET Control Theory & Applications, vol. 15, no. 13, pp. 1778–1788, 2021.

    Article  MathSciNet  Google Scholar 

  12. J. Xiong and G. Zhang, “Global fast dynamic terminal sliding mode control for a quadrotor UAV,” ISA Transactions, vol. 66, pp. 233–240, 2017.

    Article  Google Scholar 

  13. X. Yu, Y. Feng, and Z. Man, “Terminal sliding mode control - An overview,” IEEE Open Journal of the Industrial Electronics Society, vol. 2, pp. 36–52, 2021.

    Article  Google Scholar 

  14. B. Mu, Y. Pei, and Y. Shi, “Integral sliding mode control for a quadrotor in the presence of model uncertainties and external disturbances,” Proc. of American Control Conference, pp. 5818–5823, 2017.

  15. Z. Hou, X. Yu, and P. Lu, “Terminal sliding mode control for quadrotors with chattering reduction and disturbances estimator: Theory and application,” Journal of Intelligent & Robotic Systems, vol. 105, no. 4, 2022.

  16. A. Modirrousta and M. Khodabandeh, “Adaptive non-singular terminal sliding mode controller: New design for full control of the quadrotor with external disturbances,” Transactions of the Institute of Measurement and Control, vol. 39, no. 3, pp. 371–383, 2016.

    Article  Google Scholar 

  17. Y. Niu, H. Ban, H. Zhang, W. Gong, and F. Yu, “Nonsingular terminal sliding mode based finite-time dynamic surface control for a quadrotor UAV,” Algorithms, vol. 14, no. 11, 315, 2021.

    Article  Google Scholar 

  18. U. Ansari, A. Bajodah, and M. Hamayun, “Quadrotor control via robust generalized dynamic inversion and adaptive non-singular terminal sliding mode,” Asian Journal of Control, vol. 21, no. 3, pp. 1237–1249, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  19. P. Tang, F. Zhang, J. Ye, and D. Lin, “An integral TSMC-based adaptive fault-tolerant control for quadrotor with external disturbances and parametric uncertainties,” Aerospace Science and Technology, vol. 109, 106415, 2021.

    Article  Google Scholar 

  20. A. Najafi, M. Vu, S. Mobayen, J. Asad, and A. Fekih, “Adaptive barrier fast terminal sliding mode actuator fault tolerant control approach for quadrotor UAVs,” Mathematics, vol. 10, no. 16, 3009, 2022.

    Article  Google Scholar 

  21. Y. Tang and R. Patton, “Reconfigurable fault tolerant control for nonlinear aircraft based on concurrent SMC-NN adaptor,” Proc. of the American Control Conference, pp. 1267–1272, Portland, OR, 2014.

  22. N. P. Nguyen, W. Kim, and J. Moon, “Observer-based super-twisting sliding mode control with fuzzy variable gains and its application to overactuated quadrotors,” Proc. of the IEEE Conference on Decision and Control, pp. 5993–5998, Miami Beach, FL, 2018.

  23. S. Mallavalli and A. Fekih, “A fault tolerant tracking control for a quadrotor UAV subject to simultaneous actuator faults and exogenous disturbances,” International Journal of Control, vol. 93, no. 3, pp. 655–668, March 2020

    Article  MathSciNet  MATH  Google Scholar 

  24. B. Gao, Y. Liu, and L. Liu, “Adaptive neural fault-tolerant control of a quadrotor UAV via fast terminal sliding mode,” Aerospace Science and Technology, vol. 129, 107818, 2022.

    Article  Google Scholar 

  25. S. Han, Q. Zhong, L. Cui, K. Shi, X. Cai, and O. Kwon, “Extended dissipativity analysis for T-S fuzzy systems based on reliable memory control and aperiodic sampled-data method,” Journal of the Franklin Institute, vol. 359, no. 5, pp. 2156–2175, 2022.

    Article  MathSciNet  MATH  Google Scholar 

  26. F. Chen, W. Lei, K. Zhang, G. Tao, and B. Jiang, “A novel nonlinear resilient control for a quadrotor UAV via back-stepping control and nonlinear disturbance observer,” Nonlinear Dynamics, vol. 85, no. 2, pp. 1281–1295, 2016.

    Article  MATH  Google Scholar 

  27. Z. Jin, G. Meng, and L. Wang, “Backstepping based trajectory tracking control for a quadrotor aircraft with nonlinear disturbance observer,” International Journal of Control and Automation, vol. 8, no. 11, pp. 169–182, 2015.

    Article  Google Scholar 

  28. H. Lu, C. Liu, M. Coombes, L. Guo, and W. Chen, “Online optimisation-based backstepping control design with application to quadrotor,” IET Control Theory & Applications, vol. 10, no. 14, pp. 1601–1611, 2016.

    Article  MathSciNet  Google Scholar 

  29. M. M. Basri, A. Husain, and K. Danapalasingam, “Intelligent adaptive backstepping control for MIMO uncertain non-linear quadrotor helicopter systems,” Transactions of the Institute of Measurement and Control, vol. 37, no. 3, pp. 345–361, 2014.

    Article  Google Scholar 

  30. F. Chen, R. Jiang, K. Zhang, B. Jiang, and G. Tao, “Robust backstepping sliding-mode control and observer-based fault estimation for a quadrotor UAV,” IEEE Transactions on Industrial Electronics, vol. 63, no. 8, pp. 5044–5056, August 2016.

    Google Scholar 

  31. S. Zeghlache, A. Djerioui, L. Benyettou, T. Benslimane, H. Mekki, and A. Bouguerra, “Fault tolerant control for modified quadrotor via adaptive type-2 fuzzy backstepping subject to actuator faults,” ISA Transactions, vol. 95, pp. 330–345, 2019.

    Article  Google Scholar 

  32. N. Nguyen and S. Hong, “Active fault-tolerant control of a quadcopter against time-varying actuator faults and saturations using sliding mode backstepping approach,” Applied Sciences, vol. 9, no. 19, 4010, 2019.

    Article  Google Scholar 

  33. A. Merheb, H. Noura, and F. Bateman, “Emergency control of AR drone quadrotor UAV suffering a total loss of one rotor,” IEEE/ASME Transactions on Mechatronics, vol. 22, no. 2, pp. 961–971, April 2017.

    Article  Google Scholar 

  34. A. Lanzon, A. Freddi, and S. Longhi, “Flight control of a quadrotor vehicle subsequent to a rotor failure,” Journal of Guidance, Control, and Dynamics, vol. 37, no. 2, pp. 580–591, 2014.

    Article  Google Scholar 

  35. A. Freddi, A. Lanzon, and S. Longhi, “A feedback linearization approach to fault tolerance in quadrotor vehicles,” IFAC Proceedings Volumes, vol. 44, pp. 5413–5418, January 2011.

    Article  Google Scholar 

  36. J. Stephan, L. Schmitt, and W. Fichter, “Linear parameter-varying control for quadrotors in case of complete actuator loss,” Journal of Guidance, Control, and Dynamics, vol. 41, no. 10, pp. 2232–2246, 2018.

    Article  Google Scholar 

  37. R. Falcón, H. Ríos, A. Dzul, “A sliding-mode-based active fault-tolerant control for robust trajectory tracking in quad-rotors under a rotor failure,” International Journal of Robust and Nonlinear Control, vol. 32, no. 15, pp. 8451–8469, 2022.

    Article  MathSciNet  Google Scholar 

  38. V. Lippiello, F. Ruggiero, and D. Serra, “Emergency landing for a quadrotor in case of a propeller failure: A PID based approach,” Proc. of the IEEE International Symposium on Safety, Security, and Rescue Robotics, pp. 1–7, Hokkaido, 2014.

  39. P. Lu and E. Kampen, “Active fault-tolerant control for quadrotors subjected to a complete rotor failure,” Proc. of the International Conference on Intelligent Robots and Systems, pp. 4698–4703, Hamburg, 2015.

  40. N. Nguyen, I. Prodan, F. Stoican, and L. Lefèvre, “Reliable nonlinear control for quadcopter trajectory tracking through differential flatness,” IFAC-PapersOnLine, vol. 50, no. 1, pp. 6971–6976, 2017.

    Article  Google Scholar 

  41. L. An and G. Yang, “Secure state estimation against sparse sensor attacks with adaptive switching mechanism,” IEEE Transactions on Automatic Control, vol. 63, no. 8, pp. 2596–2603, August 2018.

    Article  MathSciNet  MATH  Google Scholar 

  42. A. Merheb, H. Noura, and F. Bateman, “Passive fault tolerant control of quadrotor UAV using regular and cascaded sliding mode control,” Conference on Control and Fault-tolerant Systems, 2013.

  43. J. Boskovic, S. Bergstrom, and R. Mehra, “Robust integrated flight control design under failures, damage, and state-dependent disturbances,” Journal of Guidance, Control, and Dynamics, vol. 28, no. 5, pp. 902–917, 2005.

    Article  Google Scholar 

  44. M. Chen, K. Yan, and Q. Wu, “Multiapproximator-based fault-tolerant tracking control for unmanned autonomous helicopter with input saturation,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 52, no. 9, pp. 5710–5722, Sept. 2022

    Article  Google Scholar 

  45. S. Bhat and D. Bernstein, “Finite-time stability of continuous autonomous systems,” SIAM Journal on Control and Optimization, vol. 38, no. 3, pp. 751–766, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  46. P. Li, J. Ma, Z. Zheng, and L. Geng, “Fast nonsingular integral terminal sliding mode control for nonlinear dynamical systems,” Proc. of the 53rd IEEE Conference on Decision and Control, Los Angeles, CA, 2014, pp. 4739–4746.

  47. S. Mallavalli and A. Fekih, “A fault tolerant control approach for a quadrotor UAV subject to time varying disturbances and actuator faults,” Proc. of the IEEE Conference on Control Technology and Applications, pp. 59–-601, Mauna Lani, HI, 2017.

  48. J. Bošković and R. Mehra, “A decentralized fault-tolerant control system for accommodation of failures in higher-order flight control actuators,” IEEE Transactions on Control Systems Technology, vol. 18, no. 5, pp. 1103–1115, September 2010.

    Article  Google Scholar 

  49. J. Bošković, L. Chen, and R. Mehra, “Adaptive control design for non-affine models arising in flight control,” AIAA Journal of Guidance, Control, and Dynamics, vol. 27, no. 2, pp. 209–217, 2004.

    Article  Google Scholar 

  50. A. Hasan and T. Johansen, “Model-based actuator fault diagnosis in multirotor UAVs,” Proc. of the International Conference on Unmanned Aircraft Systems, pp. 1017–1024, Dallas, TX, 2018.

  51. AscTec Pelican R&D UAS for Computer Vision & SLAM, Ascending Technologies, 2022, [online] Available: https://www.aeroexpo.online/prod/ascending-technologies/product-181442-24426.html.

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Authors and Affiliations

  1. School of Electrical and Computer Engineering, University of Louisiana at Lafayette, Lafayete, LA, 70504, USA

    Seema Mallavalli & Afef Fekih

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  1. Seema Mallavalli
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Correspondence to Seema Mallavalli.

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Seema Mallavalli received her Ph.D. degree in systems engineering from the University of Louisiana at Lafayette in 2022. Her research interests include robust and non-linear control, fault tolerant control, unmanned systems, and autonomous systems. She has served as a reviewer for several journals and conferences.

Afef Fekih received her B.S., M.S., and Ph.D. degrees all in electrical engineering from the National Engineering School of Tunis, Tunisia, in 1995, 1998, and 2002, respectively. Currently, she is a Full Professor in the Department of Electrical and Computer Engineering and the Chevron/BORSF Professor in Engineering at the University of Louisiana at Lafayette. Her research interests focus on control theory and applications, including nonlinear and robust control, optimal control, fault tolerant control with applications to power systems, wind turbines, unmanned vehicles, and automotive engines. Dr. Fekih is a senior member of the Institute of Electrical and Electronics Engineers (IEEE), a member of the IEEE control systems society, IEEE Power and Energy society and the IEEE women in Engineering society. She is the co-chair and media coordinator of the IEEE Control System Society (CSS) Women in Control group (WiC). She is an appointed member of the Board of Governors of the IEEE Control Systems Society (2023–2024). She is a member of the IFAC Technical Committee on Power and Energy Systems, the American Automatic Control Council (AACC) Technical Committee on Control Education, and the IEEE Systems Council on Diversity & Inclusion Committee. She is a member of the IEEE Technology conference editorial board and serves as Associate Editor for the IEEE-IAS Industrial Automation and Control Committee. She has served as reviewer and guest editor for numerous journals and conferences.

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Mallavalli, S., Fekih, A. An Observer-based Backstepping Integral Nonsingular Fast Terminal Sliding Mode Fault Tolerant Control Design for Quadrotors Under Different Types of Actuator Faults. Int. J. Control Autom. Syst. 21, 4015–4031 (2023). https://doi.org/10.1007/s12555-022-0951-5

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