Skip to main content
SpringerLink
Log in

Finite-time Adaptive Integral Backstepping Fast Terminal Sliding Mode Control Application on Quadrotor UAV

  • Regular Papers
  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper presents a reliable and novel quadrotor flight control system designed to enhance trajectory tracking performance, robustness and adaptiveness against the uncertain parameters and the external wind disturbance. By combining a recursive control methodology with a robust control algorithm, a finite-time adaptive integral backstepping fast terminal sliding mode control is designed for major control loops related to position tracking and attitude stabilization. To estimate quadrotor mass and inertia moments, only four adaptation laws are developed. To compensate the unknown upper bound on the disturbances, a robust and adaptive switching gain is designed. The designed controller guarantees that all the closed signals are semi-global practical finite-time stability while the tracking error converges to a small neighborhood of the origin. The obtained numerical results and comparison studies show the effectiveness, robustness, adaptiveness and energy efficiency of the proposed flight control system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

x, y, z :

longitudinal, lateral, and altitude motions in Earth-fixed frame, respectively, m

ϕ, θ, ψ :

roll, pitch, and heading angles in Earth-fixed frame, respectively, rad

p, q, r :

roll, pitch, and heading rotational velocities in body-fixed frame, respectively, rad/s

Ix, Iy, Iz :

roll, pitch, and yaw inertia moments, Kg.m2

g :

gravity acceleration, m/s2

m :

mass, Kg

l :

distance between quadrotor center mass and the axis of the propeller, m

uϕ, uθ, uψ :

aerodynamic roll, pitch, and heading moments, respectively, N.m

u z :

lift force, N

ω j :

rotor j velocity, j = {1,2,3,4}, rad/s

References

  1. A. Lavaei and M. A. A. Atashgah, “Optimal 3D trajectory generation in delivering missions under urban constraints for a flying robot,” Intelligent Service Robotics, vol. 10, no. 3, pp. 241–256, July 2017.

    Google Scholar 

  2. K. Eliker, G. Zhang, S. Grouni, and W. Zhang, “An optimization problem for quadcopter reference flight trajectory generation,” Journal of Advanced Transportation, vol. 2018, Article ID 6574183, July 2018.

  3. H. Liu, J. Xi, and Y. Zhong, “Robust attitude stabilization for nonlinear quadrotor systems with uncertainties and delays,” IEEE Trans. on Industrial Electronics, vol. 64, no. 7, pp. 5585–5594, July 2017.

    Google Scholar 

  4. Y. Feng, X. Yu, and Z. Man, “Non-singular terminal sliding mode control of rigid manipulators,” Automatica, vol. 38, no. 12, pp. 2159–2167, December 2002.

    MathSciNet  MATH  Google Scholar 

  5. S. Yu, X. Yu, B. Shirinzadeh, and Z. Man, “Continuous finite-time control for robotic manipulators with terminal sliding mode,” Automatica, vol. 41, no. 11, pp. 1957–1964, November 2005.

    MathSciNet  MATH  Google Scholar 

  6. Z. Zhu, Y. Xia, and M. Fu, “Attitude stabilization of rigid spacecraft with finite-time convergence,” International Journal of Robust and Nonlinear Control, vol. 21, no. 6, pp. 686–702, April 2011.

    MathSciNet  MATH  Google Scholar 

  7. M. Chen, Q. Wu, and R. Cui, “Terminal sliding mode tracking control for a class of SISO uncertain nonlinear systems,” ISA Trans., vol. 52, no. 2, pp. 198–206, March 2013.

    Google Scholar 

  8. N. Wang, C. Qian, J. Sun, and Y. Liu, “Adaptive robust finite-time trajectory tracking control of fully actuated marine surface vehicles,” IEEE Trans. on Control Systems Technology, vol. 24, no. 4, pp. 1454–1462, July 2016.

    Google Scholar 

  9. Y. Li, D. Ye, and Z. Sun, “Robust finite time control algorithm for satellite attitude control,” Aerospace Science and Technology, vol. 68, pp. 46–57, September 2017.

    Google Scholar 

  10. J. Sun, S. Xu, S. Song, and X. Dong, “Finite-time tracking control of hypersonic vehicle with input saturation,” Aerospace Science and Technology, vol. 71, pp. 272–284, December 2017.

    Google Scholar 

  11. S. B. F. Asl and S. S. Moosapour, “Adaptive backstepping fast terminal sliding mode controller design for ducted fan engine of thrust-vectored aircraft,” Aerospace Science and Technology, vol. 71, pp. 521–529, December 2017.

    Google Scholar 

  12. J. Qiao, D. Zhang, Y. Zhu, and P. Zhang, “Disturbance observer-based finite-time attitude maneuver control for micro satellite under actuator deviation fault,” Aerospace Science and Technology, vol. 82–83, pp. 262–271, November 2018.

    Google Scholar 

  13. H. T. Chen, S. M. Song, and Z. B. Zhu, “Robust finite-time attitude tracking control of rigid spacecraft under actuator saturation,” International Journal of Control, Automation and Systems, vol. 16, no. 1, pp. 1–15, February 2018.

    Google Scholar 

  14. X. Huang, Y. Yan, and Z. Huang, “Finite-time control of underactuated spacecraft hovering,” Control Engineering Practice, vol. 68, pp. 46–62, November 2017.

    Google Scholar 

  15. F. Wang, X. Zhang, B. Chen, C. Lin, X. Li, and J. Zhang, “Adaptive finite-time tracking control of switched nonlinear systems,” Information Sciences, vol. 421, pp. 126–135, December 2017.

    MathSciNet  Google Scholar 

  16. Q. Khan, R. Akmeliawati, A. I. Bhatti, and M. A. Khan, “Robust stabilization of underactuated nonlinear systems: A fast terminal sliding mode approach,” ISA Trans., vol. 66, pp. 241–248, January 2017.

    Google Scholar 

  17. H. Wang, B. Chen, C. Lin, Y. Sun, and F. Wang, “Adaptive finite-time control for a class of uncertain high-order nonlinear systems based on fuzzy approximation,” IET Control Theory & Applications, vol. 11, no. 5, pp. 677–684, March 2017.

    Google Scholar 

  18. G. Zhang, Y. Deng, and W. Zhang, “Robust neural path-following control for underactuated ships with the DVS obstacles avoidance guidance,” Ocean Engineering, vol. 143, pp. 198–208, October 2017.

    Google Scholar 

  19. Q. Hu and B. Jiang, “Continuous finite-time attitude control for rigid spacecraft based on angular velocity observer,” IEEE Trans. on Aerospace and Electronic Systems, vol. 54, no. 3, pp. 1082–1092, June 2018.

    MathSciNet  Google Scholar 

  20. L. Zhao, J. Yu, C. Lin, and Y. Ma, “Adaptive neural consensus tracking for nonlinear multiagent systems using finite-time command filtered backstepping,” IEEE Trans. on Systems, Man, and Cybernetics: Systems, vol. 48, no.11, pp. 2003–2012, November 2018.

    Google Scholar 

  21. B. Li, Q. Hu, Y. Yang, and O. A. Postolache, “Finite-time disturbance observer based integral sliding mode control for attitude stabilisation under actuator failure,” IET Control Theory & Applications, vol. 13, no.1, pp. 50–58, January 2019.

    MathSciNet  Google Scholar 

  22. B. Li, Q. Hu, and Y. Yang, “Continuous finite-time extended state observer based fault tolerant control for attitude stabilization,” Aerospace Science and Technology, vol. 84, pp. 204–213, January 2019.

    Google Scholar 

  23. A. Tayebi and S. McGilvray, “Attitude stabilization of a VTOL quadrotor aircraft,” IEEE Trans. on Control Systems Technology, vol. 14, no. 3, pp. 562–571, May 2006.

    Google Scholar 

  24. H. Bolandi, M. Rezaei, R. Mohsenipour, H. Nemati, and S. M. Smailzadeh, “Attitude control of a quadrotor with optimized PID controller,” Intelligent Control and Automation, vol. 4, no. 3, pp. 335–342, August 2013.

    Google Scholar 

  25. D. Gautam and C. Ha, “Control of a quadrotor using a smart self-tuning fuzzy PID controller,” International Journal of Advanced Robotic Systems, vol. 10, no. 11, pp. 335–342, January 2013.

    Google Scholar 

  26. I. D. Cowling, O. A. Yakimenko, J. F. Whidborne, and A. K. Cooke, “Direct method based control system for an autonomous quadrotor,” Journal of Intelligent and Robotic Systems, vol. 60, no. 2, pp. 285–316, November 2010.

    MATH  Google Scholar 

  27. A. Das, K. Subbarao, and F. Lewis, “Dynamic inversion with zero-dynamics stabilisation for quadrotor control,” IET Control Theory & Applications, vol. 3, no. 3, pp. 303–314, March 2009.

    MathSciNet  Google Scholar 

  28. A. A. Mian and D. B. Wang, “Dynamic modeling and nonlinear control strategy for an underactuated quad rotor rotorcraft,” Journal of Zhejiang University-SCIENCE A, vol. 9, no. 4, pp. 539–545, April 2008.

    MATH  Google Scholar 

  29. R. Amin, L. Aijun, and S. Shamshirband, “A review of quadrotor UAV: control methodologies and performance evaluation,” International Journal of Automation and Control, vol. 10, no. 2, pp. 87–103, May 2016.

    Google Scholar 

  30. H. Mo and G. Farid, “Nonlinear and adaptive intelligent control techniques for quadrotor UAV — a survey,” Asian Journal of Control, vol. 21, no. 2, pp. 989–1008, March 2019.

    MathSciNet  MATH  Google Scholar 

  31. T. Madani and A. Benallegue, “Backstepping control for a quadrotor helicopter,” Proc. of the 2006 IEEE/RSJ International Conf. Intelligent Robots and Systems, pp. 3255–3260, January 2006.

  32. H. Bouadi, M. Bouchoucha, and M. Tadjine, “Modelling and stabilizing control laws design based on backstepping for an UAV type quad-rotor,” IFAC Proceedings Volumes, vol. 40, no. 15, pp. 245–250, April 2007.

    Google Scholar 

  33. S. Bouabdallah and R. Siegwart, “Full control of a quadrotor,” Proc. of the 2007 IEEE/RSJ International Conf. Intelligent Robots and Systems, pp. 153–158, December 2007.

  34. A. Das, F. Lewis, and K. Subbarao, “Backstepping approach for controlling a quadrotor using lagrange form dynamics,” Journal of Intelligent and Robotic Systems, vol. 56, no. 1–2, pp. 127–151, September 2009.

    MATH  Google Scholar 

  35. X. Huo, M. Huo, and H. R. Karimi, “Attitude stabilization control of a quadrotor UAV by using backstepping approach,” Mathematical Problems in Engineering, vol. 2014, Article ID 749803, February 2014.

  36. K. Eliker, H. Bouadi, and M. Haddad, “Flight planning and guidance features for an uav flight management computer,” Proc. of the IEEE 21st International Conf. Emerging Technologies and Factory Automation, pp. 1–6, November 2016.

  37. B. Y. Lee, D. W. Yoo, and M. J. Tahk, “Performance comparison of three different types of attitude control systems of the quad-rotor UAV to perform flip maneuver,” International Journal of Aeronautical and Space Sciences, vol. 14, no. 1, pp. 58–66, March 2013.

    Google Scholar 

  38. M. J. Reinoso, L. I. Minchala, P. Ortiz, D. F. Astudillo, and D. Verdugo, “Trajectory tracking of a quadrotor using sliding mode control,” IEEE Latin America Trans., vol. 14, no. 5, pp. 2157–2166, May 2016.

    Google Scholar 

  39. T. Madani and A. Benallegue, “Backstepping sliding mode control applied to a miniature quadrotor flying robot,” Proc. of the IECON 2006 — 32nd Annual Conf. IEEE Industrial Electronics, pp. 700–705, April 2007.

  40. H. Ramirez-Rodriguez, V. Parra-Vega, A. Sanchez, and O. Garcia, “Integral sliding mode backstepping control of quadrotors for robust position tracking,” Proc. of the International Conf. Unmanned Aircraft Systems, pp. 423–432, July 2013.

  41. 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 Trans. on Industrial Electronics, vol. 63, no. 8, pp. 5044–5056, August 2016.

    Google Scholar 

  42. Z. Jia, J. Yu, Y. Mei, Y. Chen, Y. Shen, and X. Ai, “Integral backstepping sliding mode control for quadrotor helicopter under external uncertain disturbances,” Aerospace Science and Technology, vol. 68, pp. 299–307, September 2017.

    Google Scholar 

  43. B. J. Emran and H. Najjaran, “A review of quadrotor: An underactuated mechanical system,” Annual Reviews in Control, vol. 46, pp. 165–180, October 2018.

    MathSciNet  Google Scholar 

  44. D. Lee, H. J. Kim, and S. Sastry, “Feedback linearization vs. adaptive sliding mode control for a quadrotor helicopter,” International Journal of Control, Automation and Systems, vol. 7, no. 3, pp. 419–428, June 2009.

    Google Scholar 

  45. J. Escareno, S. Salazar, H. Romero, and R. Lozano, “Trajectory Control of a Quadrotor Subject to 2D Wind Disturbances,” Journal of Intelligent and Robotic Systems, vol. 70, no. 1–4, pp. 51–63, April 2013.

    Google Scholar 

  46. I. Palunko and R. Fierro, “Adaptive control of a quadrotor with dynamic changes in the center of gravity,” IFAC world congress, vol. 44, no. 1, pp. 2626–2631, January 2011.

    Google Scholar 

  47. X. Gong, Z. C. Hou, C. J. Zhao, Y. Bai, and Y. T. Tian, “Adaptive backstepping sliding Mode trajectory tracking control for a quad-rotor,” International Journal of Automation and Computing, vol. 9, no. 5, pp. 555–560, October 2012.

    Google Scholar 

  48. M. Mohammadi and A. M. Shahri, “Adaptive nonlinear stabilization control for a quadrotor UAV: theory, simulation and experimentation,” Journal of Intelligent and Robotic Systems, vol. 72, no. 1, pp. 105–122, October 2013.

    Google Scholar 

  49. S. Barghandan, M. A. Badamchizadeh, and M. R. Jahed-Motlagh, “Improved adaptive fuzzy sliding mode controller for robust fault tolerant of a quadrotor,” International Journal of Control, Automation and Systems, vol. 15, no. 1, pp. 427–441, February 2017.

    Google Scholar 

  50. D. Ma, Y. Xia, G. Shen, Z. Jia, and T. Li, “Flatness-based adaptive sliding mode tracking control for a quadrotor with disturbances,” Journal of the Franklin Institute, vol. 355, no. 14, pp. 6300–6322, September 2018.

    MathSciNet  MATH  Google Scholar 

  51. C. Wang, B. Song, P. Huang, and C. Tang, “Trajectory tracking control for quadrotor robot subject to payload variation and wind gust disturbance,” Journal of Intelligent and Robotic Systems, vol. 83, no. 2, pp. 315–333, August 2016.

    Google Scholar 

  52. Y. Zou and B. Zhu, “Adaptive trajectory tracking controller for quadrotor systems subject to parametric uncertainties,” Journal of the Franklin Institute, vol. 354, no. 15, pp. 6724–6746, October 2017.

    MathSciNet  MATH  Google Scholar 

  53. H. Bouadi and F. Mora-Camino, “Modeling and adaptive flight control for quadrotor trajectory tracking,” Journal of Aircraft, vol. 55, no. 2, pp. 666–681, March 2018.

    Google Scholar 

  54. M. Vahdanipour and M. Khodabandeh, “Adaptive fractional order sliding mode control for a quadrotor with a varying load,” Aerospace Science and Technology, vol. 86, pp. 737–747, March 2019.

    Google Scholar 

  55. C. Hua, J. Chen, and X. Guan, “Adaptive prescribed performance control of QUAVs with unknown time-varying pay-load and wind gust disturbance,” Journal of the Franklin Institute, vol. 355, no. 14, pp. 6323–6338, September 2018.

    MathSciNet  MATH  Google Scholar 

  56. M. Chadli, “An LMI approach to design observer for unknown inputs Takagi-Sugeno fuzzy models,” Asian Journal of Control, vol. 12, no. 4, pp. 524–530, July 2010.

    MathSciNet  Google Scholar 

  57. H. Dahmani, M. Chadli, A. Rabhi, and A. El Hajjaji, “Road curvature estimation for vehicle lane departure detection using a robust Takagi-Sugeno fuzzy observer,” Vehicle System Dynamics, vol. 51, no. 5, pp. 582–599, December 2011.

    Google Scholar 

  58. H. Liu, P. Shi, H. R. Karimi, and M. Chadli, “Finite-time stability and stabilisation for a class of nonlinear systems with time-varying delay,” International Journal of Systems Science, vol. 47, no. 6, pp. 1433–1444, June 2014.

    MathSciNet  MATH  Google Scholar 

  59. A. Chibani, M. Chadli, and N. B. Braiek, “A sum of squares approach for polynomial fuzzy observer design for polynomial fuzzy systems with unknown inputs,” International Journal of Control, Automation and Systems, vol. 14, no. 1, pp. 323–330, February 2016.

    MATH  Google Scholar 

  60. H. Hassani, J. Zarei, M. Chadli, and J. Qiu, “Unknown input observer design for interval type-2 T-S fuzzy systems with immeasurable premise variables,” IEEE Trans. on Cybernetics, vol. 47, no. 9, pp. 2639–2650, September 2017.

    Google Scholar 

  61. D. W. Kun and I. Hwang, “Linear matrix inequality-based nonlinear adaptive robust control of quadrotor,” Journal of Guidance Control, and Dynamics, vol. 39, no. 5, pp. 996–1008, May 2016.

    Google Scholar 

  62. E. Zheng and J. Xiong, “Quad-rotor unmanned helicopter control via novel robust terminal sliding mode controller and under-actuated system sliding mode controller,” Optik, vol. 125, no. 12, pp. 2817–2825, June 2014.

    Google Scholar 

  63. H. Wang, X. Ye, Y. Tian, G. Zheng, and N. Christov, “Model-free-based terminal SMC of quadrotor attitude and position,” IEEE Trans. on Aerospace and Electronic Systems, vol. 52, no. 5, pp. 2519–2528, October 2016.

    Google Scholar 

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

    Google Scholar 

  65. O. Mofid and S. Mobayen, “Adaptive sliding mode control for finite-time stability of quad-rotor UAVs with parametric uncertainties,” ISA Trans., vol. 72, pp. 1–14, January 2018.

    Google Scholar 

  66. A. Modirrousta and M. Khodabandeh, “A novel nonlinear hybrid controller design for an uncertain quadrotor with disturbances,” Aerospace Science and Technology, vol. 45, pp. 294–308, September 2015.

    Google Scholar 

  67. N. Wang, Q. Deng, G. Xie, and X. Pan, “Hybrid Finite-Time Trajectory Tracking Control of a Quadrotor,” ISA Trans., vol. 90, pp. 278–286, July 2019.

    Google Scholar 

  68. L. Derafa, T. Madani, and A. Benallegue, “Dynamic modelling and experimental identification of four rotors helicopter parameters,” Proc. of the 2006 IEEE International Conf. Industrial Technology, pp. 1834–1839, June 2007.

  69. A. Aboudonia, A. El-Badawy, and R. Rashad, “Disturbance observer-based feedback linearization control of an unmanned quadrotor helicopter,” Proc. of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 230, no. 9, pp. 1–15, July 2016.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Automation, Shanghai Jiao Tong University, Shanghai, 200240, P. R. China

    Karam Eliker & Weidong Zhang

  2. Peng Cheng Laboratory, Shenzhen, P. R. China

    Weidong Zhang

Authors
  1. Karam Eliker
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Weidong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Weidong Zhang.

Additional information

Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Seung Keun Kim under the direction of Editor Myo Taeg Lim. This work is partly supported by the National Science Foundation of China (61473183,U1509211,61627810), and National Key R&D Program of China (SQ2017YFGH001005).

We would like to express our gratitude to Bahij Eliker, English language supervisor, Zahia Oueldkherroubi, and Nafissa Zouad for their support and helpful feedbacks.

Karam Eliker received his Mag, M.S., and B.E. degrees in control engineering from Ecole Militaire Polytechnique, Faculté des Sciences de l’Ingénieur, Institut National d’Electronique et de Génie Electrique, Algeria, in 2016, 2014, and 2013, respectively. He is currently preparing a Ph.D. degree in Shanghai Jiao Tong University, China. His main research interests are trajectory generation, adaptive control, robust control, and observer-based control.

Weidong Zhang received his B.S., M.S., and Ph.D. degrees from Zhejiang University, China, in 1990, 1993, and 1996, respectively. He joined Shanghai Jiao Tong University in 1998 as an Associate Professor and has been a Full Professor since 1999. From 2003 to 2004, he worked at the University of Stuttgart, Germany, as an Alexander von Humboldt Fellow. He is a recipient of National Science Fund for Distinguished Young Scholars of China and Shanghai Subject Chief Scientist. In 2011 he was appointed Chair Professor at Shanghai Jiao Tong University. Presently he is Director of the Engineering Research Center of Marine Automation, Shanghai Municipal Education Commission and Deputy Dean of the Department of Automation, Shanghai Jiao Tong University. His research interests include control theory and information processing theory and their applications in several fields, including power/chemical processes, USV/ROV and aerocraft. He is the author of 1 book and more than 300 refereed papers, and holds 32 patents.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Eliker, K., Zhang, W. Finite-time Adaptive Integral Backstepping Fast Terminal Sliding Mode Control Application on Quadrotor UAV. Int. J. Control Autom. Syst. 18, 415–430 (2020). https://doi.org/10.1007/s12555-019-0116-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-019-0116-3

Keywords

Search

Navigation