Skip to main content
SpringerLink
Log in

Nonlinear Adaptive Backstepping with ESO for the Quadrotor Trajectory Tracking Control in the Multiple Disturbances

  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

In this paper, we present a nonlinear adaptive backstepping with extended state observer (ESO) trajectory tracking controller for a quadrotor unmanned aerial vehicle (UAV) subject to the multiple disturbances, which include the parametric uncertainties, actuator faults and external disturbance. First, a six-degrees of freedom quadrotor UAV model with the multiple disturbances function is built. Second, the adaptive backstepping controller is designed to track the desired trajectory command aim at internal disturbance. And the adaptive backstepping controller with ESO is designed to track the desired trajectory command aim at external disturbance. Third, the stability of the system is proved by the circle criterion. Finally, under different flight scenarios, simulation results are given to demonstrate the effectiveness of the proposed method.

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

Access this article

Log in via an institution

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

References

  1. T. Lee, “Geometric control of quadrotor UAVs transporting a cable-suspended rigid body,” IEEE Transactions on Control Systems Technology, vol. 26, no. 1, pp. 225–264, February 2017.

    Google Scholar 

  2. L. Derafa, A. Benallegue, and L. Fridman, “Super twisting control algorithm for the attitude tracking of a four rotors UAV,” Journal of the Franklin Institute, vol. 349, no. 2, pp. 685–699, March 2012.

    Article  MathSciNet  MATH  Google Scholar 

  3. D. J. Zhao and D. G. Yang, “Model-free control of quad-rotor vehicle via finite-time convergent extended state observer,” International Journal of Control, Automation and Systems, vol. 14, no. 1, pp. 242–254, February 2016.

    Article  Google Scholar 

  4. P. Serra, R. Pedro, and T. Hamel, “Landing of a quadrotor on a moving target using dynamic image-based visual servo control,” IEEE Transactions on Robotics, vol. 32, no. 6, pp. 1524–1535, December 2016.

    Article  Google Scholar 

  5. 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.

    Article  MathSciNet  MATH  Google Scholar 

  6. L. Wang and H. Jia, “The trajectory tracking problem of quadrotor UAV: global stability analysis and control design based on the cascade theory,” Asian Journal of Control, vol. 16, no. 2, pp. 574–588, March 2014.

    Article  MathSciNet  MATH  Google Scholar 

  7. T. Lee, M. Leok, and N. H. Mcclamroch, “Nonlinear robust tracking control of a quadrotor UAV on SE(3),” Asian Journal of Control, vol. 15, no. 2, pp. 391–408, June 2012.

    Article  MathSciNet  MATH  Google Scholar 

  8. A. P. Sandiwan, A. Cahyadi, and S. Herdjunanto, “Robust proportional-derivative control on SO(3) with disturbance compensation for quadrotor UAV,” International Journal of Control Automation & Systems, vol. 15, no. 4, pp. 1–14, September 2017.

    Google Scholar 

  9. M. H. Amoozgar, A. Chamseddine, and Y. Zhang, “Fault-tolerant fuzzy gain-scheduled PID for a quadrotor helicopter testbed in the presence of actuator faults,” IFAC Proceedings Volumes, vol. 45, no. 3, pp. 282–287, May 2012.

    Article  Google Scholar 

  10. F. Rinaldi, S. Chiesa, and F. Quagliotti, “Linear quadratic control for quadrotors UAVs dynamics and formation flight,” Journal of Intelligent & Robotic Systems, vol. 70, no. 4, pp. 203–220, July 2012.

    Google Scholar 

  11. B. Hasan and E. Prempain, “Low order H controllers for a quadrotor UAV,” Ukacc International Conference on Control, IEEE, pp. 127–132, July 2014.

    Google Scholar 

  12. W. Gai, J. Liu, and J. Zhang, “A new closed-loop control allocation method with application to direct force control,” International Journal of Control Automation & Systems, vol. 16, no. 3, pp. 1355–1366, May 2018.

    Article  Google Scholar 

  13. V. T. Duong, H. K. Kim, and T. T. Nguyen, “Position control of a small scale quadrotor using block feedback linearization control,” Lecture Notes in Electrical Engineering, vol. 282, no. 2, pp. 525–534, March 2014.

    Article  Google Scholar 

  14. F. Chen and W. Lei, “A novel nonlinear resilient control for a quadrotor UAV via backstepping control and nonlinear disturbance observer,” Nonlinear Dynamics, vol. 85, no. 2, pp. 1281–1295, April 2016.

    Article  MATH  Google Scholar 

  15. P. Yang and R. Guo, “Study on the sliding mode fault tolerant predictive control based on multi agent particle swarm optimization,” International Journal of Control, Automation and Systems, vol. 15, no. 5, pp. 2034–2042, September 2017.

    Article  Google Scholar 

  16. Z. Su and H. Wang, “Exact docking flight controller for autonomous aerial refueling with back-stepping based high order sliding mode,” Mechanical Systems and Signal Processing, vol. 101, no. 2, pp. 338–360, February 2018.

    Article  Google Scholar 

  17. R. Wang and J. Liu, “Trajectory tracking control of a 6-DOF quadrotor UAV with input saturation via backstepping,” Journal of the Franklin Institute, vol. 355, no. 7, pp. 3288–3309, May 2018.

    Article  MathSciNet  MATH  Google Scholar 

  18. F. Chen, R. Jiang, and K. Zhang, “Robust backstepping sliding mode control and observer-based fault estimation for a quadrotor UAV,” IEEE Transactions on Industrial Electronics, vol. 63, no. 8, pp. 1–12, April 2016.

    Article  Google Scholar 

  19. M. Chen, G. Tao, and B. Jiang, “Dynamic surface control using neural networks for a class of uncertain nonlinear systems with input saturation,” IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 9, pp. 2086–2097, December 2017.

    Article  MathSciNet  Google Scholar 

  20. R. C. Avram, X. Zhang, and J. Muse, “Nonlinear adaptive fault-tolerant quadrotor altitude and attitude tracking with multiple actuator faults,” IEEE Transactions on Control Systems Technology, vol. 26, no. 2, pp. 1–7, March 2018.

    Article  Google Scholar 

  21. X. Shao, J. Liu, and H. Cao, “Robust dynamic surface trajectory tracking control for a quadrotor UAV via extended state observer,” International Journal of Robust & Nonlinear Control, vol. 28, no. 7, pp. 2700–2719, January 2018.

    Article  MathSciNet  MATH  Google Scholar 

  22. Q. Hu, X. Shao, and L. Guo, “Adaptive fault-tolerant attitude tracking control of spacecraft with prescribed performance,” IEEE/ASME Transactions on Mechatronics, vol. 23, no. 1, pp. 331–341, February 2018.

    Article  Google Scholar 

  23. C. Wang, Z. Chen, and Q. Sun, “Design of PID and ADRC based quadrotor helicopter control system,” Control and Decision Conference, pp. 5860–5865, May 2016.

    Google Scholar 

  24. N. Zhang and W. Gai, “An active disturbance rejection control guidance law based collision avoidance for unmanned aerial vehicles,” Aerospace Science & Technology, vol. 77, no. 3, pp. 658–669, June 2018.

    Article  Google Scholar 

  25. J. Li and Y Xia, “Absolute stability analysis of non-linear active disturbance rejection control for single-inputsingle-output systems via the circle criterion method,” IET Control Theory & Applications, vol. 9, no. 15, pp. 2320–2329, October 2015.

    Article  MathSciNet  Google Scholar 

  26. Z. Gan and J. Han, “Lyapunov function of general Lurie systems with multiple nonlinearities,” Applied Mathematics Letters, vol. 16, no. 1, pp. 119–126. January 2003.

    Article  MathSciNet  MATH  Google Scholar 

  27. P. Curran, “Proof of the circle criterion for state space systems via quadratic Lyapunov functions-Part 2,” International Journal of Control, vol. 57, no. 4, pp. 957–969, Jun 2010.

    Article  MATH  Google Scholar 

  28. B. Z. Guo and Z. L. Zhao, “On the convergence of extended state observer for nonlinear systems with uncertainty,” Systems & Control Letters, vol. 60, no. 6, pp. 420–430, June 2011.

    Article  MathSciNet  MATH  Google Scholar 

  29. L. Yang, W Zhang, and D. Huang, “Robust trajectory tracking for quadrotor aircraft based on ADRC attitude decoupling control,” Journal of Beijing University of Aeronautics & Astronautics, vol. 41, no. 6, pp. 1026–1033, June 2015.

    Google Scholar 

  30. H. Wang, X. Ye, and T. Yang, “Model-free-based terminal SMC of quadrotor attitude and position,” IEEE Transactions on Aerospace & Electronic Systems, vol. 52, no. 5, pp. 2519–2528, October 2017.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266590, China

    Jie Liu, Wendong Gai, Jing Zhang & Yuxia Li

Authors
  1. Jie Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wendong Gai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jing Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yuxia Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wendong Gai.

Additional information

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

Recommended by Associate Editor Shun-ichi Azuma under the direction of Editor Jessie (Ju H.) Park. This work is supported by the National Natural Science Foundation of China (No. 61603220, 61473177, 61733009), the Research Fund for the Taishan Scholar Project of Shandong Province of China, the SDUST Young Teachers Teaching Talent Training Plan (No. BJRC20180503).

Jie Liu received her B.Eng. degree in Automation from Shandong University of Science and Technology, China, in 2015. She is currently an M.Eng. candidate in Control Engineer, Shandong University of Science and Technology. Her research interests include nonlinear flight control, system identification and adaptive control.

Wendong Gai received his Ph.D. degree in Navigation, Guidance and Control from Beihang University, China, in 2013. He joined the College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, China, in 2013. His research interests include modeling and nonlinear flight control of unmanned aerial vehicle, fault tolerant control, sense and avoid in multiple UAVs.

Jing Zhang received her Ph.D. degree in Pattern Recognition and Intelligent System from South China University of Technology, China, in 2011. She joined the College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, China, in 2011. Her research interests include intelligent control theory, image process and pattern recognition, and the application of advanced control and optimization technique to robots.

Yuxia Li received her B.S. degree from Shenyang Jianzhu University, China, in 1990, and her Ph.D. degree from Guangdong University of Technology, China, in 2005. She has been a Professor at the College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, China, since 2008. Her current research interest covers memristor-based circuits and systems, nonlinear circuits and systems, intelligent robot.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, J., Gai, W., Zhang, J. et al. Nonlinear Adaptive Backstepping with ESO for the Quadrotor Trajectory Tracking Control in the Multiple Disturbances. Int. J. Control Autom. Syst. 17, 2754–2768 (2019). https://doi.org/10.1007/s12555-018-0909-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-018-0909-9

Keywords

Search

Navigation