Skip to main content
SpringerLink
Log in

Velocity-sensorless proportional–derivative trajectory tracking control with active damping for quadcopters

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

The proposed observer-based control mechanism solves the trajectory tracking problem in the presence of external disturbances with the reduction in sensor numbers. This systematically considers the quadcopter nonlinear dynamics and parameter and load variations by adopting the standard controller design approach based on a disturbance observer (DOB). The first feature is designing first-order observers for estimating the velocity and angular velocity error, with their parameter independence obtained from the DOB design technique. As the second feature, the resultant velocity observer-based control action including active damping and DOBs secures first-order tracking behavior for the position and attitude (angle) loops through pole zero cancellation, thereby forming a proportional–derivative control structure. Closed-loop analysis results reveal the performance recovery and steady-state error removal properties in the absence of tracking error integrators. The numerical verification confirms the effectiveness of the proposed mechanism using MATLAB/Simulink.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Xian, B., Wang, S., Yang, S.: Nonlinear adaptive control for an unmanned aerial payload transportation system: theory and experimental validation. Nonlinear Dyn. 98, 1745–1760 (2019)

    Article  Google Scholar 

  2. Shang, B., Liu, J., Zhang, Y., et al.: Fractional-order flight control of quadrotor UAS on vision-based precision hovering with larger sampling period. Nonlinear Dyn. 97, 1735–1746 (2019)

    Article  Google Scholar 

  3. Lin, X., Yu, Y., Sun, C.: A decoupling control for quadrotor UAV using dynamic surface control and sliding mode disturbance observer. Nonlinear Dyn. 97, 781–795 (2019)

    Article  Google Scholar 

  4. Liu, J., An, H., Gao, Y., Wang, C., Wu, L.: Adaptive control of hypersonic flight vehicles with limited angle-of-attack. IEEE/ASME Trans. Mechatron. 23, 883–894 (2018)

    Article  Google Scholar 

  5. Zuo, Z.: Trajectory tracking control design with command-filtered compensation for a quadrotor. IET Control Theory Appl. 4, 2343–2355 (2009)

    Article  MathSciNet  Google Scholar 

  6. Barnes, W., McCormick, W.: Aerodynamics Aeronautics and Flight Mechanics. Wiley, New York (1995)

    Google Scholar 

  7. Das, A., Subbarao, K., Lewis, F.: Dynamic inversion with zero-dynamics stabilisation for quadrotor control. IET Control Theory Appl. 3, 303–314 (2008)

    Article  MathSciNet  Google Scholar 

  8. Lee, D., Jin Kim, H., Sastry, S.: Feedback linearization vs. adaptive sliding mode control for a quadrotor helicopter. Int. J. Control Autom. Syst. 7, 419–428 (2009)

    Article  Google Scholar 

  9. Castillo, P., Dzul, A., Lozano, R.: Real-time stabilization and tracking of a four-rotor mini rotorcraft. IEEE Trans. Control Syst. Technol. 12, 510–516 (2004)

    Article  Google Scholar 

  10. Yao, D., Dou, C., Yue, D., et al.: Adaptive neural network consensus tracking control for uncertain multi-agent systems with predefined accuracy. Nonlinear Dyn. 1, 1–10 (2020). https://doi.org/10.1007/s11071-020-05885-z

    Article  Google Scholar 

  11. Luo, C., Lei, H., Li, J., et al.: A new adaptive neural control scheme for hypersonic vehicle with actuators multiple constraints. Nonlinear Dyn. 100, 3529–3553 (2020)

    Article  Google Scholar 

  12. Liu, H., Chen, G.: Robust trajectory tracking control of marine surface vessels with uncertain disturbances and input saturations. Nonlinear Dyn. 100, 3513–3528 (2020)

    Article  Google Scholar 

  13. Glida, H.E., Abdou, L., Chelihi, A., et al.: Optimal model-free backstepping control for a quadrotor helicopter. Nonlinear Dyn. 100, 3449–3468 (2020)

    Article  Google Scholar 

  14. Xia, K., Zou, Y.: Adaptive fixed-time fault-tolerant control for noncooperative spacecraft proximity using relative motion information. Nonlinear Dyn. 100, 2521–2535 (2020)

    Article  Google Scholar 

  15. Yin, Y., Liu, J., Sánchez, J.A., Wu, L., Vazquez, S., Leon, J.I., Franquelo, L.G.: Observer-based adaptive sliding mode control of NPC converters: an RBF neural network approach. IEEE Trans. Power Electron. 34, 3831–3841 (2019)

    Article  Google Scholar 

  16. Liu, J., Ligang, W., Chengwei, W., Luo, W., Franquelo, L.G.: Event-triggering dissipative control of switched stochastic systems via sliding mode. Automatica 103, 261–273 (2019)

    Article  MathSciNet  Google Scholar 

  17. Kayacan, E., Maslim, R.: Type-2 fuzzy logic trajectory tracking control of quadrotor VTOL aircraft with elliptic membership functions. IEEE/ASME Trans. Mechatron. 22, 339–348 (2017)

    Article  Google Scholar 

  18. Xiao, B., Yin, S.: A new disturbance attenuation control scheme for quadrotor unmanned aerial vehicles. IEEE Trans. Ind. Inf. 13, 2922–2932 (2017)

    Article  Google Scholar 

  19. Liu, H., Zhao, W., Zuo, Z., Zhong, Y.: Robust control for quadrotors with multiple time-varying uncertainties and delays. IEEE Trans. Ind. Electron. 64, 1303–1312 (2017)

    Article  Google Scholar 

  20. Chen, F., Jiang, R., Zhang, K., Jiang, B., Tao, G.: Robust backstepping sliding-mode control and observer-based fault estimation for a quadrotor UAV. IEEE Trans. Ind. Electron. 63, 5044–5056 (2016)

    Google Scholar 

  21. Tian, Y., Zheng, G., Wang, H., Ye, X., Christov, N.: Model-free-based terminal SMC of quadrotor attitude and position. IEEE Trans. Aerosp. Electron. Syst. 52, 2519–2528 (2016)

    Article  Google Scholar 

  22. Zou, Y., Meng, Z.: Immersion and invariance-based adaptive controller for quadrotor systems. IEEE Trans. Cybern. 49, 2288–2297 (2019)

    Google Scholar 

  23. Satici, A.C., Poonawala, H., Spong, M.W.: Robust optimal control of quadrotor uavs. IEEE Access 1, 79–93 (2013)

    Article  Google Scholar 

  24. Cao, N., Lynch, A.F.: Inner-outer loop control for quadrotor UAVs with input and state constraints. IEEE Trans. Control Syst. Technol. 24, 1797–1804 (2016)

    Article  Google Scholar 

  25. Lyu, X., Zhou, J., Gu, H., Li, Z., Shen, S., Zhang, F.: Disturbance observer based hovering control of quadrotor tail-sitter VTOL UAVs using \(h_\infty \) synthesis. IEEE Rob. Autom. Lett. 3, 2910–2917 (2018)

    Article  Google Scholar 

  26. An, S., Yuan, S., Li, H.: Self-tuning of PID controllers design by adaptive interaction for quadrotor UAV. In: 2016 IEEE Chinese Guidance, Navigation and Control Conference (CGNCC) (2016)

  27. Yang, J., Cai, Z., Lin, Q., Wang, Y.: Self-tuning PID control design for quadrotor UAV based on adaptive pole placement control. In: 2013 Chinese Automation Congress (2013)

  28. Sumardi, M.S., Sulila, Riyadi, M.A.: Particle swarm optimization (PSO)-based self tuning proportional, integral, derivative (PID) for bearing navigation control system on quadcopter. In: 2017 4th International Conference on Information Technology, Computer, and Electrical Engineering (ICITACEE) (2017)

  29. Sangyam, T., Laohapiengsak, P., Chongcharoen, W., Nilkhamhang, I.: Path tracking of UAV using self-tuning PID controller based on fuzzy logic. In: Proceedings of SICE Annual Conference (2010)

  30. Santoso, F., Garratt, M.A., Anavatti, S.G.: Fuzzy logic-based self-tuning autopilots for trajectory tracking of a low-cost quadcopter: a comparative study. In: 2015 International Conference on Advanced Mechatronics, Intelligent Manufacture, and Industrial Automation (ICAMIMIA) (2015)

  31. Altan, A., Hacoğlu, R.: Model predictive control of three-axis gimbal system mounted on UAV for real-time target tracking under external disturbances. Mech. Syst. Sig. Process. 138, 106548 (2020)

    Article  Google Scholar 

  32. Altan, A., Aslan, Ö., Hac1oğlu, R.: Real-time control based on NARX neural network of hexarotor UAV with load transporting system for path tracking. In: 6th International Conference on Control Engineering and Information Technology (CEIT), p. 2018. Istanbul, Turkey (2018)

  33. Altan, A., Aslan, Ö., Hac1oğlu, R.: Model predictive control of load transporting system on unmanned aerial vehicle (UAV). In: 5th International Conference on Advances in Mechanical and Robotics Engineering (AMRE), p. 2017. Italy, Rome (2017)

  34. Kim, S.-K., Ahn, C.K.: Adaptive self-tuning nonlinear tracking control algorithm for quadcopter applications. IEEE Trans. Aerosp. Electron. Syst. 1, 1–8 (2019). https://doi.org/10.1109/TAES.2019.2911768. (in press)

    Article  Google Scholar 

  35. Kim, S.-K., Ahn, C.K.: Auto-tuner based controller for quadcopter attitude tracking applications. IEEE Trans. Circuits Syst. II Express Briefs 66, 2012–2016 (2019)

    Article  Google Scholar 

  36. Kim, S.-K., Ahn, C.K., Shi, P.: Performance recovery tracking-controller for quadcopters via invariant dynamic surface approach. IEEE Trans. Ind. Inf. 15, 5235–5243 (2019)

    Article  Google Scholar 

  37. Lee, D., Burg, T.C., Dawson, D.M., Shu, D., Xian, B., Tatlicioglu, E.: Robust tracking control of an underactuated quadrotor aerial-robot based on a parametric uncertain model. In: IEEE International Conference on Systems, Man and Cybernetics, p. 2009. San Antonio (2009)

  38. Farrell, J., Sharma, M., Polycarpou, M.: Backstepping-based flight control with adaptive function approximation. J. Guid Control Dyn. 28, 1089–1102 (2005)

    Article  Google Scholar 

  39. Hassan, K.: Nonlinear Systems. Prentice Hall, Khalil (2002)

    MATH  Google Scholar 

Download references

Acknowledgements

This research was supported in part by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2018R1A6A1A03026005) and was supported in part by the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science and ICT) (No. NRF-2020R1A2C1005449).

Author information

Authors and Affiliations

  1. Department of Creative Convergence Engineering, Hanbat National University, Daejeon, 341-58, Korea

    Seok-Kyoon Kim

  2. School of Electrical Engineering, Korea University, Seoul, 136-701, Korea

    Choon Ki Ahn

Authors
  1. Seok-Kyoon Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Choon Ki Ahn
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Choon Ki Ahn.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kim, SK., Ahn, C.K. Velocity-sensorless proportional–derivative trajectory tracking control with active damping for quadcopters. Nonlinear Dyn 103, 1681–1692 (2021). https://doi.org/10.1007/s11071-020-06193-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-020-06193-2

Keywords

Search

Navigation