Skip to main content
SpringerLink
Log in

Nonlinear adaptive tracking control for a small-scale unmanned helicopter using a learning algorithm with the least parameters

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

Abstract

This paper puts forward a new nonlinear adaptive controller for a small-scale unmanned helicopter with unknown mass. The controller is developed under the framework of backstepping technique, with the unknown mass estimated by a novel identifier and the internal and external uncertainties approximated by radial basis function neural networks (RBFNNs). The overall closed-loop system, which consists of three parts: longitudinal–lateral subsystem, heave subsystem, and heading subsystem, is proved to be semi-globally uniformly ultimately bounded by the strict Lyapunov stability theory. Furthermore, the proposed method is more practical in actual applications with an improved online learning algorithm of the least parameters used in the RBFNNs. Finally, the effectiveness and the robustness of the proposed strategy are exhibited through two simulations compared with the classic PID 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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Cai, G., Chen, B.M., Dong, X., Lee, T.H.: Design and implementation of a robust and nonlinear flight control system for an unmanned helicopter. Mechatronics 21(5), 803–820 (2011)

    Article  Google Scholar 

  2. Cai, G., Chen, B.M., Tong, H.L., Kai, Y.L.: Comprehensive nonlinear modeling of an unmanned-aerial-vehicle helicopter. In: Proceedings of the 2008 AIAA Guidance, Navigation and Control Conference (2008)

  3. Calvo-Rolle, J.L., Fontenla-Romero, O., Pérez-Sánchez, B., Guijarro-Berdiñas, B.: Adaptive inverse control using an online learning algorithm for neural networks. Informatica 25(3), 401–414 (2014)

    Article  Google Scholar 

  4. Das, A., Lewis, F., Subbarao, K.: Neural network based robust backstepping control approach for quadrotors. In: Proceedings of the 2008 AIAA Guidance, Navigation and Control Conference, pp. 1–17 (2008)

  5. Dierks, T., Jagannathan, S.: Output feedback control of a quadrotor uav using neural networks. IEEE Trans. Neural Netw. 21(1), 50–66 (2010)

    Article  Google Scholar 

  6. Fang, X., Wu, A., Shang, Y., Dong, N.: A novel sliding mode controller for small-scale unmanned helicopters with mismatched disturbance. Nonlinear Dyn. 83(1), 1053–1068 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  7. Fang, X., Wu, A., Shang, Y., Du, C.: Multivariable super twisting based robust trajectory tracking control for small unmanned helicopter. Math. Probl. Eng. 2015, 1–13 (2015)

    MathSciNet  Google Scholar 

  8. Farrell, J.A., Polycarpou, M., Sharma, M., Dong, W.: Command filtered backstepping. IEEE Trans. Autom. Control 54(6), 1391–1395 (2009)

    Article  MathSciNet  Google Scholar 

  9. Gadewadikar, J., Chen, B.M., Subbarao, K.: Structured \(h_\infty \) command and control-loop design for unmanned helicopters. J, Guid. Control Dyn. 31(4), 1093–1102 (2008)

    Article  Google Scholar 

  10. Gavrilets, V., Mettler, B., Feron, E.: Human-inspired control logic for automated maneuvering of miniature helicopter. J. Guid. Control Dyn. 27(5), 752–759 (2004)

    Article  Google Scholar 

  11. Godbolt, B., Vitzilaios, N.I., Lynch, A.F.: Experimental validation of a helicopter autopilot design using model-based pid control. J. Intell. Robot. Syst. 70(1), 385–399 (2013)

    Article  Google Scholar 

  12. Heffley, R.K., Mnich, M.A.: Minimum-complexity helicopter simulation math model. Technical report usaavscom technical report 87-a-7, NASA, Moffett Field, CA (1988)

  13. Islam, S., Liu, P.X., El Saddik, A.: Nonlinear adaptive control for quadrotor flying vehicle. Nonlinear Dyn. 78(1), 117–133 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  14. Jca, V., Brogliato, B., Dzul, A., Lozano, R.: Nonlinear modelling and control of helicopters. Automatica 39(9), 1583–1596 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  15. Lai, G., Liu, Z., Zhang, Y., Chen, C.L.: Adaptive position/attitude tracking control of aerial robot with unknown inertial matrix based on a new robust neural identifier. IEEE Trans. Neural Netw. Learn. Syst. 27(1), 18–31 (2016)

    Article  MathSciNet  Google Scholar 

  16. Lee, C.T., Tsai, C.C.: Nonlinear adaptive aggressive control using recurrent neural networks for a small scale helicopter. Mechatronics 20(4), 474–484 (2010)

    Article  Google Scholar 

  17. Leonard, F., Martini, A., Abba, G.: Robust nonlinear controls of model-scale helicopters under lateral and vertical wind gusts. IEEE Trans. Control Syst. Technol. 20(1), 154–163 (2012)

    Article  Google Scholar 

  18. Li, T., Feng, G., Zou, Z., Liu, Y.: Robust adaptive fuzzy tracking control for a class of mimo systems: a minimal-learning-parameters algorithm. In: Proceedings of the 2009 American Control Conference, pp. 3106–3111 (2009)

  19. Liu, H., Derawi, D., Kim, J., Zhong, Y.: Robust optimal attitude control of hexarotor robotic vehicles. Nonlinear Dyn. 74(4), 1155–1168 (2013)

    Article  MATH  Google Scholar 

  20. Liu, H., Lu, G., Zhong, Y.: Robust lqr attitude control of a 3-dof laboratory helicopter for aggressive maneuvers. IEEE Trans. Ind. Electron. 60(10), 4627–4636 (2013)

    Article  Google Scholar 

  21. Liu, J.: Radial Basis Function (RBF) Neural Network Control for Mechanical Systems: Design. Analysis and Matlab Simulation. Springer-Verlag, Berlin Heidelberg (2013)

    Book  MATH  Google Scholar 

  22. Liu, L., Wang, Z., Zhang, H.: Adaptive fault-tolerant tracking control for mimo discrete-time systems via reinforcement learning algorithm with less learning parameters. IEEE Trans. Autom. Sci. Eng. (2016). doi:10.1109/TASE.2016.2517155

  23. Liu, Y.J., Tang, L., Tong, S., Chen, C.L.P., Li, D.J.: Reinforcement learning design-based adaptive tracking control with less learning parameters for nonlinear discrete-time mimo systems. IEEE Trans. Neural Netw. Learn. Syst. 26(1), 165–176 (2015)

    Article  MathSciNet  Google Scholar 

  24. Marconi, L., Naldi, R.: Robust full degree-of-freedom tracking control of a helicopter. Automatica 43(11), 1909–1920 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  25. Mettler, B.: Identification Modeling and Characteristics of Miniature Rotorcraft. Kluwer Academic Publishers, Norwell (2003)

    Book  Google Scholar 

  26. Mettler, B., Dever, C., Feron, E.: Scaling effects and dynamic characteristics of miniature rotorcraft. J Guid. Control Dyn. 27(3), 466–478 (2004)

    Article  Google Scholar 

  27. Nodland, D., Zargarzadeh, H., Jagannathan, S.: Neural network-based optimal adaptive output feedback control of a helicopter uav. IEEE Trans. Neural Netw. Learn. Syst. 24(7), 1061–1073 (2013)

    Article  Google Scholar 

  28. Peng, K., Cai, G., Chen, B.M., Dong, M., Lum, K.Y., Lee, T.H.: Design and implementation of an autonomous flight control law for a uav helicopter. Automatica 45(10), 2333–2338 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  29. Pounds, P.E.I., Dollar, A.M.: Stability of helicopters in compliant contact under pd-pid control. IEEE Trans. Robot. 30(6), 1472–1486 (2014)

    Article  Google Scholar 

  30. Puttige, V.R., Anavatti, S.G.: Comparison of real-time online and offline neural network models for a uav. In: Proceedings of the 2007 international joint conference on neural networks, pp. 412–417 (2007)

  31. Raptis, I.A., Valavanis, K.P., Moreno, W.A.: A novel nonlinear backstepping controller design for helicopters using the rotation matrix. IEEE Trans. Control Syst. Technol. 19(2), 465–473 (2011)

    Article  Google Scholar 

  32. Sheng, S., Sun, C.: An adaptive attitude tracking control approach for an unmanned helicopter with parametric uncertainties and measurement noises. Int. J. Control Autom. Syst. 14(1), 217–228 (2016)

    Article  MathSciNet  Google Scholar 

  33. Simplcio, P., Pavel, M., Kampen, E.V., Chu, Q.P.: An acceleration measurements-based approach for helicopter nonlinear flight control using incremental nonlinear dynamic inversion. Control Eng. Pract. 21(8), 1065–1077 (2013)

  34. Tang, S., Zhang, L., Wang, L., Jiang, M.: Nonlinear robust control design of a small-scale helicopter. In: Proceedings of the 2015 Chinese control conference (CCC), pp. 2854–2859 (2015)

  35. Tang, S., Zheng, Z., Qian, S., Zhao, X.: Nonlinear system identification of a small-scale unmanned helicopter. Control Eng. Pract. 25(1), 1–15 (2014)

    Article  Google Scholar 

  36. Wang, X., Chen, Y., Lu, G., Zhong, Y.: Robust attitude tracking control of small-scale unmanned helicopter. Int. J. Syst. Sci. 46(8), 1472–1485 (2015)

    MATH  Google Scholar 

  37. Xian, B., Diao, C., Zhao, B., Zhang, Y.: Nonlinear robust output feedback tracking control of a quadrotor uav using quaternion representation. Nonlinear Dyn. 79(4), 2735–2752 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  38. Zhou, B., Zheng, Z., Li, Z., Tang, S.: Implementation of a robust and nonlinear attitude control system for a small-scale unmanned helicopter. In: Proceedings of the 2015 IEEE international conference on information and automation, pp. 2487–2492 (2015)

  39. Zhu, B.: Nonlinear adaptive neural network control for a model-scaled unmanned helicopter. Nonlinear Dyn. 78(3), 1695–1708 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  40. Zhu, B., Zuo, Z.: Approximate analysis for main rotor flapping dynamics of a model-scaled helicopter with bell-hiller stabilizing bar in hovering and vertical flights. Nonlinear Dyn. 85(3), 1705–1717 (2016)

    Article  Google Scholar 

  41. Zou, Y.: Adaptive trajectory tracking control approach for a model-scaled helicopter. Nonlinear Dyn. 83(4), 2171–2181 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  42. Zou, Y., Zheng, Z.: A robust adaptive rbfnn augmenting backstepping control approach for a model-scaled helicopter. IEEE Trans. Control Syst. Technol. 23(6), 2344–2352 (2015)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant No. 61403470) and the Basic and Advanced Research Project of ChongQing (Grant No. cstc2016jcyjA0563). The authors of this paper owe great thanks to Dr. Peng Li and Dr. Yadong Liu for their constructive suggestions.

Author information

Authors and Affiliations

  1. College of Mechatronic Engineering and Automation, National University of Defense Technology, Changsha, 410073, People’s Republic of China

    Bin Zhou, Zhibin Li & Zhiqiang Zheng

  2. Department of Machinery and Electrical Engineering, Logistical Engineering University, Chongqing, 401311, People’s Republic of China

    Shuai Tang

Authors
  1. Bin Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhibin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhiqiang Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shuai Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bin Zhou.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhou, B., Li, Z., Zheng, Z. et al. Nonlinear adaptive tracking control for a small-scale unmanned helicopter using a learning algorithm with the least parameters. Nonlinear Dyn 89, 1289–1308 (2017). https://doi.org/10.1007/s11071-017-3516-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-017-3516-z

Keywords

Search

Navigation