Skip to main content
SpringerLink
Log in

Approximate analysis for main rotor flapping dynamics of a model-scaled helicopter with Bell–Hiller stabilizing bar in hovering and vertical flights

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

Abstract

In this paper, the effects of the rotor flapping dynamics in the control design for the model-scaled autonomous helicopter are analyzed in detail. The analysis is based on a specific model-scaled helicopter equipped with a Bell–Hiller stabilizing bar. A simplified analytic model for the flapping dynamics in hovering flight mode is derived and then expanded to the vertical flight mode. Eigenvalues of the approximated linear system indicate that flapping dynamics in both flight modes is comparatively fast and asymptotically stable. Effects of the rotor dynamics with Bell–Hiller stabilizing bar are assessed with both simulation and experimental results, indicating that static approximation of the rotor dynamics in control design is acceptable.

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

Similar content being viewed by others

References

  1. Bramwell, A.R.S., Done, G., Balmford, D.: Bramwell’s Helicopter Dynamics, 2nd edn. Butterworth Heinmann, Oxford (2001)

    Google Scholar 

  2. Nikolsky, A.: Helicopter Analysis. Wiley, New York (1951)

    Google Scholar 

  3. Padfield, G.: Helicopter Flight Dynamics: The Theory and Application of Flying Qualities and Simulation Modeling, 2nd edn. Blackwell, Oxford (2007)

    Book  Google Scholar 

  4. Cunha, R., Silvestre, C.: Dynamic modeling and stability analysis of model-scale helicopters with Bell–Hiller stabilizing bar. In: Proceedings of AIAA Guidance, Navigation, and Control Conference and Exibit, Austin, Texas, 11–14 Aug (2003)

  5. Gavrilets, V.: Autonomous aerobatic maneuvering of miniature helicopters. Ph.D. Dissertation, Massachusetts Institute of Technology, Cambridge (2003)

  6. Bogdanov, A., Carlsson, M., Harvey, G., Hunt, J.: State-dependent Riccati equation control of a small unmanned helicopter. In: Proceedings of AIAA Guidance, Navigation and Control Conference and Exibit, 11–14 Aug (2003)

  7. Budiyono, A., Wibowo, S.S.: Optimal tracking controller design for a small scale helicopter. J. Bionic Eng. 4, 271–280 (2007)

  8. Shim, D.H., Kim, H.J., Sastry, S.: Hierarchical control system synthesis for rotorcraft-based unmanned aerial vehicles. In: Proceedings of AIAA Guidance, Navigation and Control Conference and Exibit, 14–17 Aug (2000)

  9. Civita, M.L., Papageorgiou, G., Messner, W.C., Kanade, T.: Design and flight testing of an \(H_\infty \) controller for a robotic helicopter. J. Guid. Control Dyn. 29(2), 485–494 (2006)

    Article  Google Scholar 

  10. Johnson, E.N., Kannan, S.K.: Adaptive trajectory control for autonomous helicopters. J. Guid. Control Dyn. 28(3), 524–538 (2005)

    Article  Google Scholar 

  11. 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 

  12. Isidori, A., Marconi, L., Serrani, A.: Robust nonlinear motion control of a helicopter. IEEE Trans. Autom. Control 48(3), 413–426 (2003)

    Article  MathSciNet  Google Scholar 

  13. Teel, A.R., Moreau, L., Nesic, D.: A unified framework for input-to-state stability in systems with two time scales. IEEE Trans. Autom. Control 48(9), 1526–1544 (2003)

    Article  MathSciNet  Google Scholar 

  14. Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice-Hall Inc., Upper Saddle River (2002)

    MATH  Google Scholar 

  15. Johnson, W.: Helicopter Theory. Princeton University Press, Prinston (1980)

    Google Scholar 

  16. Miller, R.H.: Helicopter control and stability in hovering flight. J. Aeronaut. Sci. 15(8), 453–472 (1948)

    Article  Google Scholar 

  17. Zhu, B., Wang, Q., Huo, W.: Longitudinal-lateral velocity control design and implementation for a model-scaled unmanned helicopter. Nonlinear Dyn. 76, 1579–1589 (2014)

    Article  MATH  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 61203022). The authors own great thanks to Professor Wei Huo from Beihang University for his extensive and helpful advices on this research.

Author information

Authors and Affiliations

  1. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, 639798, Singapore

    Bing Zhu

  2. The Seventh Research Division, Beihang University, Beijing, 100191, People’s Republic of China

    Zongyu Zuo

Authors
  1. Bing Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zongyu Zuo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zongyu Zuo.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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, 1705–1717 (2016). https://doi.org/10.1007/s11071-016-2788-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-016-2788-z

Keywords

Search

Navigation