Linearization and Identification of Helicopter Model for Hierarchical Control Design

  • Kenzo Nonami
  • Farid Kendoul
  • Satoshi Suzuki
  • Wei Wang
  • Daisuke Nakazawa


This chapter presents an analytical modeling and model-based controller design for a small unmanned helicopter. Generally, it can be said that helicopter dynamics are nonlinear, with coupling of each axis. However, for low speed flights, i.e., speeds less than 5 m/s, the dynamics can be expressed by a set of linear equations of motion as a SISO (Single Input Single Output) system. The dynamics of the helicopter are divided into several components. We derive a model for each component from either the geometric relation or equation of motion. By combining all components, we derive two linear state equations that describe the helicopter’s lateral and longitudinal motion. The parameters of the model are decided by helicopter specs. Based on the derived models, we design A control system by using the linear quadratic integral (LQI). The validity of these approaches is then verified by flight tests.


Tilt Angle Pitch Angle Main Rotor Rotor Frame Swash Plate 
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  1. 1.
    Rahideh A, Shaheed MH (2008) Dynamic modeling of a twin rotor MIMO system using grey box approach. In: Proceedings of the 5th international symposium on mechatronics and its applications, Amman, Jordan, pp 1–6Google Scholar
  2. 2.
    Kato A, Kobayashi T, Katayama H, Ichikawa A (2003) Attitude control of a helicopter model by nonlinear sampled-data H control. In: Proceedings of the SICE annual conference, Fukui, Japan, pp 930–935Google Scholar
  3. 3.
    Casilo CL, Moreno W, Valavanis KP (2007) Unmanned helicopter waypoint trajectory tracking using model predictive control. In: Proceedings of the Mediterranean conference on control and automation, Athens, Greece, pp 1–8Google Scholar
  4. 4.
    Fujiwara D, Nonami K, Shin J, Hazawa K (2004) H hovering and guidance control for autonomous small-scale unmanned helicopter. In: Proceedings of the 2004 IEEE/RSJ international conference on intelligent robots and systems, Sendai, Japan, pp.2463–2468Google Scholar
  5. 5.
    Song D, Qi J, Dai L, Han J, Liu G (2008) Modeling a small-size unmanned helicopter using optimal estimation in the frequency domain. In: Proceedings of the 15th international conference on mechatronics and machine vision in practice, Auckland, New Zealand, pp 97–102Google Scholar
  6. 6.
    Yinzhe D, Liang L, Zhenbarg G (2005) Modeling analysis and designing the flight control system on a sub-mini unmanned helicopter robot. In: Proceedings of the conference on high density microsystem design and packaging and component failure analysis, Shanghai, Japan, pp 1–4Google Scholar
  7. 7.
    Yinzhe D, Liang L, Zhenbang G (2005) Modeling analysis of vibration for subminiature unmanned helicopter. In: Proceedings of the 2005 IEEE international workshop on safety and rescue robotics, Kobe, Japan, pp 131–136Google Scholar
  8. 8.
    Johnson EN, Kannan SK (2005) Adaptive trajectory control for autonomous helicopters. AIAA J Guid Cont Dynam 28(3):524–538CrossRefGoogle Scholar
  9. 9.
    Wang H, Duan H (2007) Modeling and hover control of a novel unmanned coaxial rotor/ducted-fan helicopter. In: Proceedings of the IEEE international conference on automation and logistics, Jinan, China, pp 1768–1773Google Scholar
  10. 10.
    Carro J, Valero J, Barrientos A (2005) Identification of a small unmanned helicopter model using genetic algorithms. In: Proceedings of the 2005 IEEE/RSJ international conference on intelligent robots and systems, Alberta, Canada, pp 3360–3365Google Scholar
  11. 11.
    Civita ML, Papageorgiou G, Messner WC, Kanade T (2006) Design and flight testing of an H controller for a robotic helicopter. J Guid Contr Dynam 29(2):485–494CrossRefGoogle Scholar
  12. 12.
    Song P, Qi G, Li K (2009) The flight control system based on multivariable PID neural network for small-scale unmanned helicopter. In: Proceedings of the international conference on information technology and computer science, Kiev, Ukraine, pp 538–541Google Scholar
  13. 13.
    Rebeschiess S, Roloff M (1999) Position control by feedback linearization for a simplified helicopter model. In: Proceedings of the 1999 IEEE international conference on control applications, Kohala Coast, Hawaii, pp 143–145Google Scholar
  14. 14.
    Gen SS, Red B, Tee KP, Lee TH (2009) Approximation-based control of uncertain helicopter dynamics. IET Contr Theor Appl 3(7):941–956CrossRefGoogle Scholar
  15. 15.
    Westerberg S, Mettin U, SHriaev AS, Freidvich LB, Orlov Y (2009) Motion planning and control of a simplified helicopter model based on virtual holonomic constraints. In: Proceedings of the international conference on advanced robotics, Munich, Germany, pp 1–6Google Scholar
  16. 16.
    Benjanarasuth T (2008) Experimental study on servo adaptive pitch control of a model helicopter. In: SICE Annual Conference, Chofu, Tokyo, Japan, pp 209–213Google Scholar
  17. 17.
    Xianpqing W, Yimin H (2008) Model system design for small-size unmanned helicopter based on moment theory, blade element theory and FlightLab software. In: Proceedings of the 2nd international symposium on systems and control in aerospace and astronautics, Shenzhen, China, pp 1–4Google Scholar
  18. 18.
    Jiang Z, Han J, Wang Y, Song Q (2006) Enhanced LQR control for unmanned helicopter in hover. In: Proceedings of the 1st International Symposium on Systems and Control in Aerospace and Astronautics, Harbin, China, pp 1438–1443Google Scholar
  19. 19.
    Mettler B (2003) Identification modeling and characteristics of miniature rotorcraft. Kluwer Academic Publishers, NorvellCrossRefGoogle Scholar
  20. 20.
    Done G, Balmford D (2001) Bramwell’s helicopter dynamics, 2nd edn. Butterworth Heinemann, BostonGoogle Scholar
  21. 21.
    Leishman JG (2000) Principles of helicopter aerodynamics, Cambridge Aerospace Series. Cambridge University Press, New YorkGoogle Scholar
  22. 22.
    Kato K, Imanaga I (1988) Introduction to helicopters. The University of Tokyo Press, TokyoGoogle Scholar

Copyright information

© Springer 2010

Authors and Affiliations

  • Kenzo Nonami
    • 1
  • Farid Kendoul
    • 2
  • Satoshi Suzuki
    • 3
  • Wei Wang
    • 4
  • Daisuke Nakazawa
    • 5
  1. 1.Faculty of EngineeringChiba UniversityChibaJapan
  2. 2.CSIRO Queensland Centre for Advanced TechnologiesAutonomous Systems LaboratoryPullenvaleAustralia
  3. 3.International Young Researchers Empowerment CenterShinshu UniversityUedaJapan
  4. 4.College of Information and Control EngineeringNanjing University of Information Science & TechnologyNanjingP.R. China
  5. 5.Advanced Technology R&D CenterMitsubishi Electric CorporationAmagasakiJapan

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