Stabilizing Quadrotor Helicopter with Uncertainties Based on Controlled Lagrangians and Disturbance Observer

  • Zhonglin Li
  • Wei HuoEmail author
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 528)


How to apply the Controlled Lagrangian method to stabilization controller design for the quadrotor helicopter with uncertainties is investigated in this paper. The dynamical model of the uncertain quadrotor is transformed to a linear model without uncertainties and an uncertain term to facilitate controller design. First, a stabilization controller for linearized model is design based on the Controlled Lagrangian method. For the under-actuated quatrotor, its uncertainties and control inputs are mismatched, the mismatched uncertainties are replaced with equivalent matched uncertainties by utilizing the equivalent disturbance method, then a disturbance observer is constructed to estimate the matched uncertainties, and added to the controller for linearized model to compensate the effect of uncertainties. It is proved that states of the controlled quadrotor are uniformly ultimately bounded and converge to a small neighborhood of the desired equilibrium point. Simulation results verify effectiveness of the proposed controller with the observer.


Quadrotor helicopter Controlled Lagrangians Disturbance observer Stabilization 



This work is supported by National Natural Science Foundation (NNSF) of China under Grant No. 61673043.


  1. 1.
    S. Bouabdallah, A. Noth, R. Siegwart, PID vs LQ control techniques applied to an indoor micro quadrotor, in IEEE/RSJ International Conference on Intelligent Robots and Systems (Sendai, 2004), pp. 2451–2456Google Scholar
  2. 2.
    T. Madani, A. Benallegue, Backstepping control for a quadrotor helicopter, in IEEE/RSJ International Conference on Intelligent Robots and Systems (Beijing, 2006), pp. 3255–3260Google Scholar
  3. 3.
    B. Zhu, W. Huo, Trajectory linearization control for a quadrotor helicopter, in IEEE International Conference on Control and Automation (Xiamen, 2010), pp. 34–39Google Scholar
  4. 4.
    T. Dierks, S. Jagannathan, Output feedback control of a quadrotor UAV using neural networks. IEEE Trans. Neural Netw. 21(1), 50–66 (2010)CrossRefGoogle Scholar
  5. 5.
    H. Liu, Y. Bai, L. Geng, Z. Shi, Y. Zhong, Robust tracking control of a quadrotor helicopter. J. Intell. Robot. Syst. 75(3-4), 595–608 (2014)Google Scholar
  6. 6.
    A.M. Bloch, N. Ehrich Leonard, J.E. Marsden, Stabilization of mechanical systems using controlled Lagrangians, in IEEE Conference on Decision and Control (San Diego, 1997), pp. 2356–2361Google Scholar
  7. 7.
    M.A. Bloch, N. Ehrich Leonard, J.E. Marsden, Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem. IEEE Trans. Auto. Control 45(12), 2253–2270 (2000)Google Scholar
  8. 8.
    M.A. Bloch, D.E. Chang, N. Ehrich Leonard, J.E. Marsden, Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping. IEEE Trans. Auto. Control 46(10), 1556–1571 (2001)Google Scholar
  9. 9.
    M.-Q. Li, W. Huo, Controller design for mechanical systems with underactuation degree one based on controlled Lagrangians method. Int. J. Control 82(9), 1747–1761 (2009)Google Scholar
  10. 10.
    K. Machleidt, J. Kroneis, S. Liu, Stabilization of the Furuta Pendulum using a nonlinear control law based on the method of controlled Lagrangians, in IEEE International Symposium on Industrial Electronics (Vigo, 2007), pp. 2129–2134Google Scholar
  11. 11.
    Z. Liao, W. Huo, Tracking control of underactuated mechanical systems based on controlled Lagrangians, in IEEE International Conference on Industrial Technology (Athens, 2012), pp. 278–283Google Scholar
  12. 12.
    B. Zhang, W. Huo, Stabilizing quadrotor helicopter based on controlled Lagrangians, in Chinese Intelligent Systems Conference (Mudanjiang, 2017), pp. 685–695Google Scholar
  13. 13.
    B. Zhang, W. Huo, Stabilization of quadrotor with air drag based on controlled Lagrangians method, in Chinese Automation Congress (Jinan, 2017), pp. 5798–5801Google Scholar
  14. 14.
    Z. Zuo, C. Wang, Adaptive trajectory tracking control of output constrained multi-rotors systems. IET Control Theory Appl. 8(13), 1163–1174 (2014)Google Scholar
  15. 15.
    J.-H. She, M. Fang, Y. Ohyama, H. Hashimoto, W. Min, Improving disturbance-rejection performance based on an equivalent-input-disturbance approach. IEEE Trans. Industr. Electr. 55(1), 380–389 (2008)Google Scholar
  16. 16.
    W.-H. Chen, Disturbance observer based control for nonlinear systems. IEEE/ASME Trans. Mechatr. 9(4), 706–710 (2004)Google Scholar

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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.The Seventh Research Division, School of Automation Science and Electrical EngineeringBeihang UniversityBeijingPeople’s Republic of China

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