Stabilization of a 3-Link Pendulum in Vertical Position

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1196)


The aim of the paper is to verify the linearizabilty conditions for the triple inverted pendulum driven by 2 inputs, and stabilize it in the upright position. Moreover, the zero dynamics is derived and illustrated graphically.


Nonlinear dynamics Control theory 3-link pendulum Linearization Zero dynamic 



We express our thanks to Prof. W. Respondek for fruitful discussion and useful comments.


  1. 1.
    Eltohamy, K.G., Kuo, C.Y.: Nonlinear optimal control of a triple link inverted pendulum with single control input. International Journal of Control 69(2), 239–256 (1998)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Furuta, K., Ochiai, T., Ono, N.: Attitude control of a triple inverted pendulum. International Journal of Control 39(6), 1351–1365 (1984)CrossRefGoogle Scholar
  3. 3.
    Glück, T., Eder, A., Kugi, A.: Swing-up control of a triple pendulum on a cart with experimental validation. Automatica 49(3), 801–808 (2013). Scholar
  4. 4.
    Jakubczyk, B., Respondek, W.: On linearization of control systems. Biuletyn Polskiej Akademii Nauk 28(9–10), (1980)Google Scholar
  5. 5.
    Kozłowski, K., Kowalski, M., Michalski, M., Parulski, P.: Universal multiaxis control system for electric drives. IEEE Transactions on Industrial Electronics 60(2), 691–698 (2013)Google Scholar
  6. 6.
    Li, S., Moog, C., Respondek, W.: Maximal feedback linearization and its internal dynamics with applications to mechanical systems on \({R}^4\). International Journal of Robust and Nonlinear Control 29(9), 2639–2659 (2019).
  7. 7.
    Medrano-Cerda, G.A.: Robust stabilization of a triple inverted pendulum-cart. International Journal of Control 68(4), 849–866 (1997)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Michalski, M., Kowalski, M., Pazderski, D.: Quadruped walking robot WR-06 - design, control and sensor subsystems. In: Kozłowski, K. (ed.) Robot Motion and Control 2009, pp. 175–184. Springer, London, London (2009)CrossRefGoogle Scholar
  9. 9.
    Respondek, W.: Partial linearization, decompositions and fibre systems. Theory and Applications of Nonlinear Control Systems 85, 137–154 (1986)Google Scholar
  10. 10.
    Spong, M.W.: Partial feedback linearization of underactuated mechanical systems. In: Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS’94), vol. 1, pp. 314–321 vol.1 (1994)Google Scholar
  11. 11.
    Xin, X., Zhang, K., Wei, H.: Linear strong structural controllability for an n-link inverted pendulum in a cart. In: 2018 IEEE Conference on Decision and Control (CDC), pp. 1204–1209 (2018)Google Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Poznan University of TechnologyPoznañPoland

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