Archive of Applied Mechanics

, Volume 88, Issue 4, pp 517–524 | Cite as

Coupled inverted pendulums: stabilization problem

  • Mikhail E. Semenov
  • Andrey M. Solovyov
  • Mikhail A. Popov
  • Peter A. Meleshenko
Original
  • 95 Downloads

Abstract

A mathematical model of an unstable system in the form of inverted coupled pendulums is developed and simulated. Dynamics of such a system is investigated, and the stability zones are identified in the explicit form. The algorithm of stabilization of the pendulums near the vertical position is constructed and verified.

Keywords

Inverted pendulum Coupled oscillators Stabilization problem 

Notes

Acknowledgements

This work is supported by the RFBR Grants 16-08-00312-a and 17-01-00251-a.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Mikhail E. Semenov
    • 1
    • 2
    • 3
  • Andrey M. Solovyov
    • 3
  • Mikhail A. Popov
    • 2
    • 3
  • Peter A. Meleshenko
    • 3
    • 4
  1. 1.Geophysical Survey of Russia Academy of SciencesObninskRussia
  2. 2.Applied Mathematics and Mechanics DepartmentVoronezh State Technical UniversityVoronezhRussia
  3. 3.Digital Technologies DepartmentVoronezh State UniversityVoronezhRussia
  4. 4.Communication DepartmentZhukovsky–Gagarin Air Force AcademyVoronezhRussia

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