Nonlinear Dynamics

, Volume 82, Issue 1–2, pp 677–688 | Cite as

Elastic inverted pendulum with backlash in suspension: stabilization problem

  • Mikhail E. Semenov
  • Andrey M. Solovyov
  • Peter A. Meleshenko
Original Paper


In this paper, we investigate the elastic inverted pendulum with hysteretic nonlinearity (a backlash) in the suspension point. Namely, the problems of stabilization and optimization of such a system are considered. The algorithm (based on the bionic model) which provides the effective procedure for finding of optimal parameters is presented and applied to considered system. The results of numerical simulations, namely the phase portraits and the dynamics of Lyapunov function, are also presented and discussed.


Elastic inverted pendulum Hysteretic control Stabilization problem Bionic algorithm 



This work is supported by the RFBR Grant 13-08-00532-a.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Mikhail E. Semenov
    • 1
    • 2
    • 3
    • 4
  • Andrey M. Solovyov
    • 4
  • Peter A. Meleshenko
    • 4
    • 5
  1. 1.Meteorology DepartmentZhukovsky–Gagarin Air Force AcademyVoronezhRussia
  2. 2.Mathematics DepartmentVoronezh State University of Architecture and Civil EngineeringVoronezhRussia
  3. 3.The National University of Science and Technology MISiSStaryi OskolRussia
  4. 4.Digital Technologies DepartmentVoronezh State UniversityVoronezhRussia
  5. 5.Communication DepartmentZhukovsky–Gagarin Air Force AcademyVoronezhRussia

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