Stick balancing with reflex delay in case of parametric forcing

Research output: Article

20 Citations (Scopus)


The effect of parametric forcing on a PD control of an inverted pendulum is analyzed in the presence of feedback delay. The stability of the time-periodic and time-delayed system is determined numerically using the first-order semi-discretization method in the 5-dimensional parameter space of the pendulum's length, the forcing frequency, the forcing amplitude, the proportional and the differential gains. It is shown that the critical length of the pendulum (that can just be balanced against the time-delay) can significantly be decreased by parametric forcing even if the maximum forcing acceleration is limited. The numerical analysis showed that the critical stick length about 30. cm corresponding to the unforced system with reflex delay 0.1. s can be decreased to 18. cm with keeping maximum acceleration below the gravitational acceleration.

Original languageEnglish
Pages (from-to)2160-2168
Number of pages9
JournalCommunications in Nonlinear Science and Numerical Simulation
Issue number4
Publication statusPublished - ápr. 1 2011

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

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