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Control of oscillations from the k-zero bifurcation

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  • Verduzco, Fernando

Abstract

In this paper, an analytical method for the analysis and control of oscillations in non-linear control systems, whose linearization around the origin has k eigenvalues zero, is presented. The main idea consists in exploit, for the particular case of the double-zero (or Takens–Bognadov) bifurcation, the existence of a curve of Hopf bifurcation points on its versal deformation, to control oscillations. Then the general case is reduced to the double-zero case through a change of coordinates and a change in the input control. The method is illustrated with the pendubot, an underactuated robot manipulator of two degrees of freedom.

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  • Verduzco, Fernando, 2007. "Control of oscillations from the k-zero bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 492-504.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:2:p:492-504
    DOI: 10.1016/j.chaos.2006.01.030
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    Cited by:

    1. Mayra Antonio-Cruz & Victor Manuel Hernández-Guzmán & Ramón Silva-Ortigoza & Gilberto Silva-Ortigoza, 2019. "Implementation of a Controller to Eliminate the Limit Cycle in the Inverted Pendulum on a Cart," Complexity, Hindawi, vol. 2019, pages 1-13, February.

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