Control of oscillations from the k-zero bifurcation

Fernando Verduzco

Chaos, Solitons & Fractals, 2007, vol. 33, issue 2, 492-504

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.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:33:y:2007:i:2:p:492-504

DOI: 10.1016/j.chaos.2006.01.030

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