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A Study of the Pendulum Equation with a Periodic Impulsive ForceBifurcation and Control
Tetsushi UETA Hiroshi KAWAKAMI Ikuro MORITA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E78A
No.10
pp.12691275 Publication Date: 1995/10/25 Online ISSN:
DOI: Print ISSN: 09168508 Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and Its Applications) Category: Keyword: impulsive force, bifurcation, controlling chaos, stepping motor,
Full Text: PDF(508.1KB)>>
Summary:
The pendulum equation with a periodic impulsive force is investigated. This model described by a second order differential equation is also derived from dynamics of the stepping motor. In this paper, firstly, we analyze bifurcation phenomena of periodic solutions observed in a generalized pendulum equation with a periodic impulsive force. There exist two topologically different kinds of solution which can be chaotic by changing system parameters. We try to stabilize an unstable periodic orbit embedded in the chaotic attractor by small perturbations for the parameters. Secondly, we investigate the intermittent drive characteristics of twophase hybrid stepping motor. We suggest that the unstable operations called pullout are caused by bifurcations. Finally, we proposed a control method to avoid the pullout by changing the repetitive frequency and stepping rate.

