A Study of the Pendulum Equation with a Periodic Impulsive Force--Bifurcation and Control--

Tetsushi UETA; Hiroshi KAWAKAMI; Ikuro MORITA

A Study of the Pendulum Equation with a Periodic Impulsive Force--Bifurcation and Control--

Tetsushi UETA, Hiroshi KAWAKAMI, Ikuro MORITA

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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 two-phase hybrid stepping motor. We suggest that the unstable operations called pull-out are caused by bifurcations. Finally, we proposed a control method to avoid the pull-out by changing the repetitive frequency and stepping rate.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E78-A No.10 pp.1269-1275

Publication Date: 1995/10/25

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Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)

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Tetsushi UETA, Hiroshi KAWAKAMI, Ikuro MORITA, "A Study of the Pendulum Equation with a Periodic Impulsive Force--Bifurcation and Control--" in IEICE TRANSACTIONS on Fundamentals, vol. E78-A, no. 10, pp. 1269-1275, October 1995, doi: .
Abstract: 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 two-phase hybrid stepping motor. We suggest that the unstable operations called pull-out are caused by bifurcations. Finally, we proposed a control method to avoid the pull-out by changing the repetitive frequency and stepping rate.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e78-a_10_1269/_p

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@ARTICLE{e78-a_10_1269,
author={Tetsushi UETA, Hiroshi KAWAKAMI, Ikuro MORITA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Study of the Pendulum Equation with a Periodic Impulsive Force--Bifurcation and Control--},
year={1995},
volume={E78-A},
number={10},
pages={1269-1275},
abstract={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 two-phase hybrid stepping motor. We suggest that the unstable operations called pull-out are caused by bifurcations. Finally, we proposed a control method to avoid the pull-out by changing the repetitive frequency and stepping rate.},
keywords={},
doi={},
ISSN={},
month={October},}

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TY - JOUR
TI - A Study of the Pendulum Equation with a Periodic Impulsive Force--Bifurcation and Control--
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1269
EP - 1275
AU - Tetsushi UETA
AU - Hiroshi KAWAKAMI
AU - Ikuro MORITA
PY - 1995
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E78-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 1995
AB - 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 two-phase hybrid stepping motor. We suggest that the unstable operations called pull-out are caused by bifurcations. Finally, we proposed a control method to avoid the pull-out by changing the repetitive frequency and stepping rate.
ER -