Tetsushi Ueta, Hiroshi Kawakami, Ikuro Morita, A Study of the Pendulum Equation with a Periodic Impulsive Force, Bifurcation and ControlInstitute of Electronics, Information and Communication Engineers, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol.E78-A, No.10, pp.1269-1275, Oct. 1995.
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.