Initiation and Directional Control of Period-1 Rotation for Vertically or Horizontally Excited Parametric Pendulum

Abstract

Initiation of period-1 rotation of a vertically or horizontally excited parametric pendulum from arbitrary initial conditions has been studied using a switch delayed feedback control. We also study the possibility of controlling the preferential direction of rotation. In order to choose the control parameters, a systematic linear stability analysis of the various periodic solutions is performed using the Floquet theory. The control gains are obtained using the variation of the dominant Floquet multipliers with the control gain. Our procedure has been verified to work well with both the case of vertical and horizontal excitation.