Swing-up and stabilization of an inverted pendulum without feedback control

—Application of a bifurcation control to a pendulum with two degrees of rotational freedom—

Abstract

In this paper, we propose a method for swing-up and stabilization of a inverted pendulum without feedback control. By using high-frequency excitation the state where the pendulum hangs down is destabilized, while the up-right position of the inverted pendulum is stabilized. These phenomena correspond to sub-critical and super-critical pitchfork bifurcations, respectively. By the perturbation of these bifurcation phenomena based on a bifurcation control, the swiug-up and the stabilization are carried out. By a simple apparatus, the validity of the theoretically proposed method is experimentally confirmed.