Hiroshi Yabuno

Bifurcation control for a parametrically excited cantilever beam by linear feedback

In this article, we propose a bifurcation control method for a parametrically excited cantilever beam by linear feedback. Quadratic damping plays a dominant role in the nonlinear response of the parametrically excited cantilever beam, and two transcritical bifurcations can exist in the frequency–response curve. In the relatively high-amplitude excitation or in sweeping the excitation amplitude, there are two saddle-node bifurcations in addition to the transcritical bifurcations. The discontinuous bifurcation as a saddle-node bifurcation induces jumping phenomena in the sweeps of the excitation amplitude and the excitation frequency. In this article, we focus on the case of the excitation amplitude sweep and propose a control method to avoid the jumping phenomena by bifurcation control, i.e. by shifting the bifurcation set based on the linear feedback. The validity of the control method is experimentally confirmed using a simple apparatus.

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

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 swing-up and the stabilization are carried out. By a simple apparatus, the validity of the theoretically proposed method is experimentally confirmed.