Hysteresis Analysis and Feedback Stabilization of Snap-through Buckling

Abstract

We study a preloaded two-bar linkage that exhibits hysteresis due to the presence of multiple attracting equilibria. The dynamics at the unstable equilibrium, through which a snap-through buckle occurs, are not linearizable due to a singularity that is solution-dependent. We stabilize the unstable equilibrium using two distinct nonlinear controllers. The feedback linearization controller requires knowledge of the linkage parameters, whereas the potential shaping PD-type controller requires only an upper bound on the stiffness.