Feedback stabilization of snap-through buckling in a preloaded two-bar linkage with hysteresis

Abstract

We study a linearly damped 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 solution-dependent singularity. We stabilize the unstable equilibrium using two distinct non-linear controllers. The feedback-linearization controller requires knowledge of the linkage parameters, whereas the robust version of the intrinsic non-linear proportional-derivative controller requires only an upper bound on the stiffness.