Atrioventricular (AV) nodal alternans is a pathological cardiac condition characterized by a beat-to-beat alternation (period-2 rhythm) in AV nodal conduction time. Here we implement an AV nodal conduction model which undergoes a period-doubling bifurcation into alternans. We show that additive noise can be used to locate the unstable period-1 fixed point which underlies the alternans rhythm. We then use chaos control to suppress alternans by stabilizing the model about its unstable period-1 fixed point. We also show that the period-doubling bifurcation into alternans can be prevented by tracking the period-1 rhythm into its unstable regime. We demonstrate that these techniques are robust to imprecise measurements and experimental noise. Importantly, these methods require no knowledge of the underlying system equations. These findings suggest that chaos control and tracking may be useful for suppressing alternans in a clinical environment.