Cardiac alternans is a beat-to-beat alternation of the action potential duration (APD), which has been implicated as a possible cause of ventricular fibrillation. Previous studies have shown that alternans can originate via a period doubling bifurcation caused by the nonlinear dependence of the APD on the previous diastolic interval. In this case, it has been demonstrated that alternans can be eliminated by applying feedback control on the pacing cycle length. However, studies have shown that alternans can also originate due to unstable calcium (Ca) cycling in cardiac myocytes. In this study, we explore the effectiveness of APD feedback control to suppress alternans when the underlying instability is due to unstable Ca cycling. In particular, we explore the role of the bi-directional coupling between Ca and voltage and determine the effectiveness of feedback control under a wide range of conditions. We also analyze the applicability of feedback control on a coupled two cell system and show that APD control induces spatially out-of-phase alternans. We analyze the onset and the necessary conditions for the emergence of these out-of-phase patterns and assess the effectiveness of feedback control to suppress Ca driven alternans in a multi-cellular system.