This article presents an integrated model of the human circulatory system that incorporates circulatory support by a brushless DC axial flow ventricular assist device (VAD), and a feedback VAD controller designed to maintain physiologically sufficient perfusion. The developed integrated model combines a network type model of the circulatory system with a nonlinear dynamic model of the brushless DC pump We show that maintaining a reference differential pressure between the left ventricle and aorta leads to adequate perfusion for different pathologic cases, ranging from normal heart to left heart asystole, and widely varying physical activity scenarios from rest to exercise.