Ventricular assist devices (VADs) are blood pumps that offer an option to support the circulation of patients with severe heart failure. Since a failing heart has a remaining pump function, its interaction with the VAD influences the hemodynamics. Ideally, the heart's action is taken into account for actuating the device such that the device is synchronized to the natural cardiac cycle. To realize this in practice, a reliable real-time algorithm for the automatic synchronization of the VAD to the heart rate is required. This paper defines the tasks such an algorithm needs to fulfill: the automatic detection of irregular heart beats and the feedback control of the phase shift between the systolic phases of the heart and the assist device. We demonstrate a possible solution to these problems and analyze its performance in two steps. First, the algorithm is tested using the MIT-BIH arrhythmia database. Second, the algorithm is implemented in a controller for a pulsatile and a continuous-flow VAD. These devices are connected to a hybrid mock circulation where three test scenarios are evaluated. The proposed algorithm ensures a reliable synchronization of the VAD to the heart cycle, while being insensitive to irregularities in the heart rate.