Left ventricular assist devices (LVAD) have been used as a treatment option for end-stage heart failure patients, which can assist an ailing heart to pump blood into human body to meet body's circulatory demand. For long-term use an LVAD as a destination therapy, the device must be able to automatically adjust its pump speed to meet the cardiac demands at different levels of activity without inducing suction. Suction happens when an LVAD seeks to pump out more blood from the left ventricle than the available blood, which can collapse the heart and result in death. In this work, a new control system was developed, which involves two consecutive steps, i.e., the calculation of a pulsatility control index and the adjustment of pump speed to meet the blood flow requirement at different physiological conditions. The control strategy can prevent suction, while maintaining a desired cardiac output. The performance of the feedback controller has been tested with computer simulations, which demonstrates the feasibility and the efficiency of the proposed control algorithm.