Left ventricular assist devices (LVADs) can provide mechanical support for a failing heart as bridge to transplant and destination therapy. Physiological control systems for LVADs should be designed to respond to changes in hemodynamic across a variety of clinical scenarios and patients by automatically adjusting the heart pump speed. In this study, a novel adaptive physiological control system for an implantable heart pump was developed to respond to interpatient and intrapatient variations to maintain the left-ventricle-end-diastolic-pressure (LVEDP) in the normal range of 3 to 15 mmHg to prevent ventricle suction and pulmonary congestion. A new algorithm was also developed to detect LVEDP from pressure sensor measurement in real-time mode. Model free adaptive control (MFAC) was employed to control the pump speed via simulation of 100 different patient conditions in each of six different patient scenarios, and compared to standard PID control. Controller performance was tracked using the sum of the absolute error (SAE) between the desired and measured LVEDP. The lower SAE on control tracking performance means the measured LVEDP follows the desired LVEDP faster and with less amplitude oscillations preventing ventricle suction and pulmonary congestion (mean and standard deviation of SAE(mmHg) for all 600 simulations were 18813+-29345 and 24794+-28380 corresponding to MFAC and PID controller respectively). In four out of six patient scenarios, MFAC control tracking performance was better than the PID controller. This study shows the control performance can be guaranteed across different patients and conditions when using MFAC over PID control, which is a step towards clinical acceptance of these systems.