Tissue-engineered heart valves, cultured from human stem cells, are a possible alternative for replacing failing aortic heart valves, where nowadays biological and mechanical heart valves are used. Growing and conditioning is done by mechanically stimulating the tissue in a bioreactor. The disposable injection molded bioreactor  uses flexible membranes and steering valves to mimic a physiological heart cycle. In this work, an air pressure actuation control system for this bioreactor is designed. One membrane is position controlled to achieve a desired flow through the heart valve, while another membrane controls the aortic pressure. A third actuator controls a steering valve used to impose a resistance on the flow back to the first membrane, in order to control the heart valve closing pressure. Due to the repetitive character of the setpoints, iterative learning controllers are implemented. A high position tracking performance is achieved and pressure setpoints are mimicked successfully, but the main focus is on preventing large pressure oscillations and other events that could be damaging for the tissue heart valve. The control system allows full adjustability of operating conditions needed for the growing, conditioning and testing phases.