A noninvasive continuous blood pressure measurement technique that has been developed lately requires precise control of the blood flow through a superficial artery. The flow is measured using ultrasound and influenced via manipulating the pressure inside an inflatable air balloon which is placed over the artery. This contribution is concerned with the design and evaluation of a learning cascaded control structure for such measurement devices. Two feedback control loops are designed in discrete time via pole placement and then combined with an iterative learning control. The latter exploits the repetitive nature of the disturbance that is induced by the oscillating arterial pressure. Experimental results indicate that the proposed controller structure yields considerably smaller set point deviations than previous approaches.