Normally compressor load control is realized either passively with a bypass loop with high energy consumption or by an active valve. Actively controlled valves must fulfill a set of conditions which can be expressed as a constrained optimal control. However, compressor valves are subject to serious disturbances which might be unpredictable and difficult to describe, and have complex dynamics. This makes the solution of the real optimal problem difficult and even questionable. Against this background, this paper proposes a two step design approach: first a problem approximation is derived for which an explicit solution of the problem can be computed, then iterative learning control (ILC) is used with the real plant to enforce it. Due to limitation of the actuators, basically a switching solution results, and the tracking of this solution yields a satisfactory solution near to the optimal one. The method has been tested in simulation and experimentally on a special valve design including a small rotational electrical motor and a high gear rate spindle.