The control design of an airborne wind energy system with rigid aircraft, vertical take-off and landing, and pumping operation is described. A hierarchical control structure is implemented, in order to address all operational phases: take-off, transition to power generation, pumping energy generation cycles, transition to hovering, and landing. Control design at all hierarchical levels is described. The design approach is conceived and developed with real-world applicability as main driver. Aircraft design considerations in light of system maneuverability are presented, too, as well as three possible alternative strategies for the retraction phase of the pumping cycle. The automatic control approach is assessed in simulation with a realistic model of the overall system, and the results yield a comparison among the three retraction strategies, clearly indicating the most efficient one. The presented results allow one to simulate the dynamical behavior of an AWE system in all operational phases, enabling further studies on all-round system automation, towards fully autonomous and reliable operation.