Closed-loop systems have been developed for controlling the flow above a three-dimensional turret. The top of the turret is hemispherical, houses a flat optical aperture, and can rotate about two axes (pitch and yaw). The extent of separation and concomitant turbulence levels in the flow above the aperture change as the turret rotates. The control objective is to minimize the separation and turbulence in the dynamic environment created by the articulating turret. The closed-loop control systems include dynamical and measurementbased estimators, regulators, filters, and compensators. These components are developed using both computational data from CFD simulations and experimental data from wind tunnel runs within the common framework of SMARTflow-engineering software for flow control system design. The control systems are evaluated through a series of control-in-theloop CFD simulations and wind tunnel runs, demonstrating the merits of feedback control through robustness in the presence of measurement noise, modeling errors, and highly unsteady conditions and through reductions in actuation energy below levels required by open-loop systems. Controller designs and computational tests are described here; wind tunnel tests are described in the companion paper, "Feedback Flow Control for a Pitching Turret (Part II)."