This paper focuses on the closed-loop control of an incompressible flow past an open cavity. We propose a delayed feedback controller to suppress the self-sustained oscillations of the shear layer. The control law shows robustness to changes in flow conditions. An extension of the Eigensystem Realization Algorithm (ERA) to closed-loop identification, the so-called OCID technique, is used to extract the unstable linear dynamics of the cavity flow. The model-based analysis actually captures the modes against which the steady flow becomes unstable. The identified model is used to design an optimal controller, which shows both efficiency and robustness to stabilize the cavity flow.