Long-span suspension bridges must satisfy at the same time spanning very long distances and limited responses against external loads, even if of high intensity. Structural control can offer a reliable con- tribution to limit internal forces and displacements in structural elements when extreme events occur. Wind buffeting is regarded as one of the most important dynamic excitation for long span flexible bridges owing to the low frequency content which characterize its spectrum. In this paper a suspension bridge model with steel frame deck is accounted as a case study for performing numerical simulations and evaluating, at first, a wide collection of control strategies, including tuned mass dampers, for mitigat- ing the buffeting dynamic vibrations induced by strong wind loading. Subsequently the scope is extended, with reference to the issue of robustness of control strategies, assessing the proposed control solutions with respect to changes of parameters. The control implementations include optimal tuned mass damper schemes. These are identified through a reduced two degrees of freedom structural model and their efficacy is tested on the full bridge finite element model. Such passive control strategy is compared with different ones implementing pas- sive or semi-active hysteretic dampers that link the deck to the piers, as well as with hybrid control schemes that adopt at the same time tuned mass dampers and hysteretic dampers. The important issue of robustness of control strategies is studied with reference to the proposed con- trol schemes. Hence the proposed control solutions are evaluated with respect their capability to perform with a satisfactorily behavior when damage in some of their elements occurs. Besides the numerical sim- ulations, necessary to derive a quantitative approach, the formulation and evaluation of a robustness index for the control system is explored and the reasons at the base of the satisfactorily behavior observe are highlighted.