Offshore wind energy capitalizes on the higher and less turbulent wind speeds at sea. To enable deployment of wind turbines in deep-water locations, structures are being explored, where wind turbines are placed on a floating platform. This combined structure presents a new control problem, due to the partly unconstrained movement of the platform and ocean wave excitation. If this additional complexity is not dealt with properly, this may lead to a significant increase in the structural loads and, potentially, instability of the controlled system. In this paper, the wave excitation is investigated, and we show the influence that both wind speed, wave frequencies and misalignment between wind and waves have on the system dynamics. A new control model is derived that extends standard turbine models to include the hydrodynamics, additional platform degrees of freedom, the platform mooring system and tower side-side motion, including gyroscopic effects. The models support a model-based design that includes estimators for wind speed and wave frequency. The design is applied to a number of examples representing different wind and wave conditions and successfully demonstrates a reduction in the structural oscillations, while improving power performance.