Floating Offshore Wind Power is an emerging and promising technology that is particularly interesting from a Norwegian point of view because of our long and windy coast. There are however still several remaining challenges with this technology and one of them is a possible stability problem due to positive feedback from tilt motion of the turbine tower. The focus of this report is to develope a simulator for a floating offshore wind turbine that includes individual, vibrating blades. Several controllers are developed, aiming to use the blade pitch angle and the generator power to control the turbine speed and output power, while at the same time limit the low-frequent motions of the tower and the high-frequent motions of the turbine blades. The prime effort is placed on developing a solution using Model Predictive Control(MPC). On the issue of blade vibrations no great progress has been made. It is not possible to conclude from the simulation results that the designed controllers are able to reduce the blade vibrations. However, the MPC controller works very well for the entire operating range of the turbine. A "fuzzy"-inspired switching algorithm is developed and this handles the transitions between the different operating ranges of the turbine convincingly. The problem of positive feedback from the tower motion is handled well, and the simulations do not indicate that this issue should jeopardize the viability of floating offshore wind turbines.