The application describes a wind turbine having a control method and controller for performing predictive control of a wind turbine generator. Based on the measured instantaneous wind speed, it is known to provide control signals to a wind turbine in order to control the pitch of the wind turbine rotor blades and the speed of the generator. However, it is difficult using instantaneous wind speed measurements to achieve smooth control, due to finite response speeds of the associated electro-mechanical systems, as well as the constantly changing control system inputs. The predictive control system described in the application assumes a model of generator speed based on the values of the incident wind speed v(t) and the values of a control signal u(t) output to the wind turbine in a feed forward loop. Here, the control signal can be for one or more of controlling either the power setting of the generator, or the pitch angle of the rotor blades. The predictive controller uses a rolling time series of values for v(t) and u(t) and based on a predicted response of the generator speed w(t) optimizes the time series control signal u(t). The predicted response of the generator speed w(t) is based on model, that can be refined in real time as the wind turbine operates.