A novel Subspace Predictive Repetitive Control (SPRC) methodology is presented and used to control trailing edge flaps for wind turbines. First, the dynamics of the wind turbine are identified online. This is especially important for trailing edge flaps on a large wind turbine, where a local change in wind conditions can result in significantly altered aerodynamics. Next, a repetitive control (RC) law is formulated for the multivariable problem from the identified dynamics, that guarantees stability when the identification converges to the true system parameters. This is done in a lower-dimensional basis-function subspace, which reduces computations and gives high control over the shape of the actuator signal. The SPRC methodology is validated in a high-fidelity wind turbine simulation environment.