Due to the increased share of (offshore) wind turbines, more stringent power requirements have been established. Importantly, the low-voltage ride-through requirement states that a wind turbine must remain connected to the electrical grid after a short intermittent grid fault. In the industry and academia many solutions have been proposed, but these are limited by requirements of detailed system knowledge, lack of optimality guarantees, or no testing on high-fidelity models. Therefore, two Iterative Learning Control (ILC) algorithms are presented aimed to solve these issues. The ILC algorithms apply model-free learning based on iterations. Shown is that these ILC algorithms can yield improved performance on a low- and high-fidelity models, with fast convergence of the 2-norm of the output error. The major contributions of this work lie in the application of ILC on grid fault control for wind turbines and in the extension of the norm-optimal ILC to include input constraints using optimisation methods.