A fractional-order controller with a PIα structure is proposed for controlling the position of the electrodes of an electric arc furnace (EAF). The dynamics of one of the electrodes of an industrial EAF process was experimentally identified yielding an equivalent fourth order plus time delay transfer function which showed strong plant parameter variations and measured and unmeasured disturbances. A new methodology for the design of fractional-order robust controllers for this system has been proposed. It was shown that the attained controllers significantly outperformed the robustness achieved with PI and PID controllers while adding only moderate complexity to the control structure.