This paper proposes a simple fractional-order controller with a PI structure for controlling the position of the electrodes of an electric arc furnace (EAF). The dynamics of one of the three electrodes of an industrial EAF process was experimentally identified. Models of the electrode position system and the furnace electrical system (electric arc impedance model) were obtained. This identification procedure yielded an equivalent fourth order plus time delay transfer function, and showed strong plant parameter variations and measured and unmeasured disturbances. We therefore propose a new methodology for the design of fractional-order robust controllers for this system. By carrying out a partial inversion of the dynamics, a method for fractional-order robust control of first order plus time delay plants was developed and applied to this process. It was shown that the attained controllers significantly outperformed the robustness achieved with PI and PID controller (also combined with the partial dynamics inversion term), while adding only moderate complexity to the control structure.