In this paper we propose a new control scheme for the doubly–fed induction machine (DFIM) that offers significant advantages, and is considerably simpler, than the classical vector control method. In contrast with the latter, where the DFIM is represented in a stator flux–oriented frame, we propose here a model with orientation of the stator voltage. This allows for an easy decomposition of the active and reactive powers on the stator side and their regulation—acting on the rotor voltage—via stator current control. Our main contribution is the proof that a linear PI control around the stator currents ensures global stability for a feedback linearized DFIM, provided the gains are suitably selected. The feedback linearization stage requires only measurement of the rotor and stator currents, hence is easily implementable. Furthermore, to improve the robustness, an adaptive version that estimates the rotor resistance is proposed. Tuning rules for the PI gains are also provided. Finally, an outer loop control for the mechanical speed is introduced. The complete control system is tested both in simulations and experiments, showing good transient performance and robustness properties.