This paper presents a new control strategy for the rotor side converter of Doubly-Fed Induction Generator based Wind Turbine systems, under severe voltage dips. The main goal is to fulfill the Low Voltage Ride Through performance, required by modern grid codes. In this respect, the key point is to limit oscillations (particularly on rotor currents) triggered by line faults, so that the system keeps operating with graceful behavior. To this aim, a suitable feedforward-feedback control solution is proposed for the DFIG rotor side. The feedforward part exploits oscillation-free reference trajectories, analytically derived for the system internal dynamics. State feedback, designed accounting for control voltage limits, endows the system with robustness and further tame oscillations during faults. Moreover, improved torque and stator reactive power tracking during faults is achieved, proposing an exact mapping between such quantities and rotor-side currents, which are conventionally used as controlled outputs. Numerical simulations are provided to validate the capability of the proposed approach to effectively cope with harsh faults.