The motor that you described above, sounds not unlike a Wound Rotor Induction motor.
The Armature is wound in Star and is fed through the slip-rings at the back of the Armature shaft.
The motor also has a normal Stator winding, as in a normal Cage induction motor.
It is the Rotor windings that have the Resistances in series with them and as the resistance is lowered the motor speeds up.
There is no actual supply to the Rotor windings, all that is varied is the currents caused by the Magnetic field in the Stator windings.