We proposed a new rotational transformation. By this new transformation the transformed equations of the singlephase induction motor become similar to the equations of a balanced motor. The advantage of the presented method is that it can be used for the vector controlling of all of faulty motors. Also, in this paper, a method for estimation of rotor speed of single-phase induction motor with using EKF, is presented. Results show that good performance of the proposed methods, especially in controlling the torque oscillation.