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An electric vehicle (EV) drive must feature fast torque response, high efficiency over wide speed and torque ranges, and reasonable cost. This paper proposes an efficient and robust control scheme for a speed sensorless EV with an induction motor. The main control strategy is a hybrid field oriented control (FOC) and direct torque control (DTC) which combines the advantages of both FOC and DTC and eliminates certain implementation difficulties. For robust operation above the rated speed, a control scheme for field weakening is developed. Since sensorless control is a lower-cost alternative to the position or speed encoder-based control, an extended Kalman filter based speed estimation method is adopted in the main control strategy. Furthermore, a loss-model-based controller (LMC) is employed to optimize the efficiency of the drive. Simulation results verify the effectiveness of the proposed method.