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This paper proposes a torque tracking algorithm via steer by wire to achieve the target steering feel and proposed a modified friction model to obtain return-ability. A three dimensional reference steering wheel torque map is designed using the measurement data of the steering characteristics of the target vehicle at a transition test and a weave test. In order to track the reference steering wheel torque, a sliding mode control is used in the tracking algorithm. In addition, to achieve return-ability, the modified friction model for steer by wire is used instead of the friction model defined in the reference steering wheel torque map. The modified friction model is composed of various models according to the angular velocity. The angular velocity and the angular acceleration used in the control algorithm are estimated using a kalman filter.