In the context of automated driving, Electric Power Steering (EPS) systems represent an enabling technology. They introduce the ergonomic function of reducing the physical effort required by the driver during the steering maneuver. Furthermore, EPS gives the possibility of high precision control of the steering system, thus paving the way to autonomous driving capability. In this context, the present work presents a performance assessment of an EPS system designed for a full-electric all-wheel-drive electric prototype racing in Formula Student Driverless (FSD) competitions. Specifically, the system is based on the linear actuation of the steering rack by using a ball screw. The screw nut is rotated through a belt transmission driven by a brushless DC motor. Modeling and motion control techniques for this system are presented. Moreover, the numerical model is tuned through a grey-box identification approach. Finally, the performance of the proposed EPS system is tested experimentally on the vehicle through both sine-sweep profiles and co-simulated driverless sessions. The system performance is assessed in terms of reference tracking capability, thus showing favorable results for the proposed actuation solution.