Abstract-Periodic speed errors can occur in permanent magnet linear synchronous machines for two reasons: 1) a periodic reference signal; 2) cogging force and friction. For reducing such periodic errors, iterative learning control or repetitive control approaches, used in conjunction with more common control actions, can be strongly effective. However, the design of the stability filter, robustness filter and other parameters for a traditional repetitive controller can be a complex task and may need to be adjusted when the frequency of such periodic error varies. Existing solutions tend to develop more adaptive tuning methods for repetitive controller to enhance the whole control system. This paper shows that the performance of a traditional speed loop can be enhanced with a repetitive controller without complicating the tuning of the repetitive controller. Consequently, a position-based repetitive control combined with deadbeat current control method is proposed. Simulation results show that the proposed method is effective for reducing speed ripple at difference frequencies without necessarily adjusting its parameters.