Robust periodic motion control of the mover of a permanent magnet (PM) linear synchronous motor (LSM) drive is achieved by use of a recurrent neural network (RNN) controller in this study. First, an integral‐proportional (IP) controller is introduced to control the mover position of the LSM for periodic step input. The IP position controller is designed according to the estimated mover parameters to match the time‐domain command tracking specifications. Then, to increase the robustness of the LSM drive system for periodic step command input, an RNN position controller is proposed to reduce the influence of parameter variations and external disturbances on the drive system. The RNN position controller can track periodic sinusoidal input precisely. Moreover, a dynamic backpropagation algorithm is developed to train the RNN on line using the delta adaptation law. The effectiveness of the proposed control scheme is demonstrated by some simulated and experimental results.