A robust recurrent wavelet neural network (RWNN) controller is proposed in this study to control the mover of a permanent magnet linear synchronous motor (PMLSM) servo drive to track periodic reference trajectories. First, the dynamic model of the PMLSM drive system is derived. Next, a perfect control law designed in the sense of feedback linearization is derived. However, in the perfect control law, the exact values of the system parameters, external force disturbance, and friction force are unknown in practical applications. Therefore, an RWNN is proposed to mimic the perfect control law and a robust compensator is proposed to compensate the approximation error. Moreover, the online learning algorithms of the connective weights, translations, and dilations of the RWNN are derived using Lyapunov stability and back-propagation (BP) method. Furthermore, an improved particle swarm optimization (IPSO) is adopted in this study to adapt the learning rates of the RWNN to improve the learning capability. Finally, the control performance of the proposed robust RWNN controller with IPSO is verified by some simulated and experimental results.