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A recurrent functional link (FL)-based fuzzy neural network (FNN) 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 recurrent FL-based FNN controller is proposed in this study to control the PMLSM. Moreover, the online learning algorithms of the connective weights, means, and standard deviations of the recurrent FL-based FNN are derived using the back-propagation (BP) method. However, divergence or degenerated responses will result from the inappropriate selection of large or small learning rates. Therefore, an improved particle swarm optimization (IPSO) is adopted to adapt the learning rates of the recurrent FL-based FNN online. Finally, the control performance of the proposed recurrent FL-based FNN controller with IPSO is verified by some simulated and experimental results.