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A field-programmable gate array (FPGA)-based functional link radial basis function network (FLRBFN) control is proposed in this study to control the mover of a permanent magnet linear synchronous motor (PMLSM) servo drive system to track periodic reference trajectories. First, the dynamics of the field-oriented control PMLSM servo drive with a lumped uncertainty, which contains parameter variations, external disturbances and non-linear friction force, is derived. Then, to achieve accurate trajectory tracking performance with robustness, an intelligent control approach using FLRBFN is proposed for the field-oriented control PMLSM servo drive system. The proposed FLRBFN is a radial basis function network (RBFN) embedded with a functional link neural network (FLNN). Moreover, the on-line learning algorithm of the FLRBFN, including the connective weights, the centres and the centres' width of the receptive field functions, are derived using back-propagation (BP) method. Furthermore, an FPGA chip is adopted to implement the developed control and on-line learning algorithms for possible low-cost and high-performance industrial applications using PMLSM. Finally, the effectiveness of the proposed control scheme and the robustness to parameter variations, external disturbances and friction force of the PMLSM servo drive system are verified by some experimental results.