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A robust fuzzy neural network (RFNN) control system is proposed in this study to control the position of the mover of a permanent magnet linear synchronous motor (PMLSM) drive system to track periodic reference trajectories. First, an ideal feedback linearization control law is designed based on the backstepping technique. Then, a fuzzy neural network (FNN) controller is designed to be the main tracking controller of the proposed RFNN control system to mimic an ideal feedback linearization control law, and a robust controller is proposed to confront the shortcoming of the FNN controller. Moreover, to relax the requirement for the bound of uncertainty term, which comprises a minimum approximation error, optimal parameter vectors and higher order terms in Taylor series, an adaptive bound estimation is investigated where a simple adaptive algorithm is utilized to estimate the bound of uncertainty. Furthermore, the simulated and experimental results due to periodic reference trajectories demonstrate that the dynamic behaviors of the proposed control systems are robust with regard to uncertainties.