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This study addresses the design and properties of an intelligent optimal control of a nonlinear flexible robot arm that is driven by a permanent magnet (PM) synchronous servo motor. The dynamic model of a flexible robot arm system with a tip mass is introduced initially. Moreover, an intelligent optimal control system is proposed to control the motor-mechanism coupling system for periodic motion. In the intelligent optimal control system a fuzzy neural network (FNN) controller is used to learn a nonlinear function in the optimal control law, and a robust controller is designed to compensate the approximate error. In addition, a simple adaptive algorithm is proposed to adjust the uncertain bound in the robust controller avoiding the chattering phenomena. The effectiveness of the proposed control scheme is verified by both the numerical simulation and experimental results.