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This paper is aimed to design a learning-based controller for robotic manipulators. A controller is proposed to estimate the nonlinear system dynamics and minimize tracking error in motion. In order to improve the learning speed and performance, a new CMAC (cerebellar model articulation controller) controller with grey learning rate is proposed. The grey learning rate, which is based on a grey relational analysis, is utilized to adjust the learning rate online. Real-time tracking control can be achieved with the proposed controller. To demonstrate the performance of the proposed controller, ADMAS and MATLAB/Simulink are used for simulation. The NI sbRIO-9642 is employed to realize the control algorithm on the NTU robot arm, which is developed by our laboratory. The simulation and experimental results show that the proposed learning-based controller can provide better tracking performance than the conventional ones.