This paper presents the development of a generalized predictive controller applied to a flexible single-link manipulator robot to compare to a fuzzy supervisory controller in input tracking and end-point vibration suppression. A dynamic model of the flexible manipulator is derived using finite elements method and Lagrange’s equations to determine dynamics behavior. A generalized predictive controller is then developed and introduced in the system closed-loop to minimize end-point residual vibrations. A fuzzy supervisory controller is also synthesized to compare simulation results between the two methods of control in terms of input tracking and disturbance rejection.