This paper studies the problems of tip position regulation and vibration suppression of flexible manipulators without using the model. Because of the two-timescale characteristics of flexible manipulators, applying the existing model-free control methods may lead to ill-conditioned numerical problems. In this paper, the dynamics of a flexible manipulator is decomposed into two subsystems which are linear and controllable at different timescales by singular perturbation theory and a model-free composite controller is designed to alleviate the ill-conditioned numerical problems. To do this, (...) a model-free composite control strategy is constructed which facilitates in designing the controller in slow and fast timescales. In the slow timescale, the slow subsystem controller is designed by adaptive dynamic programming based on the measurements of the slow inputs and the position, while the vibration in the slow timescale is estimated by the least square method. In the fast timescale, the vibration is reconstructed based on the measurements of vibration and its estimate in the slow timescale, by which the fast controller is designed using ADP. Stability of the closed-loop system is proved by SP theory. Finally, simulations are given to show the feasibility and effectiveness of the proposed methods. (shrink)