This paper focuses on using a singularly perturbed approach to derive a vibration damping control law in which a pole assignment feedback method is utilized. The composite control system is characterized by two components which can be computed separately. The one is Cartesian-based PI control which drives the end-effector of a flexible manipulator to track the desired time-based trajectory. The other is pole assignment feedback control which damps out vibrations during and at the end of trajectory tracking. An advantage of this composite control method in real implementation is that it does not require a derivative of the end-effector's position, and the derivatives of signals from the strain gauges. From the characteristics and implementation points of view, it appears to be simple to use. Laboratory experiments were conducted to evaluate the performance of the proposed control method.