Vibration or oscillation is an important problem when controlling the system in many areas where motion controls are required in the industry. This becomes even more important in controls that require high precision. Therefore, it is necessary to develop control methods that can perform both position and vibration suppression control at the same time. According to open literature, it is seen that there is not enough work on the position and vibration suppression control of the table of ball screw drive systems, which are widely preferred in motion controls. It is aimed to contribute to this subject, which has an unlimited application area for precision machine controls, with both theoretical and practical work. In the study, vibration suppression control of a flexible Euler-Bernoulli beam rigidly clamped to the table of a ball screw drive system driven by a direct current servomotor is performed. With the control signal generated by PID and model free sliding mode control, the position of the table and the vibration suppression control of the flexible beam are carried out simultaneously. Controller gains are adjusted with the optimization approach in order to create a control signal that can satisfactorily provide both the position control of the table and the vibration control of the bar. In order to obtain better results, the necessity of using advanced control techniques such as sliding mode control is presented and suggestions are made for future studies.