In a CNC Video Measuring System, both very-low-speed motion and high-speed motion are required. Very-low-speed motion is highly influenced by friction. Currently, PID control with look-up-table gains is used to handle with this problem. However, the process of developing this table tends to be a trial-and-error scheme. In the present paper, we investigate a model-based control system design. System identification techniques are used for constructing a model for a control system design and a sliding mode controller with a frequency-shaped hyperplane is designed using that model. Both strong attenuation of disturbances at low frequencies and stability at high frequencies are achieved in a real machine.