A control device includes a position command generation part, an oscillation command generation part, and a storage part for storing machining operation conditions and servo control conditions. The oscillation command generation part includes an estimation part which estimates an oscillation amplitude and an oscillation frequency of an oscillation command based on a rotation speed of a workpiece and a position command generated by the position command generation part, and a determination part which determines whether or not the estimated oscillation frequency is an optimum value based on the machining operation conditions and the servo control conditions.