A control apparatus for a machine tool, wherein the machine tool includes: a cutting tool configured to cut a workpiece; rotating means configured to rotate the cutting tool and the workpiece relative to each other; feeding means (150, 160) configured to feed the cutting tool and the workpiece in a predetermined feeding direction; and repetitive movement means configured to repetitively move the cutting tool and the workpiece in a mutually relative manner in repeated cycles of relative movement of the cutting tool and the workpiece in the predetermined feeding direction, each of the repeated cycles consisting of a relative movement of the cutting tool and the workpiece at a first speed and a relative movement of the cutting tool and the workpiece at a second speed being zero or slower than the first speed in the same direction as the relative movement at the first speed in the feeding direction; the control apparatus comprising control means configured to allow the machine tool to machine the workpiece by the relative rotation between the cutting tool and the workpiece and by the feed movement of the cutting tool toward the workpiece with the repeated cycles of relative movement, wherein the feeding means (150, 160) is configured to feed the cutting tool and the workpiece while vibrating them by the feeding of relatively moving the cutting tool and the workpiece at the first speed and relatively moving the cutting tool and the workpiece at the second speed, and wherein the control means is configured to execute an operating instruction to move the cutting tool or the workpiece at the first speed for a predetermined amount of movement and then move it at the second speed for a predetermined amount of movement by controlling the feeding means (150, 160), and set the number of rotations of the relative rotation for executing machining of the workpiece and the number of repetitions of the repetitive movement during one rotation of the relative rotation in a relation where the number of rotations and the number of repetitions are inversely related to each other with a constant being a repetitive movement frequency at which the repetitive relative movement can be performed and which is based on a cycle during which the operation instruction by which the feeding means (150, 160) is controlled to be driven can be issued. a cutting tool configured to cut a workpiece; rotating means configured to rotate the cutting tool and the workpiece relative to each other; feeding means (150, 160) configured to feed the cutting tool and the workpiece in a predetermined feeding direction; and repetitive movement means configured to repetitively move the cutting tool and the workpiece in a mutually relative manner in repeated cycles of relative movement of the cutting tool and the workpiece in the predetermined feeding direction, each of the repeated cycles consisting of a relative movement of the cutting tool and the workpiece at a first speed and a relative movement of the cutting tool and the workpiece at a second speed being zero or slower than the first speed in the same direction as the relative movement at the first speed in the feeding direction; the control apparatus comprising control means configured to allow the machine tool to machine the workpiece by the relative rotation between the cutting tool and the workpiece and by the feed movement of the cutting tool toward the workpiece with the repeated cycles of relative movement, wherein the feeding means (150, 160) is configured to feed the cutting tool and the workpiece while vibrating them by the feeding of relatively moving the cutting tool and the workpiece at the first speed and relatively moving the cutting tool and the workpiece at the second speed, and wherein the control means is configured to execute an operating instruction to move the cutting tool or the workpiece at the first speed for a predetermined amount of movement and then move it at the second speed for a predetermined amount of movement by controlling the feeding means (150, 160), and set the number of rotations of the relative rotation for executing machining of the workpiece and the number of repetitions of the repetitive movement during one rotation of the relative rotation in a relation where the number of rotations and the number of repetitions are inversely related to each other with a constant being a repetitive movement frequency at which the repetitive relative movement can be performed and which is based on a cycle during which the operation instruction by which the feeding means (150, 160) is controlled to be driven can be issued.