A numerical controller has a first axis (reference axis) and a second axis (superimposed axis), and performs superimposed control which superimposes a movement amount of the reference axis on a movement amount of the superimposed axis, and thereby controls the movement of the superimposed axis. The numerical controller controls an acceleration start time of the axis to be accelerated, in a superimposition interval in which the reference axis is accelerated and the superimposed axis is decelerated (or reference axis is decelerated and superimposed axis is accelerated). After the axis to be decelerated is sufficiently decelerated, the axis to be accelerated is accelerated, and a moving speed of the superimposed axis does not exceed a speed limit of a machine in an acceleration/deceleration interval.

A numerical control apparatus includes: a curvature radius calculating portion which calculates a first radius r.sub.a which is a radius of a passage arc C passing through three points of a start point P.sub.s, an object point P.sub.t, and an end point P.sub.e as a curvature radius R at the object point P.sub.t; a point sequence evaluating portion which calculates a chord error E to the passage arc C and compares the calculated chord error E and a previously defined permissible error; and a curvature radius correcting portion which calculates a second radius which is a radius of an arc in which a chord error with a front line segment and a rear line segment is the permissible error or less when the calculated chord error E exceeds the permissible error and corrects a curvature radius at the object point P.sub.t to the second radius.

A position control apparatus includes an inversion detector which detects an inversion of a position command and generates an inversion detection signal, a deflection characteristic storage unit which stores a deflection characteristic representing an amount of deflection with respect to a torque command, and an inversion correction calculator which calculates an inversion correction amount. The inversion correction calculator stores a torque command immediately before the inversion, and calculates the inversion correction amount from a difference between an amount of deflection immediately before inversion in which the stored torque command is checked with the deflection characteristic, and an amount of deflection after the inversion in which a value obtained by inverting a sign of the stored torque command is checked with the deflection characteristic. A value obtained by adding the inversion correction amount to the position command value is used for position error calculation.

A numerical control apparatus includes: a curvature radius calculating portion which calculates a first radius r.sub.a which is a radius of a passage arc C passing through three points of a start point P.sub.s, an object point P.sub.t, and an end point P.sub.e as a curvature radius R at the object point P.sub.t; a point sequence evaluating portion which calculates a chord error E to the passage arc C and compares the calculated chord error E and a previously defined permissible error; and a curvature radius correcting portion which calculates a second radius which is a radius of an arc in which a chord error with a front line segment and a rear line segment is the permissible error or less when the calculated chord error E exceeds the permissible error and corrects a curvature radius at the object point P.sub.t to the second radius.

A position control apparatus includes an inversion detector which detects an inversion of a position command and generates an inversion detection signal, a deflection characteristic storage unit which stores a deflection characteristic representing an amount of deflection with respect to a torque command, and an inversion correction calculator which calculates an inversion correction amount. The inversion correction calculator stores a torque command immediately before the inversion, and calculates the inversion correction amount from a difference between an amount of deflection immediately before inversion in which the stored torque command is checked with the deflection characteristic, and an amount of deflection after the inversion in which a value obtained by inverting a sign of the stored torque command is checked with the deflection characteristic. A value obtained by adding the inversion correction amount to the position command value is used for position error calculation.