Abstract: A velocity detection device includes a rotational direction discriminator calculating an x coordinate or a y coordinate in temporary coordinates on a line between an origin of the coordinates and a point obtained by rotating the actual second coordinates by as much as a rotational angle ? in a direction of a coordinate axis, the rotational direction discriminator discriminating a rotational direction from the actual first coordinates to the actual second coordinates based on either a sign of the x or y coordinate in the temporary coordinates; and a processor calculating calculational second coordinates represented by a multiplication, addition or subtraction between the actual first coordinates and one of the trigonometric function values to make calculational second coordinates closer to the actual second coordinates, and calculating the velocity of the moving body based on the temporary angles corresponding to the trigonometric function value used for the calculational second coordinates.

Abstract: A position control system comprises a position command generator for generating a position command at a prescribed sampling time k for a time k+M which is at least one sampling cycle M ahead of the prescribed sampling time. A controlled object includes a speed control loop, and a control unit for generating a control input value determined by determining a weight coefficient of each of position commands at sampling times K+l (l=1, 2, . . . , M) and a weight coefficient for the position and speed which are outputs of the controlled object in order to minimize the value of an evaluation function so that the position command at the prescribed sampling time k and the position of the controlled object will be equalized, while the position commands produced by the position command generator at the sampling times k+l (l=1, 2, . . . , M), the position and speed of the controlled object, and a control input to be applied to the controlled object are being used as variables.