Tape guides of a magnetic tape transport machine are controlled during movement by sensing the position of the member as it moves along a defined path in varying velocity corresponding to the position. The member is initially accelerated at a selected rate to a maximum velocity which is then maintained until a distance close to the end position is reached. Velocity is then reduced at a selected rate until another position closer to the end position is reached. At this position a final velocity is maintained until the end is reached. A determination is made of how closely the second distance from the end coincided with reaching the final velocity. The length of the first distance from the end position is adjusted to reduce the difference between the coincidence of reaching the second distance and the final velocity. Further, the sensed final position of the member is retained as the target final position for the subsequent operation.