An apparatus is disclosed for reducing feed rate variations when unwinding a web material. The apparatus includes a rotational position and speed determining device for determining the rotational position and speed of the parent roll, a drive system for imparting rotational movement to the parent roll, a device for measuring the radius of the parent roll, and a logic device. The logic device generates an ideal speed reference signal and utilizes calculated and measured data to establish a corrected speed reference signal to make adjustments in the driving speed based upon the corrected speed reference signal to maintain a relatively constant feed rate. By dividing the parent roll into 1, 2, . . . n sectors, the data can be refined to a relatively high degree taking into account high speed data processing capabilities as well as operating system response times to make appropriate driving speed adjustments.