A method for reducing the effects of variations in an unwinding, convolutely wound roll of web material is disclosed. The method utilizes the steps of: a. selecting a reference objective relating to a downstream operation, b. choosing at least one feedback device correlated to the reference objective, c. collecting process data from the at least one feedback device at different positions within a time-varying operation cycle for at least one operation cycle at a learning speed, d. calculating an error as the difference between the collected process data from step (c) and a reference signal related to the selected reference objective, e. generating a correction signal based upon the calculated error from step (d) and, f. applying the correction signal to the actuator during a succeeding time-varying operation cycle.