In a controller for a converting line: (a) mechanical characterization module generates an estimate of an applied web force at a driven roller based upon velocity and torque signals, and mechanical properties associated with an upstream and downstream roller, one or both of which may be the driven roller; (b) a web stiffness estimator module generates a span stiffness estimate, a previous span tension estimate, and a span time constant based upon the span length, the velocity signals from the upstream and downstream roller sensors, a span tension signal from the span tension sensor, and the applied web force estimate from the mechanical characterization module; and (c) a tension control module generates a velocity trim command signal for the driven roller based on the span stiffness estimate, the previous span tension estimate, a web span time constant, a span tension signal, and a span tension setpoint.