A digital control system, and in particular a tape drive system having a track-following servomechanism with a predictor (also referred to herein as a predictor filter), is described. In certain embodiments, the servomechanism includes an actuator, a servo channel, and a predictor coupled to the servo channel. The predictor receives from the servo channel a lateral position estimate signal and determines a modified lateral position estimate signal that reduces a difference, introduced by a tape velocity-dependent delay, e.g., introduced by the servo channel, between the modified lateral position estimate signal and an actual lateral position. The modified lateral position estimate may be used to modify a control signal sent to the actuator.