A system for compensating for the effects of friction and other forces reting from repeatable disturbances in a servo system or a numerically controlled machine employs a software-based mathematical model which has certain parameters associated therewith. The parameters are calibrated for the specific characteristics of the system using either off-line or on-line methods, and include dynamic correction for continuous correction, as would be required to compensate for forces which disturb a desired motion. The compensation model is implemented in two stages: (i) building a calibrated mathematical model that describes a repeatable disturbance force, such as friction, and (ii) using the model in real time to compensate for the disturbance force. The model provides a compensation signal which is combined with the original controller signal to yield a compensated control signal. The compensation may be in the form of a position offset. This compensation system is general in its application and can compensate for any deterministic repeatable action that disturbs or acts against the motion of a numerically controlled, or servo, system.