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This paper proposes a new model for cogging forces of linear motor systems. Sinusoidal functions of positions are used to effectively capture the largely periodic nature of cogging forces with respect to position, while B-spline functions are employed to account for the additional aperiodic part of cogging forces. This model is experimentally demonstrated to be able to capture both the periodic and nonperiodic characteristics of cogging force while having a linear parametrization form, which makes the online adaptive compensation of cogging forces possible and effective. A discontinuous-projection-based desired compensation adaptive robust controller (DCARC) is then constructed, which makes full use of the proposed cogging force model for an improved cogging force compensation. Comparative experimental results with various cogging force compensations are obtained on both axes of a linear-motor-driven industrial gantry. The results show that DCARC with the proposed model compensation achieves the best tracking performance among all the three algorithms tested, validating the proposed cogging force model. The excellent tracking performances obtained in the experiments also verify the effectiveness of the proposed ARC control algorithms in practical applications. The proposed model and control algorithm can be applied for other types of motor control systems as well.