This paper proposes a new model for cogging forces of linear motor systems. Sinusoidal functions of positions are used to capture the largely periodic nature of cogging forces with respect to position effectively 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 non-periodic characteristics of cogging force while having a linear parametrization form which makes effective on-line adaptive compensation of cogging forces possible. A discontinuous projection based desired compensation adaptive robust controller (DCARC) is then constructed for linear motors, which makes full use of the proposed cogging force model for an improved cogging force compensation. Comparative experimental results are obtained on both axes of a linear motor driven Anorad industrial gantry having a linear encoder resolution of 0.5 μm. Experiments are done with each axis running separately to compare the three algorithms: DCARC without cogging force compensation, DCARC with sinusoidal cogging force model compensation, and DCARC with the proposed cogging force model compensation. The results show that DCARC with proposed model compensation achieves the best tracking performance among the three algorithms tested, validating the proposed cogging force model. The excellent tracking performances obtained in experiments also verify the effectiveness of the proposed ARC control algorithms in practical applications.

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