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Many control methodologies have been applied to the motion control of linear motor drive systems. Compensations of nonlinearities such as frictions and cogging forces have also been carried out to obtain better tracking performance. However, the relationship between the driving current and the resulting motor force has been assumed to be linear, which is invalid for high driving coil currents due to the saturating electromagnetic field effect. This paper focuses on the effective compensation of nonlinear electromagnetic field effect so that the system can be operated at even higher acceleration or heavier load without losing achievable control performance. Specifically, cubic polynomials with unknown weights are used for an effective approximation of the unknown nonlinearity between the electromagnetic force and the driving current. The effectiveness of such an approximation is verified by offline identification experiments. An adaptive robust control (ARC) algorithm with online tuning of the unknown weights and other system parameters is then developed to account for various uncertainties. Theoretically, the proposed ARC algorithm achieves a guaranteed transient and steady-state performance for position tracking, as well as zero steady-state tracking error when subjected to parametric uncertainties only. Comparative experiments of ARC with and without compensation of electromagnetic nonlinearity done on both axes of a linear-motor-driven industrial gantry are shown. The results show that the proposed ARC algorithm achieves better tracking performance than existing ones, validating the effectiveness of the proposed approach in practical applications.