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The tracking performance of a motion system based on a permanent-magnet linear motor (PMLM) is greatly affected by nonlinearities present, such as force ripples and frictions. Although various identification and compensation schemes haven been reported for the PMLM, to the authors' best knowledge, no direct and unified modeling method for force ripples and friction is available till now. This paper proposes a new method to identify various linear and nonlinear parameters in PMLM, using a hysteretic relay feedback. Dual-input describing functions are imported to leverage on the biased limit cycles generated by even nonlinearities due to force ripple. The explicit formulae, derived from the harmonic balance condition, enable direct computation of model parameters with a minimum number of relay experiments. Simulation results and real-time experiments will be presented to verify the practical appeal of proposed method in precision motion control.