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In this paper, a complementary and modular linear flux-switching permanent magnet (MLFSPM) motor is investigated, in which both the magnets and armature windings are placed in the short mover, while the long stator consists of iron core only. The proposed MLFSPM motor incorporates the high power density of a linear permanent magnet synchronous motor and the simple structure of a linear induction motor. It is especially suitable for long stator applications such as urban rail transit. The objective of this paper is to build the mathematical model for the purpose of control of this motor. The simulation results by means of finite-element analysis (FEA) verified the theoretical analysis and the effectiveness of this model. Both the analytical model and the FEA results are validated by experiments based on a prototype motor.