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In this paper, we propose a model-based predictive current control (MBPCC) scheme for four-switch three-phase (FSTP) inverter-fed interior permanent magnet synchronous motor (IPMSM) drive systems based on a three-phase extended back-EMF estimation method. First, we estimate the three-phase extended back-EMFs of IPMSM using the information of the stator currents, the q-axis inductance, and the stator voltages. After that, the future stator currents are predicted for four possible switching states generated by the FSTP inverter. By defining a cost function which is related to current errors, one can select a switching state that minimizes the cost function. Then, the future switching state of the FSTP inverter at the next sampling time can be determined to directly control the drive signals of FSTP. In addition, to improve the performance of the closed-loop system, an adaptive backstepping complementary PI sliding-mode (ABCPISM) position controller is proposed. The stability of the closed loop system is proven by Barbalat's lemma. Simulation results are provided to validate the proposed method.