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This study presents two improved designs of eccentric-shaped permanent magnets and teeth-shaped stators in radial-flux dual three-phase permanent magnet electric machines to reduce cogging torque and torque ripple. The finite element analysis (ANSYS Electromagnetics) has been adopted in simulation, and real radial-flux dual three-phase permanent magnet electric machines have been fabricated in experiment to verify the study. Using the radial-flux dual three-phase permanent magnet electric machines in electric machine systems can improve the reliability and obtain higher output torque. In electrical drives and control, a simplified model-free predictive current control method has been proposed and implemented to drive the radial-flux dual three-phase permanent magnet electric machines, and the control law has been achieved by a TMS320F28377S microcontroller of Texas Instruments. The simplified model-free predictive current control method is senseless to parameter variations and back electromotive force of the permanent magnet electric machines, and only needs current sensors to detect six-phase current. The optimal one has been chosen by 14 various switching modes, which has the minimum cost function, and then the converter can be directly driven and controlled in the next sampling period. The features of the simplified model-free predictive current control method can reduce the algorithm calculation and avoid the defect of conventional model-based predictive current control scheme. A proportional-integral speed controller has also been designed to achieve the speed response of the fixed-speed tracking effect. Finally, the feasibility and effectiveness of the proposed simplified model-free predictive current control method for the dual three-phase permanent magnet electric machines can be verified in the experimental and quantitative results.