[Objective] To effectively suppress the electromagnetic vibration and noise generated during the operation of permanent magnet synchronous motors and enhance their silent performance to meet the application requirements of electric vehicles, precision equipment, etc. A fractional-slot interior permanent magnet synchronous motor with air-gap eccentricity with a rated power of 2 kW is taken as the research object in this paper. And its electromagnetic vibration characteristics and optimization methods are systematically analyzed. [Methods] Firstly, through electromagnetic analytical calculations and two-dimensional transient field finite element analysis, the improvement effects of the eccentric rotor on radial electromagnetic force waves at key orders and resulting vibrations were evaluated from the motor design perspective. Secondly, a field-circuit coupled co-simulation model was established to comparatively analyze electromagnetic vibration characteristics under proportional integral control, maximum torque per ampere control and model predictive current control strategies. Finally, a vibration test platform for the prototype was constructed to obtain the spectral characteristics of the vibration acceleration of the prototype under different control strategies and verify the reliability of the simulation model. [Results] The research results showed that with the eccentric rotor structure, the amplitudes of the radial electromagnetic force waves at key orders such as the 2nd and 4th orders of the motor decreased, weakening the vibration response concentrated near the modal frequency of the 2nd order. Among them, the peak value of the vibration acceleration under the rated load decreased by 47.9%. [Conclusion] Rotor eccentricity design can effectively reduce the risk of structural resonance. Model predictive current control can better suppress the additional vibration caused by current harmonics. This study provides an effective reference for the optimization of electromagnetic vibration and noise of motors.