[Objective] The system architecture of single-inverter multiple permanent magnet synchronous motor (PMSM) in parallel operation can significantly reduce hardware costs, minimize system size, and improve power density. It has become a highly cost-effective technical solution. However, traditional control strategies often adopt average models or multiple coordinate system models, which not only increase the complexity of system modeling, but may also lead to reduced control accuracy and degraded dynamic response. To address this issue, this study proposes a control strategy for a single-inverter multi-PMSM parallel system based on a unified coordinate system, aiming to simplify the control structure and enhance system performance. [Methods] First, the electromagnetic and mechanical characteristics of the system were investigated using frequency domain analysis. Building upon this, a vector control strategy based on a unified coordinate system was proposed. By employing a mathematical model in the unified coordinate system, the control complexity of the multi-motor system was reduced. Finally, a time-domain simulation model was established to validate the effectiveness of the proposed strategy. The system operation under different operating conditions was analyzed, and the dynamic response and steady-state accuracy of the control system were comprehensively tested. [Results] The simulation results showed that when the load torques between the two PMSMs differed or underwent dynamic variations, the designed control system was able to rapidly and accurately regulate motor speeds to closely follow the given speed commands. This verified the effectiveness and practicality of the proposed control strategy. [Conclusion] The control strategy for single-inverter multi-PMSM parallel systems based on a unified coordinate system proposed in this study not only simplifies the control structure of traditional multi-motor systems, but also significantly enhances both dynamic performance and steady-state accuracy. It provides new insights for control optimization in single-inverter parallel PMSM systems.