The tracking and synchronization performance of multi-motor systems are critical for industrial safety and reliability. This study proposes a prescribed-time sliding mode control method to achieve high-precision tracking and minimize synchronization errors under dynamic uncertainties. Firstly, a prescribed-time sliding mode controller (PTSMC) is designed to ensure convergence of composite errors to the vicinity of zero within a predefined time interval, while a nonlinear disturbance observer (NDO) is developed to estimate system disturbances and provide feedforward compensation to the controller. Furthermore, a control law switching strategy is introduced to eliminate singularity issues, ensuring that the controller becomes time-independent once system stability is achieved. Comparative simulation and experimental studies demonstrate that the proposed approach effectively achieves consistent coordinated tracking performance in multi-motor systems.