This study addresses key challenges in high-precision industrial motion control, including dynamic load disturbances, nonlinear parameter coupling, and degradation in synchronization accuracy. A dual-motor cross-coupled synchronous control strategy is proposed, integrating Hertzian contact theory with an adaptive fuzzy PI control algorithm. First, a precise pressure measurement model for the printing contact zone is established based on Hertzian contact theory. The model quantitatively characterizes the relationship between structural parameters and pressure distribution. Key parameters include cylinder radius and plate thickness. This provides a theoretical foundation for precise regulation. Subsequently, a fuzzy PI controller with parameter self-tuning capability is incorporated into the motor speed loop, enabling real-time adjustment of control parameters to effectively compensate for system nonlinearities and time-varying disturbances. Furthermore, a cross-coupled synchronization architecture is designed to enable bidirectional compensation between the two motors, significantly improving synchronization accuracy under complex operating conditions. Simulations were performed in MATLAB/Simulink. The tests covered typical operational scenarios, including load start-up, single-motor disturbance, and multi-disturbance conditions. The results demonstrate that the proposed system achieves high performance: dual-motor speed synchronization accuracy reaches 99.5%; the response time for disturbance compensation is within 0.3 s; and printing-pressure fluctuation is confined to ±0.8%. This performance represents a 62.5% improvement in stability over conventional single-motor control systems. This research not only resolves the long-standing issue of pressure non-uniformity in flexographic printing but also provides a generalizable framework for multi-motor synchronous control in precision manufacturing. The findings offer substantial academic insight and practical value for advancing intelligent industrial measurement and control technologies.