Abstract: With the growing demand for high-frequency astronomical observations and the increasing aperture of radio telescopes, more stringent requirements are imposed on pointing accuracy. However, backlash-induced nonlinear disturbances degrade the synchronization accuracy and stability of antenna multi-motor servo systems, thereby limiting improvements in dynamic response and pointing precision. To address this issue, we propose a composite control strategy based on a NonLinear Extended State Observer (NLESO) and Model Predictive Control (MPC) to simultaneously compensate backlash-induced nonlinear disturbances and achieve high-precision synchronization control. Cosimulation experiments were conducted for validation. The results show that, compared with conventional Proportional Integral Derivative (PID) control and standalone MPC, the NLESO-MPC strategy reduced the large-gear dead-zone width from 0.1951 s to 0.0113 s and decreased the Root Mean Square (RMS) pinion angular-displacement synchronization error from 0.6884° to 0.3546°, demonstrating the effectiveness and clear advantages of the proposed method in suppressing backlash nonlinear disturbances and improving synchronization performance.