Nonlinear disturbances, such as friction, backlash, and base vibration, are the main factors restricting the further improvement of the dynamic performance of the Acquisition, Tracking and Pointing (ATP) system. However, the modeling and compensation of the time-varying nonlinearities are still challenging. In this paper, a compound control algorithm based on model predictive control (MPC) and a Proportional Multiple-Integral State-Augmented Kalman Filter (PMISAKF) disturbance observer is proposed to improve the disturbance rejection performance. Specifically, a PMISAKF is used to estimate the system’s state and external disturbances in real-time. These observed disturbances are then treated as known external inputs at the current or future time points and incorporated into the predictive model of MPC. This allows the optimization process to take these external factors into consideration, enabling the calculation of an optimal control strategy and achieving high pointing and tracking accuracy for nonlinear time-varying disturbances. Experimental results show that the proposed method can effectively improve the system’s anti-interference ability and tracking accuracy.