Containers are widely used as transportation tools in modern industry. During the container assembly process, hydraulic operating mechanisms are essential for correcting deviations between the corrugated sheet and the base frame. To address this, the paper proposes a Model Predictive Control (MPC) combined with an Extended State Observer (ESO), aiming to realize automated and flexible positioning assembly. A nonlinear continuous-time model of a valve-controlled asymmetric hydraulic cylinder is firstly established based on fluid dynamics principles, then linearized and discretized near the nominal operating point to obtain a predictive model suitable for MPC. To compensate for unmodeled dynamics, external stochastic friction, and nonlinearities, the ESO is designed to estimate them in real time. These estimates are incorporated into both the state prediction and the optimization processes of the MPC. Furthermore, to enhance the controller’s performance, key parameters such as the prediction horizon and weight matrix are optimized using the Non-dominated Sorting Genetic Algorithm II (NSGA-II), achieving a trade-off between rapid response and minimal steady-state error. Finally, simulation and physical tests verify that the ESO-MPC improves response speed, anti-disturbance ability, and robustness to load variations, which can provide a promising control framework for intelligent container assembly systems.