<p>This paper investigates the unwinding tension control problem in lithium battery foil tensioning machines, which is characterized by strong nonlinearity, time-varying parameters, and multi-constraint conditions. The controlled plant is a roll-to-roll unwinding tension system, where the control input is the unwinding motor torque and the output is the measured foil tension. To address the limitations of conventional PID methods in handling constraints and dynamic variations, a hybrid control framework integrating Model Predictive Control (MPC) and an Extended State Observer (ESO) is proposed.An MPC-based tension controller is developed using a nonlinear dynamic model of the unwinding process, explicitly incorporating key factors such as roll radius variation and actuator constraints. The MPC employs a receding horizon optimization strategy to compute the optimal motor torque, enabling anticipatory adjustment to future tension dynamics. Meanwhile, an ESO is designed to estimate lumped disturbances and model uncertainties in real time, and its output is introduced as a feedforward compensation term to enhance robustness.Both simulation and experimental results demonstrate the effectiveness of the proposed MPC–ESO strategy. In variable tension tracking tests, the settling time is reduced from 1.40 s to 0.12 s, and the integral squared error (ISE) decreases from 3.087 to 0.9373 (a reduction of 70%), with significantly lower overshoot. In disturbance rejection experiments, the proposed method exhibits smaller tension fluctuations and faster recovery compared to PID control, confirming the effectiveness of ESO-based compensation. These results indicate that the proposed approach achieves improved control accuracy, faster dynamic response, and stronger robustness, providing a practical solution for high-precision tension control in roll-to-roll manufacturing systems.</p>