The three-motor winding system is a strongly coupled nonlinear time-varying system with time-varying parameters such as spool radius, rotational inertia, and friction coefficient, which lead to low accuracy of tension cooperative control. To improve the accuracy of the winding system model and enhance the dynamic performance of the tension cooperative control system in real-time, we propose a multi-kernel least squares support vector regression prediction model based on an improved Whale Algorithm optimization and a model-predictive tension cooperative control system utilizing crisscross optimization. According to the principle of least squares support vector machine regression, a multi-kernel LSSVR regression model is established, and the improved adaptive whale algorithm is used for offline optimization to obtain the system prediction model. Employing the established prediction model, we construct an adaptive model-predictive controller. The vertical and horizontal cross-optimization algorithm is incorporated to attain the optimal solution, effectively mitigating the risk of the solution getting trapped in local optima and thereby enhancing the dynamic performance of the tension control system. Through extensive simulation and experimental analyses, it is demonstrated that the tension cooperative control system designed in this paper exhibits superior dynamic performance and robustness.