GPU-Based Model Predictive Control of Nonlinear Parabolic Partial Differential Equations System and Its Application in Continuous Casting

Temperature control of steel billets plays an important role in the quality of steel billets. This paper was motivated by the necessity for setting a value of spray cooling water flow with regard to the accuracy, fast applicability to real-time optimization, and capability of non-steady operation scenarios, especially for the change of casting speed. Therefore, this paper is focused on the GPU-based model predictive control (MPC) for temperature control of steel billets. The system dynamics in MPC is a heat transfer model characterized by the nonlinear parabolic partial differential equations (PDEs). This paper presented two algorithms. First, an adaptive trust-region Levenberg–Marquardt method (ATR-LM) based on the measured surface temperature is presented to estimate the unknown parameters in the heat transfer model. The corresponding experimental results indicate that the presented method can reduce the iteration time. Second, for the purpose of satisfying the real-time requirement, the stream parallel sparse Jacobian method (SP-SJ) is presented to solve the dynamic optimization problem associated with the PDEs. The corresponding experimental results show that the presented method exhibits satisfactory computational performance and achieves satisfactory control performance.