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

Abstract

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. INDEX TERMS MPC, PDEs, graphic processing unit (GPU), parallel computation, continuous casting.

A GPU based accelerated solver for simulation of heat transfer during metal casting process

“…GPU-based acceleration has also been applied in various fields for numerical modeling of physical phenomena such as aerodynamics, heat conduction (Wei et al 2014), conjugate heat transfer applications (Afzal et al 2020), atmospheric modeling (Xu et al 2019), supersonic flow (Kloss et al 2010) and so on. In the domain of casting process modeling GPU solvers have been developed for the continuous casting process by Wang et al (2019aWang et al ( , 2019b and Liu et al (2022). A GPU-accelerated 3D phase field-lattice Boltzmann method solver, by Guo et al (2022) has also been used for the prediction of multi-dendritic growth of a Fe-C binary alloy.…”

Self-Optimizing Control Strategy for Distributed Parameter Systems

“…11,12 Additionally, sparse computation is applied to reduce the complexity of online optimization. 13 Nevertheless, model simplification can potentially result in the loss of critical distribution information. 14 It remains a challenge to exploit practical real-time operation optimization methods for DPSs based on high-fidelity models.…”

“…Since MPC requires frequently solving an approximate model for repetitive online optimization, it is computationally intensive and time-consuming. To mitigate this issue, some MPC methods based on low-order models derived by data-driven approaches such as encoder-decoder or neural networks are developed, demanding less optimizing cost. , Additionally, sparse computation is applied to reduce the complexity of online optimization . Nevertheless, model simplification can potentially result in the loss of critical distribution information .…”

Exponential Stability Analysis of Stochastic Semi-Linear Systems With Lèvy Noise

“…Mainly, semi-linear reaction-diffusion PDEs are commonly used to model a variety of real-world phenomenon such as population dynamics and chemical reactions etc., [31], [40]. Many researchers have focused their attention on reactiondiffusion equations due to their wide range of applications, see [1], [11], [12], [17], [25], [33]. Random noise in dynamical systems is caused by external disruptions, measurement errors, and a lack of knowledge of specific parameters.…”