Model predictive control of a dynamic nonlinear PDE system with application to continuous casting

Setting the value of the water flow rate in the secondary cooling zone of continuous casting systems plays a crucial role in the slab quality. The standard method to achieve it is unsuitable when the casting speed changes. Therefore, this paper focuses on model predictive control (MPC) for the continuous casting process, based on a heat transfer model described by a dynamic nonlinear partial differential equation (PDE). Realising this MPC is difficult, because some parameters in the nonlinear PDE are unknown. Hence the MPC scheme is designed in the following two steps. First, we introduce a new iterative algorithm to identify the unknown parameters with the help of measured data. Both synthetic and real data are used to illustrate the validity of this method. The experimental results show that this new algorithm reduces the number of iterations and running time as compared to the methods of Landweber and Cao. Second, the dynamic optimisation problem of the MPC strategy is described according to metallurgical principles. To obtain a more stable temperature, an adaptive step size quasi-Newton method is presented to solve this dynamic optimisation problem. The reliability and accuracy of our MPC approach is confirmed by simulation and real steel data.