Reduced-Order Modeling of a Radiative Heating Process with Movable Radiators

Abstract

A reduced-order model for a heating process with dominant radiation and movable radiators is derived. The process is described by a nonlinear integro-partial differential equation with full domain coupling for the thermal part and ordinary differential equations for the mechanical part, which contains a moving radiator. The model reduction is performed with a tailored Proper Orthogonal Decomposition (POD)-Galerkin approach. In contrast to the existing works in the literature, a new computationally efficient approach is proposed to account for the nonlinear full domain coupling term due to radiation. The reduced-order model shall be used in a model predictive control in the future. Therefore, special attention is paid to the choice of the actuation function used to construct the snapshot data set. Here, a stationary distributed feedforward controller is designed and approximated using a multi-scale approach by splitting the mechanical and thermal parts. Simulative results illustrate the accuracy and computational efficiency of the proposed reduced-order model.