Nonlinear model predictive control of a radiative heating process with movable radiators

A nonlinear model predictive control concept for a heating process with dominant radiation and movable radiators is derived. Such processes can be described by a nonlinear integro-partial differential equation with full domain coupling for the thermal subsystem and an ordinary differential equation for the mechanical subsystem. For model-based control, a reduced-order model based on a tailored proper orthogonal decomposition Galerkin approach is used. To enable real-time capability, a rigorous formulation of the optimization problem is presented, which allows to split the optimization problem into two subproblems using a separation of time scales. These subproblems are subsequently simplified by employing averaging methods and appropriate analytical solutions. An extensive simulation study illustrates the high performance and fast calculation times of the proposed control concept.