Efficient QP Solution in Nonlinear MPC for an Industrial Heating Process Described by a 2-D Partial Differential Equation

This paper presents an efficient approach for solving Optimal Control Problems of an industrial heating process for furniture production, called edge banding. The proposed algorithm solves the Quadratic Program that arises within a Sequential Quadratic Programming framework, where a Gauss-Newton approximation of the Hessian matrix is applied. The core of this approach is a tailored condensing method designed to exploit the unique structure of the system model, which results from discretizing the governing Partial Differential Equation using Lagrangian coordinates. We present an efficient implementation of the algorithm and provide numerical results, showing a substantial computational speedup by more than two orders of magnitude compared to an ad-hoc implementation using a state-of-the-art QP solver.