Distributed parameter thermal system control and observation by Green-Galerkin methods

This article addresses the problem of distributed parameter control and observation in thermal processing of materials. A novel numerical technique is developed for infinite-dimensional thermal conduction systems, based on Galerkin optimization of an energy index employing Green’s functions. Various simulations are conducted to prove that despite the complexities that arise from the distributed parameter nature of the system, the proposed method successfully observes the temperature field that exists inside a solid body by employing strictly surface temperature measurements. Moreover, the existence of a duality principle between distributed parameter thermal control and thermal observation is also investigated