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

Abstract

SUMMARYThis 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.

Foraging theory for multizone temperature control

“…The temperature control problem we are addressing is essentially that of a distributed feedback control problem. Recent relevant work in this area includes spatially distributed control [8], [9] modeling and estimation of distributed processes [10], distributed control of thermal processes [11]- [14], spatially interconnected systems [15], and semiconductor processing [16]- [18]. In [9], the authors implement various decentralized and hierarchical control ideas for the actuation allocation problem of an air-jet system.…”

“…Distributed temperature control of thermal processes is addressed in [13], and the authors focus on multivariable distributed control in order to maintain a uniform temperature across a wafer during ramp-up. In [16], [18] the authors present methods where resources are allocated using geometric and adaptive techniques in order to utilize a heat source in designing a model-based control signal. In [19], the authors describe a lithographical system that is heated by 49 independently controlled zones.…”