Optimal heating strategies for a convection oven

In this study classical control theory is applied to a heat conduction mode l with convective boundary conditions. Optimal heating strategies are obtai ned through solution of an associated algebraic Riccati equation for a fini te horizon linear quadratic regulator (LQR). The large dimensional system m odels, obtained after a Galerkin approximation of the original heat-conduct ion equations, describe the dynamics of the nodal temperatures driven by a forced convection boundary condition. The models are reduced using optimal Hankel minimum degree (OHMD) reduction. Optimal control histories are obtai ned for the reduced model and applied to the 'full-scale' model. Performanc e of the regulator for various weighting matrices are compared and evaluate d in two case studies, namely the heating of a cylindrically shaped contain er of mashed potato, and a container of ready-made lasagna. The approach ta ken here is geometry independent and closed loop meaning that the input is driven by temperature through a feedback mechanism which includes an optima l feedback gain matrix, which is calculated 'off-line' through the backward s solution of an associated algebraic Riccati equation. The results indicat e a DeltaT type heating profile, including a final oscillating behaviour th at fine-regulates the temperature to an almost uniform temperature of 100 d egreesC. (C) 2001 Elsevier Science Ltd. All rights reserved.