Optimal Heating Strategies for a Convection Oven

In this study classical control theory is applied to a heat conduction model with convective boundary conditions. Optimal heating strategies are obtained through solution of an associated algebraic Riccati equation for a finite horizon linear quadratic regulator (LQR). The large dimensional system models, obtained after a Galerkin approximation of the original heat-conduction 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 obtained for the reduced model and applied to the `full-scale' model. Performance of the regulator for various weighting matrices are compared and evaluated in two case studies, namely the heating of a cylindrically shaped container of mashed potato, and a container of ready-made lasagna. The approach taken here is geometry independent and closed loop meaning that the input is driven by temperature through a feedback mechanism which includes an optimal feedback gain matrix, which is calculated `off-line' through the backwards solution of an associated algebraic Riccati equation. The results indicate a T type heating profile, including a final oscillating behaviour that fine-regulates the temperature to an almost uniform temperature of 100°C.