Nonlinear model reduction for simulation and control of temperature distribution in air conditioned rooms

In this paper, we propose a fast simulation method for the dynamic models of temperature distributions in air conditioned rooms. The finite volume method (FVM) is used for the spatial and temporal discretization of the infinite dimensional temperature distributions. The high order of the obtained linear ordinary differential equations (ODE), which equal to the number of cells used for the discretization, is further reduced by proper orthogonal decomposition (POD) method. POD modes are constructed by the method of snapshots in this study. Karhunen-Loeve (Galerkin) projections are used to project the temperature distribution onto the selected POD modes. The resulting finite-dimensional dynamical model in state-space form is suitable for the real-time temperature control. One example is provided to demonstrate the applicability of the proposed technique.