A distributed-parameter-model approach to optimal comfort control in air conditioning systems

This paper discusses the problem of optimizing the thermal comfort level in an air-conditioned room by treating the room as a distributed parameter system rather than a single-zone system with homogeneous thermal properties. A distributed room model is developed to explicitly describe the spatial distribution of room air temperature and velocity. This model is parameterized by the variable control setting of an air conditioner, e.g. temperature and velocity at the air flow outlet as well as the outlet diffuser angle. Given a certain control setting, the thermal comfort level can be expressed as an explicit function of spatial coordinates in a room. The criterion for selecting the control setting of an air conditioner is defined so as to maximize the sum of squares of comfort index values at several discrete spatial points while keeping the power consumption rate minimal. This paper presents the derivations of the distributed parametric model of the room and a recursive numerical algorithm for solving the optimization problem. Some simulation results are provided.