A State Space Model for Real-Time Control of the Temperature in Indoor Space - Principle, Calibration and Results

Real-time control of comfort in indoor spaces needs models of temperature distribution and the air velocity field. Complete models, based on CFD, give this information but, because of processing time limitations, cannot be applied to real-time calculations. Therefore, a reduced model is needed. This study proposes to reduce the complexity of a CFD model by first considering a fixed velocity field and solving only the energy balance equation, then putting this equation in the form of state-space and finally by reducing its order by Proper Orthogonal Decomposition (POD). This paper focuses on the correction of the reduced order model which is absolutely necessary before using it for real time application. This algorithm was applied to a room equipped with a fan coil with an air jet having three patterns i.e: following the ceiling and reaching the opposite wall, falling before reaching the opposite wall (two examples), and falling before reaching the ceiling. For the two-dimensional case, the reduced model has been validated by comparison with CFD results for step inputs of temperature and air velocity. As the order of the reduced model is always smaller than 7, the energy balance equation may be solved in real time and integrated into a control algorithm.