Reduced-order models for control of stratified flows in buildings

Building heating and cooling systems have potential for energy savings by employing passive devices that exploit thermal stratification and buoyancy. The resulting thermal-fluid flow patterns from such systems tend to be sensitive to disturbances, and advanced flow control techniques are important to maintain occupant comfort. In this work, we employ Eigensystems Realization Algorithm (ERA) to obtain low-order models of airflow in buildings, which capture relevant dynamics and are amenable for control design. We present an alternative interpretation that allows one to obtain models using ERA, without resorting to lifting, an approach that is typically used to introduce boundary control and boundary disturbances explicitly in the reduced-order model. Using this reduced-order model we derive an optimal control law in closed form (which is composed of a feedforward and a feedback term) for rejecting a known disturbance, while minimizing a quadratic cost related to occupant discomfort and energy consumption. We demonstrate this approach using closed loop CFD simulations of airflow in a room with a passively cooled radiant ceiling and a displacement vent.