Control and room temperature optimization of energy efficient buildings

The building sector consumes a large part of the energy used in the United States and is responsible for nearly 40% of greenhouse gas emissions. It is therefore economically and environmentally important to reduce the building energy consumption to realize massive energy savings. In this paper, a method to control room temperature in buildings is proposed. The approach is based on a distributed parameter model represented by a three dimensional (3D) heat equation in a room with heater/cooler located at ceiling. The latter is resolved using finite element methods, and results in a model for room temperature with thousands of states. The latter is not amenable to control design. A reduced order model of only few states is then derived using Proper Orthogonal Decomposition (POD). A Linear Quadratic Regulator (LQR) is computed based on the reduced model, and applied to the full order model to control room temperature.