Abstract
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.
