Modeling and Estimation of the Humans' Effect on the CO<sub>2</sub> Dynamics Inside a Conference Room

Abstract

We develop a data driven, partial differential equation-ordinary differential equation model that describes the response of the carbon dioxide (CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) dynamics inside a conference room, due to the presence of humans, or of a user-controlled exogenous source of CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> . We conduct three controlled experiments to develop and tune a model whose output matches the measured output concentration of CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> inside the room, when known inputs are applied to the model. In the first experiment, a controlled amount of CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> gas is released inside the room from a regulated supply, and in the second and third experiments, a known number of humans produce a certain amount of CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> inside the room. For the estimation of the exogenous inputs, we design an observer, based on our model, using measurements of CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> concentrations at two locations inside the room. We perform several simulation studies for the illustration of our results.