Mean square error as a criterion for temperature control

Abstract

Existing thermal comfort criteria for temperature fluctuations about neutral are reviewed and compared with the requirements for control system design and building energy management. It is argued that the mean square error about the preferred temperature is both one of the easiest measures of error to compute in control design and relates to both the mean value of the Predicted Percentage Dissatisfied (PPD) and to the probability of occupants taking unprompted action to change their thermal environment. It is argued that the development of criteria suitable for design with optimal control theory also has implications for predicting the energy saving that can be associated with conventional thermal controls. An example is given to show how the mean square error criterion would predict a sinusoidally varying temperature about neutral of amplitude 2°C as equivalent to a sinusoidally varying temperature of amplitude 1°C whose mean was systematically 1.22°C below neutral. It is also shown that this criterion unlike simpler criteria predicts that this depression may not be much easier to realise in practice than a comparable depression under conditions of accurate temperature control.