Building a model to predict the 3-D distribution of temperature in a ventilated test room

A state-space model has been developed to model the dynamic response of the 3-D temperature distribution in a laboratory test room to variations of the ventilation rate as control input. In the state-space model the wall temperature of the test room is included as an additional state variable. From 10 step-up experiments it was found that the air temperature at the 36 sensor positions in the test room shows a second order response to the step-variations of the ventilation rate. Due to the imperfect mixing of the air in the test room, the second order parameters for the 36 sensor positions were found to be different. The coefficient of determination 'R2' was calculated to evaluate the accuracy of the state-space model. From the 10 step-up experiments the state-space model was found to model the dynamic response of the air temperature at the 36 sensor positions with an average R2 of 0.9822.