A state-space model for dynamic response of indoor air temperature and humidity

• A three-zone model is developed to study thermal dynamic behaviors of room air.
• The model is linearized into a state space form depicted by vector-matrix notation.
• Errors of model results compared with experimental data are all less than 12%.
• The model is used to study thermal responses of room air under different disturbances.

The real-time control of indoor thermal conditions needs dynamic models of air temperature and humidity in rooms. The single-zone dynamic model may be inappropriate to depict the spatial variations of the air parameters, and the computational fluid dynamics model (CFD) is too computationally costly for real-time applications. In comparison, the multi-zone model, which models a space by several zones, may be a better choice. This paper presents a three-zone dynamic model to investigate the dynamic behaviors of indoor air temperature and humidity. By the means of linear approximation, the ordinary differential equations describing the dynamic thermal behaviors of indoor air are transformed into a state space form. The state equation is solved analytically, and the calculated results are then compared to a series of dynamic response experiments. It shows that the dynamic model developed in this paper predicts well the dynamic thermal responses of air in different indoor zones. The average errors of the calculated results compared with the experimental data are all less than 12% for the transient response with a time period of 2400 s. This paper also demonstrated the developed room model to simulate the transient responses of the indoor air temperatures and humidity ratios under different perturbations including a step change of supply air temperature, supply air flow rate, indoor occupant number and ambient temperature. The proposed modeling procedure may be especially useful for the development of the dynamic toolbox for the control design of HVAC components.