A procedure for calculating thermal response factors of multi-layer walls—State space method

Abstract Thermal response factors of building envelopes are fundamental information in the design of thermal systems. The conventional calculating method of these factors is first to calculate the eigenvalues of the system as a function of thermal physical properties and the thickness of materials. The roots finding process is time-consuming and occasionally may lead to micscalculation due to missing one or more roots. in this paper a new approach to calculate these factors based on the state space principle of modern control theory has been proposed. Using this approach through calculation of the state transition matrix of a system, the thermal response factors of a multi-layer wall can be obtained without finding the roots. This method is feasible and easy to use with a sufficient accuracy for engineering applications.