Thermal modeling, analysis and control using an electrical analogy

Modeling and identification of thermal systems is a problem frequently treated in theoretical and application domains. Most of these systems have been modeled using black-box structures whose parameters are identified using temperature measurements. Although black-box models have achieved good results in terms of temperature evolution, they cannot model variables which had not been measured in the identification test. In this article we present a new method to build grey-box thermal models based on electrical equivalent circuits which not only give information about temperatures evolution, but also about heat fluxes and thermal energy stored in the system. The partially unknown parameters of the models are identified using temperature measurements and applying nonlinear optimization techniques. The obtained state space representation can be used to develop a deterministic state space temperature controller that provides better accuracy than classical PID controllers. Our proposal is complemented with various examples of a real application in an electric oven.