Fractional Order, Parallel Transfer Function Models of Thermal Processes in the Microcontroller System Using Caputo and Atangana-Baleanu Operators

The paper proposes new, transfer function models of thermal processes in microcontroller evaluation board. The proposed models are required to describe the temperature of critical elements in the working microcontroller system. Measurements obtained from a thermal camera show unusual temperature behavior of some system components. Results of previous investigations show that the approach using serially concatenated transfer functions are not always fully satisfying. This motivated us to propose new forms of transfer functions to better describe this phenomenon. The proposed models have the form of the parallely connected transfer functions using Atangana-Baleanu (AB) and Caputo (C) operators. Such models have not been proposed yet. The proposed form of model is easier to implement at multicore platforms. This paper presents the numerical identification of their parameters with the use of MSE cost function and experiments. The proposed models are also compared to previously proposed, hybrid transfer function models. Results of comparison show that the selection of a proper one in particular sitiation is not unique. All proposed models can be applied for example as a “thermal digital twin” of a real system, dedicated to predict its overheating.