The goal of increasing efficiency and durability of fuel cells can be achieved through optimal control of their operating conditions. In order to implement such controllers, accurate and computationally efficient fuel cell models must be developed. This work presents a hybrid (physics-based and data-driven), control-oriented model for approximating the output voltage of proton exchange membrane fuel cells (PEMFCs) while operating under dynamical conditions. First, a physics-based model, built from simplified electrochemical, membrane dynamics and mass conservation equations, is developed and validated through experimental data. Second, a data-driven, neural network (echo state network) is trained, fitted and tested with the same dataset. Then, the hybrid model is formed as a parallel structure, where the simplified physics-based model and the trained data-driven model are merged through an algorithm based on Gaussian radial basis functions. The merging algorithm compares the output of both single models and assigns weights for computing the prediction of the hybrid result. The proposed hybrid model structure is successfully trained, validated and tested with an experimental dataset originating from fuel cells within an automotive PEMFC stack. The hybrid model is assessed through the mean square error index, with the result of a low tracking error.


control theory.

Author keywords

PEMFC; hybrid model; ESN; radial basis functions

Scientific reference

J.A. Aguilar, D. Chanal, D. Chamagne, N. Yousfi, M. Péra, A.P. Husar and J. Andrade-Cetto. A hybrid control-oriented PEMFC model based on echo state networks and Gaussian radial basis functions. Energies, 17(2): 508, 2024.