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This study presents a novel approach to optimal control utilizing a Koopman operator integrated with a linear quadratic regulator (LQR) to enhance the thermal management and power output efficiency of an open-cathode proton exchange membrane fuel cell (PEMFC) stack. First, a linear time-invariant dynamic model was derived through Koopman operator to forecast the behavior of the PEMFC stack. Second, this Koopman-based model was directly integrated with LQR for optimizing temperature, temperature variations, and output power efficiency of the PEMFC stack by regulating fan speed, with a physics-based model serving as the plant model. Finally, the performance of the Koopman-based LQRs (KLQR) was compared to a baseline proportional-integral (PI) controller across various ambient temperatures and operating conditions, focusing on temperature, temperature variations, and net power output. The results demonstrate the proposed Koopman-based approach can be seamless integration with linear optimal control algorithms, effectively minimizing temperature, temperature variations across the PEMFC stack, and the net power outputs under different ambient temperature and operating conditions.more » « lessFree, publicly-accessible full text available March 1, 2026
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Proton exchange membrane (PEM) fuel cells have emerged as a viable alternative energy production source for stationary and transportation applications. Reliable and sustainable fuel cell operation requires effective water management. Membrane water content can vary along the stack during transients which can lead to losses in fuel cell performance. To control these variations, a model that predicts the internal humidity dynamics of the stack is needed. In this study, a control-oriented model for predicting membrane water content variation was developed and implemented in MATLAB/Simulink. A lumped parameter model was initially developed and then further discretized into smaller control volumes to track humidity distribution along the stack. To validate the model’s predictions, the predicted results were compared to computer simulation results from GT-Suite. The root mean square error (RMSE) between the model’s prediction and GT-Suite’s simulation results was found to be within 1.5 membrane water content for all cases, demonstrating the model’s capability to capture the variation in membrane water content along the stack. The developed model will be useful for real-time control of membrane water content distribution in PEM fuel cells.more » « lessFree, publicly-accessible full text available February 1, 2025
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In this study, a novel application of the Koopman operator for control-oriented modeling of proton exchange membrane fuel cell (PEMFC)stacks is proposed. The primary contributions of this paper are: (1) the design of Koopman-based models for a fuel cell stack, incorporating K-fold cross-validation, varying lifted dimensions, radial basis functions (RBFs), and prediction horizons; and (2) comparison of the performance of Koopman based approach with a more traditional physics-based model. The results demonstrate the high accuracy of the Koopman-based model in predicting fuel cell stack behavior, with an error of less than 3%. The proposed approach offers several advantages, including enhanced computational efficiency, reduced computational burden, and improved interpretability. This study demonstrates the suitability of the Koopman operator for the modeling and control of PEMFCs and provides valuable insights into a novel control-oriented modeling approach that enables accurate and efficient predictions for fuel cell stacks.more » « less
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open-cathode proton exchange membrane ; data-driven modeling ; Koopman operator ; physics-based modeling ; control-oriented modeling (Ed.)Accurate modeling is crucial for the effective design and control of fuel cell stacks. Although physics-based models are widely used, data-driven methods such as the Koopman operator have not been fully explored for fuel cell modeling. In this paper, a Koopman-based approach is utilized to model the thermal dynamics of a 5 kW open cathode proton exchange membrane fuel cell stack. A physics-based model is used as the baseline for comparison. By varying the cooling fan rotational speed, the dynamics of the fuel cell stack were measured from the low load of near 0 kW to about 5 kW. Compared to experimental results, the steady-state absolute errors of Koopman-based models are within 3%. Additionally, once given sufficient dimension, the development effort required for the Koopman-based model is relatively low compared to the traditional physics-based approach, while still achieving a high level of accuracy. These findings suggest the Koopman operator may be a suitable alternative approach for fuel cell stack modeling that enables the development of more accurate and efficient modeling methods for fuel cell systems and facilitates the implementation of the linear optimal algorithms.more » « less