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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. 

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. 

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. 

Precious metals represent some of the least abundant elements in the earth’s crust. There is an urgent need to maximize the utilization efficiency of these metals and thereby attain affordable and sustainable products. One approach for achieving this goal is based on the development of hollow nanocrystals with a well-controlled surface structure, together with a wall thickness kept below 2 nm, or roughly 10 layers of atoms. The hollow structure eliminates the waste of interior atoms and creates an inner surface, while the controllable surface structures contribute to the optimization of catalytic activity and selectivity. In this article, we begin with a brief introduction to two methods that have been developed for the synthesis of hollow nanocrystals: the first relying on the galvanic replacement with a sacrificial template, and the second involving layer-by-layer deposition of metal atoms followed by etching. We then showcase some remarkable properties and applications of this novel class of nanostructures, including their use as effective catalysts for energy conversion, photoresponsive carriers for controlled release and drug delivery, and theranostic agents. A discussion of the existing barriers to their commercialization is also presented.