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.
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This content will become publicly available on March 1, 2026
Optimal Control for Thermal Management of a Proton Exchange Membrane Fuel Cell Stack With Koopman-Based Modeling
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.
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- Award ID(s):
- 2135735
- PAR ID:
- 10553737
- Publisher / Repository:
- ASME
- Date Published:
- Journal Name:
- Journal of Dynamic Systems, Measurement, and Control
- Volume:
- 147
- Issue:
- 2
- ISSN:
- 0022-0434
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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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
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This paper presents a data-driven methodology for linear embedding of nonlinear systems. Utilizing structural knowledge of general nonlinear dynamics, the authors exploit the Koopman operator to develop a systematic, data-driven approach for constructing a linear representation in terms of higher order derivatives of the underlying nonlinear dynamics. With the linear representation, the nonlinear system is then controlled with an LQR feedback policy, the gains of which need to be calculated only once. As a result, the approach enables fast control synthesis. We demonstrate the efficacy of the approach with simulations and experimental results on the modeling and control of a tail-actuated robotic fish and show that the proposed policy is comparable to backstepping control. To the best of our knowledge, this is the first experimental validation of Koopman-based LQR control.more » « less
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Abstract Purpose of Review We review recent advances in algorithmic development and validation for modeling and control of soft robots leveraging the Koopman operator theory.
Recent Findings We identify the following trends in recent research efforts in this area. (1) The design of lifting functions used in the data-driven approximation of the Koopman operator is critical for soft robots. (2) Robustness considerations are emphasized. Works are proposed to reduce the effect of uncertainty and noise during the process of modeling and control. (3) The Koopman operator has been embedded into different model-based control structures to drive the soft robots.
Summary Because of their compliance and nonlinearities, modeling and control of soft robots face key challenges. To resolve these challenges, Koopman operator-based approaches have been proposed, in an effort to express the nonlinear system in a linear manner. The Koopman operator enables global linearization to reduce nonlinearities and/or serves as model constraints in model-based control algorithms for soft robots. Various implementations in soft robotic systems are illustrated and summarized in the review.
