Document Type : Research Articles
Authors
Department of Mathematics, Payame Noor University (PNU), Tehran, Iran
Abstract
This paper introduces a new application of variable gain sliding mode control (VGST) to the air supply system of a proton exchange membrane fuel cell (PEMFC), which is crucial for its performance and longevity. The air supply system comprises a centrifugal compressor, a DC-DC converter, and a fuel cell stack, forming a complex and nonlinear system with multiple inputs and outputs. The VGST method adjusts the control gain based on the system state and the sliding level and employs a cascade structure to regulate the excess oxygen ratio and the compressor airflow. The main goals of VGST are to control the PEMFC output voltage and power under various load conditions and uncertainties and to optimize the excess oxygen ratio (λ_(O_2 )) to avoid oxygen depletion and membrane damage. The stability and robustness of the proposed controller are verified by Lyapunov theory and its performance is superior compared to other controllers such as variable gain closed-loop control and constant gain sliding mode control (single loop and cascade). The controller is validated by simulation and experimental data and demonstrates that it can enhance the efficiency and reliability of the PEMFC system. The variable gain controller of the cascade structure was also tested under noisy and uncertain conditions to further confirm its desired performance and showed that it could cope well with adverse situations and achieve the control objectives.
Keywords
- PEM fuel cell
- Oxygen excess ratio
- Variable gain super-twisting algorithm
- Lyapunov stability analysis
- Cascade structure
Main Subjects
[1] J. Kuang, J. Lv, W. Hao, X. Lin, D. Zhao, I. Matraji, et al., "Oxygen excess ratio control of PEM fuel cell systems with prescribed regulation time," ISA transactions, vol. 142, pp. 683-692, 2023.
[2] R. Y. Dahham, H. Wei, and J. Pan, "Improving thermal efficiency of internal combustion engines: recent progress and remaining challenges," Energies, vol. 15, p. 6222, 2022.
[3] D. Wu, C. Peng, C. Yin, and H. Tang, "Review of system integration and control of proton exchange membrane fuel cells," Electrochemical Energy Reviews, vol. 3, pp. 466-505, 2020.
[4] Q. Li, W. Yang, L. Yin, and W. Chen, "Real-time implementation of maximum net power strategy based on sliding mode variable structure control for protonexchange membrane fuel cell system," IEEE Transactions on Transportation Electrification, vol. 6, pp. 288-297, 2020.
[5] C. R. d. Aguiar, K. M. d. Aguiar, R. F. Bastos, W. C. Leal, M. O. Godinho, G. H. Fuzato, et al., "Energy management and operation control of fuel cells in grid-tied operation," Journal of Control, Automation and Electrical Systems, pp. 1-12, 2021.
[6] Y. Nagao, "Proton‐Conducting Polymers: Key to Next‐Generation Fuel Cells, Electrolyzers, Batteries, Actuators, and Sensors," ChemElectroChem, p. e202300846, 2024.
[7] A. Tang, L. Yang, T. Zeng, and Q. Yu, "Cascade Control Method of Sliding Mode and PID for PEMFC Air Supply System," Energies, vol. 16, p. 228, 2022.
[8] Y. Mousavi, G. Bevan, I. B. Kucukdemiral, and A. Fekih, "Sliding mode control of wind energy conversion systems: Trends and applications," Renewable and Sustainable Energy Reviews, vol. 167, p. 112734, 2022.
[9] K. R. Palepogu and S. Mahapatra, "Design of sliding mode control with state varying gains for a Benchmark Twin Rotor MIMO System in Horizontal Motion," European Journal of Control, vol. 75, p. 100909, 2024.
[10] M. Ebrahimipour and S. M. Mirhosseini-Alizamini, "Optimal Adaptive Sliding Mode Control for a Class of Nonlinear Affine Systems," Control and Optimization in Applied Mathematics, vol. 9, pp. 123-138, 2024.
[11] M. Ghamgosar, S. M. Mirhosseini-Alizamini, and M. Dadkhah, "Design of optimal sliding mode control based on linear matrix inequality for fractional time-varying delay systems," International Journal of Industrial Electronics Control and Optimization, vol. 5, pp. 317-325, 2022.
[12] M. Gholami, S. Mirhosseini-Alizamini, and A. Heidari, "Designing a sliding mode controller for a class of multicontroller COVID-19 disease model," Iranian Journal of Numerical Analysis and Optimization, vol. 15, pp. 27-53, 2025.
[13] G. Khaledi, S. M. Mirhosseini-Alizamini, and S. Khaleghizadeh, "Sliding mode control design for a class of uncertain time-delay conic nonlinear systems," Iranian Journal of Science and Technology, Transactions A: Science, vol. 46, pp. 583-593, 2022.
[14] A. Rezaie, "Sliding Mode Control for Chaotic Systems with Unknown Uncertainties," International Journal of Industrial Electronics Control and Optimization, vol. 7, pp. 53-60, 2024.
[15] F. Roshanravan and A. Heydari, "Sliding Mode Control Design for a Class of Nonlinear Fractional Systems with Application to Glucose-Insulin Systems," International Journal of Industrial Electronics Control and Optimization, vol. 5, pp. 337-347, 2022.
[16] G. R. Shahabadi and M. R. Naseh, "Novel Sliding Mode Control Approach for Quasi-Z-Source Converters with Improved Performance," International Journal of Industrial Electronics Control and Optimization, vol. 7, pp. 213-224, 2024.
[17] T. Gonzalez, J. Moreno, and L. Fridman, "Variable gain super-twisting sliding mode control," Automatic Control, IEEE Transactions on, vol. 57, pp. 2100-2105, 2012.
[18] F. Chen, J. Jiao, Z. Hou, W. Cheng, J. Cai, Z. Xia, et al., "Robust polymer electrolyte membrane fuel cell temperature tracking control based on cascade internal model control," Journal of Power Sources, vol. 479, p. 229008, 2020.
[19] S. Kart, F. Demir, İ. Kocaarslan, and N. Genc, "Increasing PEM fuel cell performance via fuzzy-logic controlled cascaded DC-DC boost converter," International Journal of Hydrogen Energy, vol. 54, pp. 84-95, 2024.
[20] Y. Du, Y. Zhang, J. Lou, J. Wang, and P. Zhao, "Conception and thermo-economic performance investigation of a novel solid oxide fuel cell/gas turbine/Kalina cycle cascade system using ammoniawater as fuel," Applied Thermal Engineering, vol. 239, p. 122118, 2024.
[21] H. Luo, J. Xiao, P. Bénard, C. Yuan, L. Tong, R. Chahine, et al., "Thermodynamic modeling and analysis of cascade hydrogen refuelling with three-stage pressure and temperature for heavy-duty fuel cell vehicles," International Journal of Hydrogen Energy, vol. 63, pp. 103-113, 2024.
[22] N. Mirrashid, S. M. Rakhtala, and M. Ghanbari, "Robust control design for air breathing proton exchange membrane fuel cell system via variable gain second‐order sliding mode," Energy Science & Engineering, vol. 6, pp. 126-143, 2018.
[23] N. Mirrashid, E. Alibeiki, and S. M. Rakhtala, "Nonlinear robust controller design for an upper limb rehabilitation robot via variable gain super twisting sliding mode," International Journal of Dynamics and Control, vol. 10, pp. 1996 2010, 2022.
[24] G. P. Incremona, M. Rubagotti, M. Tanelli, and A. Ferrara, "A general framework for switched and variable gain higher order sliding mode control," IEEE Transactions on Automatic Control, vol. 66, pp. 1718-1724, 2020.
[25] R. Ma, Y. Han, and W. Pan, "Variable-gain super-twisting sliding mode damping control of series-compensated DFIG-based wind power system for SSCI mitigation,"Energies, vol. 14, p. 382, 2021.
[26] J. J. Moré, P. F. Puleston, E. Fossas, and C. Kunusch, "Decoupled inputs sliding mode controllers for a fuel cellsupercapacitor module in hybrid generation applications," International Journal of Energy and Environmental Engineering, vol. 10, pp. 257-269, 2019.
[27] S. M. Rakhtala, A. R. Noei, R. Ghaderi, and E. Usai, "Design of finite-time high-order sliding mode state observer: A practical insight to PEM fuel cell system," Journal of Process Control, vol. 24, pp. 203-224, 2014.
[28] S. M. RakhtAla and R. Eini, "Nonlinear modeling of a PEM fuel cell system; a practical study with experimental validation," arXiv preprint arXiv:2501.08420, 2025.
[29] X. Tang, M. Yang, L. Shi, Z. Hou, S. Xu, and C. Sun, "Adaptive state-of-health temperature sensitivity characteristics for durability improvement of PEM fuel cells," Chemical Engineering Journal, vol. 491, p. 151951, 2024.
[30] T. L. Oladosu, J. Pasupuleti, T. S. Kiong, S. P. J. Koh, and T. Yusaf, "Energy management strategies, control systems, and artificial intelligence-based algorithms development for hydrogen fuel cell-powered vehicles: A review," International Journal of Hydrogen Energy, vol. 61, pp. 1380-1404, 2024.
[31] H. Obeid, S. Laghrouche, L. Fridman, Y. Chitour, and M. Harmouche, "Barrier function-based adaptive supertwisting controller," IEEE Transactions on Automatic Control, vol. 65, pp. 4928-4933, 2020.
[32] A. Levant, "Robust exact filtering differentiators," European Journal of Control, pp. 6-29, 2019.
[33] Y. Wang, H. Li, H. Feng, K. Han, S. He, and M. Gao, "Simulation study on the PEMFC oxygen starvation based
)