Abstract
In this paper, a new nature-inspired Artificial Ecosystem Optimization (AEO) methodology is presented for reducing the complexity of nonlinear PEMFC SR-12 500 W system. From the point view of this system, the hydrogen and oxygen pressures \(P_{H2} = 60\,{\text{atm}}\), \(P_{O2} = 30 \,{\text{atm}}\) as two inputs, the cell voltage and current as two outputs.By implementation of identification technique, the state space model of PEMFC stack is generated using nlarx modelling procedures where the obtained model is reduced their order by AEO method. The AEO mimics the energy flow behaviour between living organisms in a natural ecosystem, including production, consumption, and decomposition.This algorithm minimize the synergy (\({\text{H}}_{2} ,{\text{H}}_{\infty }\)) norm of error between full PEMFC model and reduced order model. The obtained results are compared with the other optimization algorithms such as MRFO,SSA,ALO and GWO, and they are confirmed that the approximate model obtained by proposed algorithm has faster convergence and better approximation performance in synergy (\({\text{H}}_{2} ,{\text{H}}_{\infty }\)) norm than those obtained by comparative algorithms in addition, it is proven to be accurate and reliable to investigate the PEMFC optimum global reduced order model which preserved the main behaviour of original PEMFC SR-12 500 W model.
Similar content being viewed by others
References
Adamo A, Riccardi M, Borghi M, Fontanesi S (2021) CFD Modelling of a Hydrogen/Air PEM Fuel Cell with a Serpentine Gas Distributor. Processes. https://doi.org/10.3390/pr9030564
Du H, Lam J, Huang B (2007) Constrained H2 approximation of multiple input-output delay systems using genetic algorithm. ISA Trans 46(2):211–221. https://doi.org/10.1016/j.isatra.2006.06.007
Glover K (1984) All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds. J Cont. https://doi.org/10.1080/00207178408933239
Guni G, Irawan A (2016) Identification and characteristics of parallel actuation robot’ s leg configuration using Hammerstein - Wiener Approach, J Electr Electron Control Instrum 1(10)
Haddad A, Bouyekhf R, El Moudni A, Wack M (2006) Non-linear dynamic modeling of proton exchange membrane fuel cell. J Power Sources 163(1):420–432. https://doi.org/10.1016/j.jpowsour.2006.09.012
Kavranoǧlu D, Bettayeb M (1993) Characterization of the solution to the optimal H∞ model reduction problem. Syst Control Lett 20(2):99–107. https://doi.org/10.1016/0167-6911(93)90021-W
Liu Y, Anderson BD (1989) Singular perturbation approximation of balanced systems. In: Proceedings of the 28th Conference on Decision and Control Tampa, Florida December 1989, vol 2, https://doi.org/10.1080/00207178408933239
Menesy AS, Sultan HM, Korashy A, Banakhr FA, Ashmawy MG, Kamel S (2020) Effective parameter extraction of different polymer electrolyte membrane fuel cell stack models using a modified artificial ecosystem optimization algorithm. IEEE Access 8:31892–31909. https://doi.org/10.1109/ACCESS.2020.2973351
Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw 83:80–98. https://doi.org/10.1016/j.advengsoft.2015.01.010
Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191. https://doi.org/10.1016/j.advengsoft.2017.07.002
Modeling DZ, Analysis M, Membrane E, Cell F (2018) Modeling and multi-dimensional analysis of a proton exchange membrane fuel cell daming Zhou To cite this version: HAL Id: tel-01868248
Moore BC (1981) Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Trans Automat Contr 26(1):17–32. https://doi.org/10.1109/TAC.1981.1102568
Nehrir MH, Wang C (2009) Modeling and control of fuel cells, distributed generation applications, vol 41. Jhon Wiley, New Jersey
Patidar NP, Panda CAS, Yadav JS (2012) Evolutionary techniques for model order reduction of large scale linear systems. World Acad Sci Eng Technol Int J Electr Comput Eng 6(9):7
Phillips JR (2000) Projection frameworks for model reduction of weakly nonlinear systems. In: Proceedings 37th Design Automation Conference , 5–9 June 2000, p 6, https://doi.org/10.1145/337292.337380
Puranik S (2009) Control of fuel cell based green energy systems for distributed generation applications. The Ohio State University
Rewienski MJ (2003) A trajectory piecewise-linear approach to model order reduction of nonlinear dynamical systems
Saad NH, El-Sattar AA, Mansour AEAM (2013) Adaptive neural controller for maximum power point tracking of ten parameter fuel cell model. J Electr Eng 13(3):233–239
Salim R, Bettayeb M (2011) H2 and H∞ optimal model reduction using genetic algorithms. J Franklin Inst 348(7):1177–1191. https://doi.org/10.1016/j.jfranklin.2009.10.016
Seyedali M, Mohammad MS, Andrew L (2014) Grey wolf optimizer. Adv Eng Softw. https://doi.org/10.1016/j.advengsoft.2013.12.007
Seyezha R, Mathur BL (2011) Mathematical modeling of proton exchange membrane fuel cells. Int J Comput Appl 20(1–2):82–96
Spiegel C (2008) Mathematical modeling of polymer exchange membrane fuel cells
Wang C, Nehrir MH (2007) A physically based dynamic model for solid oxide fuel cells. IEEE Trans Energy Convers 22(4):887–897. https://doi.org/10.1109/TEC.2007.895468
Wang C, Nehrir MH, Shaw S (2005) Dynamic models and model validation for PEM fuel cells using electrical circuits. IEEE Power Eng Soc Gen Meet 3(2):2115. https://doi.org/10.1109/pes.2005.1489284
Wang FC, Yang YP, Huang CW, Chang HP, Chen HT (2007) System identification and robust control of a portable proton exchange membrane full-cell system. J Power Sources 164(2):704–712. https://doi.org/10.1016/j.jpowsour.2006.11.040
Wang FC, Chen HT, Yang YP, Yen JY (2008) Multivariable robust control of a proton exchange membrane fuel cell system. J Power Sources 177(2):393–403. https://doi.org/10.1016/j.jpowsour.2007.11.051
Wilson DA (1970) Optimum solution of model-reduction problem. In: Proceedings of the institution of electrical engineers, vol. 117, Issue 6, pp 1161–1165 https://doi.org/10.1049/piee.1970.0227
Zhao W, Wang L (2019) Artificial ecosystem-based optimization: a novel nature-inspired meta-heuristic algorithm. Neural Comput Appl. https://doi.org/10.1007/s00521-019-04452-x
Zhao W, Zhang Z, Wang L (2020) Manta ray foraging optimization: An effective bio-inspired optimizer for engineering applications. Eng Appl Artif Intell 87:25. https://doi.org/10.1016/j.engappai.2019.103300
Funding
The authors declare that they have no any funding source for doing this research work.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
Disclosure of potential conflicts of interest: no conflicts of interest.
Human and animal rights statement
Research involving Human Participants and/or Animals: no other research participants except authors.
Informed consent
Authors are all consent.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Touati, Z., Saadi, S., Kious, M. et al. Synergy of (\({\text{H}}_{2}\), \({\text{H}}_{\infty }\)) norms for nonlinear optimal PEMFC dynamic MIMO model reduction using a novel EAO approach. Int J Syst Assur Eng Manag 13, 1396–1409 (2022). https://doi.org/10.1007/s13198-021-01485-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13198-021-01485-1