Abstract
This work proposes a fractional complex order controller (FCOC) design strategy to cope with uncertainty in a proton exchange membrane fuel cell (PEMFC) model. The fuel cell dynamic behavior is inherently nonlinear and time varying. Accordingly, a locally linearization technique is used to achieve a linear interpretation in form of transfer function instead of nonlinear dynamics. When the current load is suddenly changed, the voltage and consequently the operating point are dramatically varying. Therefore, the resultant linearized model of the PEMFC changes. The discrepancy between those deviated models from the nominal plant will be regarded as system uncertainties, which must be cured by robust controller. In PEMFC dynamic, the ratio of the oxygen with respect to the air supply, i.e. the oxygen excess ratio (\( \lambda _{{\mathrm{o}_{2} }}\)), is required to be adjusted. A sudden load variation causes huge variations in \( \lambda _{{\mathrm{o}_{2} }}\). Main purpose of this manuscript is to investigate the capability of the FCOC to regulate \( \lambda _{{\mathrm{o}_{2} }}\) in different operating conditions. The designed controller will be gained to satisfy multi-constraint problem. The performance of the controllers is verified in the presence of uncertainty by means of the frequency criteria, i.e. the phase and the gain margins, as well as the time indices. The quality of the controller will be investigated on the original nonlinear plant. The stability and performance of the proposed controller with respect to other conventional controllers, e.g. \(PI\), fractional order \(PI\) (FO-PI) and \(\hbox {H}_\infty \) will be also investigated.
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Notes
CRONE is the French acronym of “Commande Robuste d’Ordre Non Entier” which means Robust Control using Fractional Order.
Peak of sensitivity function.
Peak of complementary sensitivity function.
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Shahiri, M., Ranjbar, A., Karami, M.R. et al. Robust control of nonlinear PEMFC against uncertainty using fractional complex order control. Nonlinear Dyn 80, 1785–1800 (2015). https://doi.org/10.1007/s11071-014-1718-1
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DOI: https://doi.org/10.1007/s11071-014-1718-1