Robust control of nonlinear PEMFC against uncertainty using fractional complex order control

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 (λo2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \lambda _{{\mathrm{o}_{2} }}$$\end{document}), is required to be adjusted. A sudden load variation causes huge variations in λo2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \lambda _{{\mathrm{o}_{2} }}$$\end{document}. Main purpose of this manuscript is to investigate the capability of the FCOC to regulate λo2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \lambda _{{\mathrm{o}_{2} }}$$\end{document} 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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$PI$$\end{document}, fractional order PI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$PI$$\end{document}(FO-PI) and H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {H}_\infty $$\end{document} will be also investigated.