Controllability and Observability Analysis of the Liquid Water Distribution Inside the Gas Diffusion Layer of a Unit Fuel Cell Model

We analyze the controllability and observability (C/O) of the liquid water distribution in the gas diffusion layer (GDL) of a polymer electrolyte membrane fuel cell (PEMFC) using a one-dimensional channel-to-channel unit fuel cell model. This modeling domain is sufficient to illustrate the control objectives and analysis techniques but requires further development for stack level modeling. A comparison is made between first-principles-based numeric and reduced-order semi-analytic models with emphasis on the effects of model reduction on their analyses. The numeric model is a partial differential equation based model approximated by difference equations, including both channels and both GDLs of a PEMFC. The reduced model uses a semi-analytic solution method, which is a combination of analytic and numeric solutions, gaining physical intuition at lower computational cost. The C/O analysis is based on linearizations around three critical operating points. The results indicate that stabilizability of the anode liquid water states and, hence, management of anode water flooding is possible. If the channel water mass can be controlled to a constant value, then the GDL liquid distribution will be stable (McCain et al., 2007, “A Multi-Component Spatially-Distributed Model of Two-Phase Flow for Estimation and Control of Fuel Cell Water Dynamics,” Proceedings of the 46th IEEE Conference on Decision and Control, pp. 584–589). Further, it will be shown that if the channel liquid water mass can be brought to zero, controllability of the GDL liquid modes will be obtained. Additionally, this study will indicate the input(s) best suited to obtain this control objective and the output(s) required.