Online Parameter Estimation of the Polarization Curve of a Fuel Cell With Guaranteed Convergence Properties: Theoretical and Experimental Results

In this article, the problem of online parameter estimation of a proton exchange membrane fuel cell (PEMFC) polarization curve, that is, the static relation between the voltage and the current of the PEMFC is addressed and solved. The task of designing this estimator—even off-line—is complicated by the fact that the uncertain parameters enter the curve in a highly nonlinear fashion, namely in the form of
nonseparable
nonlinearities. We consider several scenarios for the model of the polarization curve, starting from the standard
full model
and including several popular
simplifications
to this complicated mathematical function. In all cases,
separable
regression equations are derived—either linearly or nonlinearly parameterized—which are instrumental for the implementation of the parameter estimators. We concentrate our attention on
online
estimation schemes for which, under suitable excitation conditions, global
parameter convergence
is ensured. Due to these global convergence properties, the estimators are robust to unavoidable additive noise and structural uncertainty. Moreover, since the schemes are online, they are able to track (slow) parameter variations, that occur during the operation of the PEMFC. These two features—unavailable in time-consuming offline data-fitting procedures—make the proposed estimators helpful for online time-saving characterization of a given PEMFC, and the implementation of fault-detection procedures and model-based adaptive control strategies. Simulation and
experimental
results that validate the theoretical claims are presented.