Nonlinear observation of internal states of fuel cell cathode utilizing a high-order sliding-mode algorithm

A scheme for designing a second-order sliding-mode (SOSM) observer that estimates critical internal states on the cathode side of a polymer electrolyte membrane (PEM) fuel cell system is presented. A nonlinear, isothermal dynamic model for the cathode side and a membrane electrolyte assembly are first described. A nonlinear observer topology based on an SOSM algorithm is then introduced, and equations for the SOSM observer deduced. Online calculation of the inverse matrix produces numerical errors, so a modified matrix is introduced to eliminate the negative effects of these on the observer. The simulation results indicate that the SOSM observer performs well for the gas partial pressures and air stoichiometry. The estimation results follow the simulated values in the model with relative errors within ± 2% at stable status. Large errors occur during the fast dynamic processes (<1 s). Moreover, the nonlinear observer shows good robustness against variations in the initial values of the internal states, but less robustness against variations in system parameters. The partial pressures are more sensitive than the air stoichiometry to system parameters. Finally, the order of effects of parameter uncertainties on the estimation results is outlined and analyzed.