Steady-State System Analysis of a Proton Exchange Membrane Fuel Cell Nonlinear Mathematical Model

In this paper we analyze the steady state dynamic behavior of a nonlinear model of a Proton Exchange Membrane (PEM) fuel cell. This model is used in several theoretical studies and application papers of PEM fuel cells. We indicate limitations and discuss potential constraints of this mathematical model. We establish conditions for the asymptotic stability at steady state by using the first stability method of Lyapunov. We find that the linearized model at steady state is uncontrollable. Specifically, the state variable corresponding to the hydrogen pressure is not controllable. This means that dynamics deviations of the state space variable corresponding to the hydrogen pressure around the steady state equilibrium point cannot be controlled. Due to its stability, the hydrogen pressure we go to the equilibrium point according to its internal (uncontrolled) dynamics so that the model is still applicable for theoretical and practical studies.