The paper considers the eighth-order proton exchange membrane (PEM) fuel-cell mathematical model and shows that it has a multi-time scale property, indicating that the dynamics of three model state space variables operate in the slow time scale and the dynamics of five state variables operate in the fast time scale. This multi-scale nature allows independent controllers to be designed in slow and fast time scales using only corresponding reduced-order slow (of dimension three) and fast (of dimension five) sub-models. The presented design facilitates the design of hybrid controllers, for example, the linear-quadratic optimal controller for the slow subsystem and the eigenvalue assignment controller for the fast subsystem. The design efficiency and its high accuracy are demonstrated via simulation on the considered PEM fuel cell model.

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