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The nonlinear and time‐dependent characteristic and unknown modeling uncertainty of proton exchange membrane fuel cell (PEMFC) such as complex electro‐chemical, thermal, and fluid mechanic phenomena make its controller design quite challenging. In this paper, a controller based on a super twisting algorithm (STA) with variable gains is proposed to control the air breathing system of PEMFC. The strategy includes regulating the oxygen excess ratio (λnormalO2) for preventing the stack oxygen starvation and maintaining optimum net power output in spite of external disturbances and model uncertainties. The proposed algorithm has the main advantages of the fixed gain STA, such as robustness against the disturbance and parametric uncertainties with the unknown boundary, chattering reduction, and finite time convergence. The Lyapunov analysis was proposed to assess the stability of the Variable Gain Super Twisting Algorithm (VGSTA). The results verified the effectiveness of the proposed controller with attaining robust regulation against uncertainties, disturbances, and noisy circumstance compared to fixed gain SOSM controllers.

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