The main objective of this manuscript is to design a high-order sliding-mode observer to provide #12;nite time\udestimation of unmeasurable states (x4 : oxygen mass, x5 : nitrogen mass) together with the oxygen excess ratio (ratio of\udthe input oxygen \udow to the reacted oxygen \udow in the cathode). This is done by applying second-order sliding modes\udthrough either super twisting or suboptimal controllers to control the proton exchange membrane fuel cell's breathing.\udThe estimated oxygen excess ratio is controlled in a closed-loop system using 2 distinct sliding-mode approaches: a\udcascaded super twisting controller and a single-loop suboptimal structure. Simulation results are presented to make\uda quantitative comparison between the cascade and the single-loop con#12;guration. The results verify that the cascade\udprovides accurate reference tracking while the single-loop presents faster convergence.
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