State-Space-Reconstructed High-Order Fully Actuated Control for Oxygen Excess Ratio Regulation in PEM Fuel Cells

Precise oxygen excess ratio (OER) regulation in proton exchange membrane fuel cells must prevent oxygen starvation without excessive compressor power. Direct high-order fully actuated system (HOFAS) control differentiates an OER output whose actuation gain depends on stack current and becomes nonsmooth at ideal load steps. We instead control the supply-manifold-to-cathode pressure difference, yielding a second-order model with a constant nominal input coefficient, and use a third-order linear extended state observer (LESO) to estimate gain mismatch and nonlinear terms. A composite Lyapunov analysis establishes conditional uniform ultimate boundedness under smooth-load, bounded-disturbance-derivative, and unsaturated-input assumptions, with additional conditions for internal states and OER error. Simulations with parameter mismatch, measurement noise, actuator limits, sensing and actuation nonidealities, and a WLTC-like profile show bounded trajectories and a tracking–actuation trade-off. Output reconstruction reduces dependence on instantaneous current scheduling and supports rate-limited implementation, while direct-OER-HOFAS and super-twisting benchmarks can achieve lower tracking error at higher voltage activity.