Robust observer-based-α-variable model-free supertwisting fractional order sliding mode control for nonlinear PEMFC system with uncertainties and disturbance

The service life and efficiency of proton exchange membrane fuel cells (PEMFCs) are significantly related to the control performance of the air supply system. Therefore, this research develops a novel robust observer-based- [Formula: see text]-variable model-free supertwisting fractional-order sliding mode control ([Formula: see text]-MF-STFOSMC) for complex nonlinear PEMFC air supply system with unmeasurable state variables, model uncertainties, and external disturbance. First, the fifth-order nonlinear PEMFC air supply system model is presented, and the unmeasured state variables are estimated using a nonlinear disturbance observer (NDOB1). Second, the ultra-local model (ULM) algorithm is employed to reconstruct the complex nonlinear PEMFC air supply system, avoiding the need for precise modeling and reducing the controller design difficulty. To estimate and compensate for the uncertain dynamics in the ULM algorithm, another NDOB2 is proposed to realize zero estimation error and finite-time observation. Besides, to achieve optimal control performance with less input chattering, finite-time convergence, and fast response speed, the [Formula: see text]-MF-STFOSMC is designed using super-twisting fractional-order sliding mode control (STFOSMC) algorithm. Furthermore, the stability of [Formula: see text]-MF-STFOSMC via a closed-loop system is verified using the Lyapunov theorem. Finally, the nonlinear PEMFC air supply system model with the proposed controller is realized in MATLAB/Simulink environment, and the simulation results are given to show the superiority and effectiveness of the proposed technique.