This paper addresses the challenge of tracking an arbitrary power profile in a proton exchange membrane fuel cell (PEMFC) in the presence of measurement noise and disturbances. To this end, we used an extended Kalman filter (EKF) to estimate the internal states of the PEMFC in conjunction with an adaptive sliding mode controller (SMC) that has been shown to reduce chatter. The model used by the controller captures the internal dynamics and nonlinearly, and is accurate within 0.1% of the high-fidelity model. We developed the conditions necessary for the stability of the proposed controller based on the Lyapunov stability theorem. We also developed a systematic multi-objective optimization methodology of the controller hyperparameters to simultaneously minimizing tracking error, controller-chatter, and controller input using the non-dominated sorting genetic algorithm Ⅱ (NSGA-Ⅱ). The controller performance was demonstrated using multiple simulated experiments. Based on experimental results on desired signal data, we concluded that the proposed controller scheme can track desired power profiles within a 1% error.

This paper developed an observer design for a matrix-Lipchitz nonlinear system with measurement delay that can achieve a desired ${\mathcal{L}}_2$ performance in the presence of modeling uncertainties, input disturbance, and measurement noise. The observer was shown to be stable in the absence of disturbances and modeling uncertainties. The equations for the observer design were shown to be both necessary and sufficient. Furthermore, the observer design was formulated as linear matrix inequality (LMI) that can be solved offline using commercial solvers. Compared to previous literature, the proposed observer does not require the underlying system to be stable. The observer design procedure is demonstrated through two illustrative examples.