Real-time water content regulation in PEMFC shutdown via MPC with SH-AUKF-based state Feedback: Towards improved efficiency and reduced energy consumption

Abstract

Effective regulation of membrane water content during shutdown is critical to ensuring the durability and performance recovery of proton exchange membrane fuel cells (PEMFCs). This study presents a model predictive control (MPC) strategy for purge-phase water removal, employing adaptive unscented Kalman filters (UKFs) for water content estimation. A reduced-order model is formulated to capture the essential purge dynamics while minimizing computational demands. Experimental validation is conducted using data from a 160 kW PEMFC system, incorporating purge voltage and high-frequency resistance (HFR) measurements. Based on the reduced-order model, three state observers—standard UKF, adaptive UKF (AUKF), and Sage-Husa-based AUKF (SH-AUKF), are designed and evaluated. Among them, the SH-AUKF provides the best trade-off between convergence speed and steady-state accuracy. It reconstructs internal states during the purge process from measurable signals and provides real-time feedback to the MPC controller. The MPC controller optimizes a dual-objective cost function that balances tracking accuracy and energy consumption, while enforcing constraints on purge flow magnitude and rate of change. With SH-AUKF state feedback, the MPC controller demonstrates excellent performance, maintaining a tracking error below 0.1, a response time under 12s, and an overshoot of 0.35 in a large-step test, compared to 0.57 with an augmented linear quadratic regulator (LQR). The controller's robustness is further validated under varying temperature and purge current conditions. Compared to fixed and intermittent flow strategies, the MPC-based approach significantly enhances purging efficiency and energy conservation, achieving the shortest purge duration of 11.53 s and the lowest energy consumption of 44.7 kJ. Relative to the constant excess oxygen ratio of 8 (OER = 8) strategy with similar energy use, the MPC-based method shortens purge duration by 11.56 s, indicating a 100 % improvement in time efficiency. Compared to the constant OER = 12 strategy, which achieves a similar purge duration, it lowers energy consumption by 5.5 %.