Model-based observer for vehicle proton exchange membrane fuel cell humidity based on adaptive sliding mode estimation technique

Abstract

Real-time humidity acquisition for vehicle proton exchange membrane fuel cell (PEMFC) facilitates humidity control to avoid membrane flooding or drying, improving its efficiency and stability. However, due to the frequent changes of actual vehicle conditions and expensive as well as unreliable humidity sensors, it is difficult to obtain real-time water content in PEMFC, which brings obstacles to closed-loop control of humidity. To this end, a model-based observer is proposed to obtain real-time humidity. Specifically, a dimensionless third-order model of relative humidity for PEMFC was established, which includes the dynamic of membrane water content. Based on the proposed model, an adaptive sliding mode convergence algorithm was designed to approach real-time humidity using measurable signals (voltage, current, pressure, flow rate, and temperature). The exploration of proposed adaptive sliding mode observer (ASMO) performance was compared with non-adaptive sliding mode observer (SMO) and classical ASMO by using a real 80 kW commercial fuel system experimental data. The experimental results show that compared with second-order humidity model, proposed third-order humidity model reduced recovery time under small step condition, where 250 s for cathode humidity estimation and 200 s for anode humidity estimation. In addition, under the small step condition, the average error of the three observers was less than 3%, which is accurate for engineering application. Moreover, proposed ASMO had the minimum static error, with 4% for cathode humidity estimation and 9% for anode humidity estimation under large step conditions as well as MAE, MSE, RMSE with 4%, 1.90%, 4.39% for cathode relative humidity estimation, 8.19%, 0.89%, 9.44% for anode relative humidity estimation respectively. The comprehensive results indicate that the proposed ASMO with adaptive parameters tuning has better dynamic performance than non-adaptive SMO as well as classical ASMO in terms of robustness and estimated accuracy.