Key Variable–Based Hammerstein Model for an Air Compressor of Hydrogen Fuel Cells

A block Hammerstein model consists of a static nonlinear static module followed by a linear dynamic module, offering an effective framework for modeling nonlinear engineering systems. In this article, the Hammerstein model is used to model the fuel cell air compressor, and a three-input single-output air compressor model is established, with the fuel cell air compressor pressure ratio, throttle opening and motor current as inputs, and the output performance characteristics (output flow rate, air compressor power, and isentropic efficiency of the whole machine) as outputs, respectively. A key-variable (KV) separation and least-squares (LS) algorithm (KV-LS)-based parameter optimization approach for the Hammerstein model is explored for online parameter identification; the KV-LS method was found to improve the efficiency and accuracy of the identification process by separating key variables from linear equations and utilizing the least-squares algorithm to optimize model parameters. Simulation experiments indicated that, compared with the overparametrization-based least-squares algorithm (OP-LS), the KV-LS method had fewer parameters and high estimation accuracy; compared with the key-variable separation and stochastic gradient (KV-SG) algorithm, the KV-LS method had quick convergence speed and strong stability in parameter identification. The fitting error (R2) between output flow rate and air compressor power by the KV-LS algorithm was nearly negligible, and the mean absolute value error (MAE) was less than 0.011 g/s and 0.004 kW. The root-mean square error (RMSE) was less than 0.014 g/s and 0.005 kW, demonstrating that the KV-LS algorithm–‍based Hammerstein model can accurately estimate the air compressor’s output performance characteristics. The high-precision estimation of key parameters provides a reliable foundation for implementing model-based advanced control strategies, helps achieve more precise air supply control, and enhances the dynamic response performance of fuel cell systems.