Offline and online parameter estimation of nonlinear systems: Application to a solid oxide fuel cell system

In this paper, an offline tuning strategy and an online parameter estimation method are exploited to calibrate the solid oxide fuel cell mathematical model. Different to existing offline tuning strategy, the developed strategy is designed in order to tune the model under various operation conditions. First, the particle swarm optimization method combined with the gradient-based search method is applied to tune unknown parameters in the state-space model and the steady-state model for each operation condition. Then, the sensitive parameters are expanded to the polynomial equations. Moreover, the reconstructed model including coefficients in the polynomial equations are determined by using the particle swarm optimization method with gradient-based search method for whole operation conditions. To show the slowly time-varying performance of a solid oxide fuel cell, an adaptive optimal learning law based on the optimization technology is proposed to online minimize a cost function with the information of the estimation error. The estimation error is extracted through several low-pass filters and simple algebraic calculation. Finally, the proposed offline tuning strategy and the developed online adaptive estimation method are verified by conducting experiments on a practical solid oxide fuel cell test bench.