Time-domain system identification using fractional models from non-zero initial conditions applied to Li-ion Batteries
Résumé
The main contribution of this paper is to present two distinct algorithms for fractional system identification using non-zero initial conditions, by assuming the input signal prior to $t = 0$ and the input/output signals after $t = 0$ known. Addressing this problem is particularly important, in the context of short data acquisition, mainly for two reasons (i) the effect of free response is important compared to the forced one (ii) time-domain response of fractional systems converge polynomially, as compared to the exponential convergence of rational systems. The first developed algorithm uses a two-stage iterative procedure that computes system forced response at the upper stage, and system parameters
at the lower stage. The second one relies on an output error model, estimating parameters due to the simultaneous contribution of system free and forced responses. The efficacy of both algorithms is first assessed using Monte Carlo simulations with significant signal to noise ratios. The proposed algorithms, applied to the identification of commercial Li-ion battery cells, allow solving a technical issue: straightforward data acquisition whatever the past history of the cells, i.e. the cells need not be in a completely relaxed state (with zero initial conditions) prior to collecting data, contrary to the actual practice.
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