Time-domain system identification using fractional models from non-zero initial conditions applied to Li-ion Batteries

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-time data acquisition, mainly because the effect of the free response is important compared to the forced one and because the time 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 using the forced response. The second one uses 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 allow solving a technical issue on commercial battery cells: their identification using input–output data whatever their history, i.e. the battery cells need not be in a completely relaxed state (with zero initial conditions) prior to collecting system identification data, contrary to the actual practice.