Identification of Fractional Order Models: Application to 1D Solid Diffusion System Model of Lithium Ion Cell

In this paper the simplified refined instrumental variable method for fractional order transfer function model identification is applied to a simulated diffusion system of concentration of the lithium ions in a battery cell. The diffusion process is represented by a 1D spherical diffusion partial differential equation of concentration and is solved numerically by finite volume method (FVM) in spatial and temporal domains. The fractional transfer function (FTF) model order is selected and model parameters are identified based on sampled input-output data. The main advantage of using FTF model for simulation purposes is the increased accuracy, as compared to FVM, while retaining simulation simplicity of having a reduced order model.