Estimating the frequency response of a system in the presence of an integrator

•Considerable low frequency bias is encountered when estimating frequency response.•Proposed solution gives good estimates of the low frequency response and noise power.•Method is applied on entire data set from open-loop without segmenting for averaging.•Can be used to improve impedance estimates of batteries when under a DC offset.•Robust to non-ideal situations, example if the system has a pole close to the origin.

A system with an integrator is one which does not have a steady-state gain at zero frequency. An example is a battery; when subjected to a constant charge or discharge current the voltage will continuously increase or decrease until the cell reaches its maximum/minimum cut-off voltage and not reach a steady-state value. Frequency response estimation techniques that minimises leakage errors lead to significant errors at low frequencies of the response. This paper develops and presents a technique whereby the low frequency errors are eliminated. The technique is applied over the frequencies of interest, except DC frequency, and gives better results over windowing and a local polynomial frequency response estimation method. As such, an accurate low frequency response and noise power spectrum can now be obtained which in turn can be used for estimating accurate parametric models.