Frequency response estimation for NCFs of an MIMO plant from closed-loop time-domain experimental data

Frequency response estimation from closed-loop time-domain experimental data is investigated in this paper for normalized coprime factors (NCF) of a multiple-input-multiple-output (MIMO) plant. Based on a linear fractional transformation (LFT) representation for all the NCFs of plants internally stabilizable by a known controller, this estimation problem is converted into the open-loop nonparametric estimation of an inner transfer function matrix (TFM). An estimate is derived through constrained data-matching. It is proved that when the probing signals are periodic and the NCFs of the auxiliary plant are appropriately selected, the estimate is asymptotically unbiased and with a normal/complex normal distribution. It has been made clear that the estimation bias and the estimation variance are always finite. Computationally tractable procedures are suggested for choosing the desirable auxiliary TFMs.