From input-output open loop data to closed loop poles

Closed-loop (CL) poles estimated from open-loop (OL) data can serve as useful features for system interrogation and, in control applications, for checking discrepancies between the eigenstructure specified during design, which reflects model properties, and the eigenstructure that would be realized in a test. While estimating OL poles from OL data does not depend on assumption made on the inter-sample behavior of the inputs, this is not the case for CL poles because these are affected by how the non-homogeneous part of the discrete-time model is mapped to continuous time. In this paper analysis shows that errors arising from treating typically band-limited OL inputs as zero-order hold (an assumption often adopted by default) can be significant, even at sampling rates frequently considered high enough to ignore inter-sample concerns. Also shown is the fact that the straightforward approach of closing the loop on a modally truncated state-space realization does not yield the poles of the truncated CL system and that analytical consistency requires that the feedback be accounted for at the level of the experimentally estimated transfer matrices. Albeit supplementary, it is shown that extraction of poles from the pole-residue parameterization of the transfer matrix can be decoupled from the residues by adopting a fitness function based on subspace angles, instead of transfer matrix misfit norms. Preliminary results from a pilot study support the hypothesis that the noted decoupling increases the basin of attraction of the global minimum.