Quantification of model uncertainty from data: input design, interpolation, and connection with robust control design specifications

Abstract

Identification of linear models in view of robust control design requires the identification of a control-relevant nominal model, and a quantification of model uncertainty. In this paper a procedure is presented to quantify the model uncertainty of any prespecified nominal model, from a sequence of measurement data of input and output signals from a plant. By employing a non-parametric empirical transfer function estimate (ETFE), we are able to split the model uncertainty into three parts: the inherent uncertainty in the data due to data-imperfections, the unmodelled dynamics in the nominal model, and the uncertainty due to interpolation. A frequency-dependent hard error bound is constructed, and results are given for tightening the bound through input design. When the upper bound on the model uncertainty is too conservative, in view of the control design specifications, information is provided as to which additional experiments have to be performed in order to improve the bound.