Bounds of the Modeling Errors of Black-Box MIMO (Multiple Input Multiple Output)Transfer Function Estimates

摘要

The following problem is tackled: Derive a suitable description of the modeling errors (model uncertainty) of MIMO transfer function models which are obtained by black-box identification; this description must supply the quantitative information required for robustness study of the feedback system where the black-box model is used for the controller design. An upper bound of modeling errors is estimated. The asymptotic theory of the properties of black-box transfer function estimates, developed by Ljung and Yuan (1985) is used. Their theory shows that the transfer function estimates are consistent, the errors of the estimates are asymptotically joint normal, with a very simple expression for their covariances. Their results are extended to cases where spectral analysis is used. Based on this theory, a bound of (additive) modeling errors is defined as the sum of the absolute value of the bias part and the 3 sigma bound of the variance (random) part of the modeling errors. Algorithms are proposed for the computations; a numerical test is performed to validate the theory. The bounds for other forms of the modeling errors are also derived from the bound matrix obtained.