Non-Statistical Based Robust Identification of a Lightly Damped Flexible Beam Using Kautz Orthonormal Basis Functions

Abstract

Robust identification of a lightly damped flexible beam with parametric and non-parametric uncertainties is presented; however, the main concern is about non-parametric uncertainties which are high-frequency high-amplitude unmodeled dynamics. Our approach is based on worst-case estimation theory in which uncertainties are assumed to be unknown but bounded and produces so-called hard bounds on model errors. Based on this theory, two methods named “Set Member-sip” and “Model Error Modeling” has been applied. We have also examined two outbounding algorithms (ellipsoidal and parallelotopic) to solve the Set Membership identification problem. In order to properly deal with high-amplitude non-parametric uncertainties, the proposed methods are compared. It is shown that the combination of Set Membership approach with Model Error Modeling technique will result in superior identification in that it can better handle high-frequency high-amplitude non-parametric uncertainties. For each method the mode obtained and its associated uncertainty bound is mapped to the frequency plane so that it can be utilised by robust controller design methods such as H∞.