Modeling flexible structures with unknown high-order modal parameters: a feasible set approach in frequency domain

A control-oriented uncertainty modeling on frequency domain is presented for a class of spectral systems with unknown high-order modal parameters. At any user-specified frequency, the set of all the feasible frequency responses is characterized on the complex plane where it is said to be feasible if partial modal parameters of a system are given and the other unknown modal parameters meet certain conditions. We emphasize that such a characterization enables us to quantify the least upper bounds of errors for any nominal models, and also to develop further efficient results using additional information. It is shown that the DC gain information of the system reduces the size of the feasible set to half or smaller one, for any frequencies. The efficiency of the presented scheme is demonstrated by a simple example of an ideal flexible beam.