Modeling uncertainty for unknown modal parameters in large flexible structures

A procedure for control-oriented modeling is proposed for large flexible structures with unknown modal parameters. Techniques on quantification of errors in modal truncated nominal models are developed for the case where a finite number of upper and lower bounds of the unknown modal parameters are given. A feasible set of systems matching the conditions is introduced, and then error bounds covering the feasible set are established in the frequency domain. The bounds are easily checked using linear programming for any user-specified frequency. The feasibility of the proposed scheme is illustrated by numerical study on an ideal flexible beam example.