Modeling uncertainty of flexible structures with eigenparameter bounds-frequency domain characterization for controller design

An approach to control-oriented uncertainty modeling is proposed for linear elastic vibrating systems described by a partial differential equation. Techniques are developed for the case where a finite number of upper and lower bounds of the unknown parameters are available. To solve the problem, the feasible set defined in Imai and Wada (1998) is generalized and expanded to a more useful and practical set of systems. Then, the perturbation magnitude covering the feasible set is evaluated in the frequency domain where the truncated modal model is chosen as the nominal model. An upper bound is developed, which is computed using linear programming. All the parameter bounds required for the proposed formulation are computed using finite element analysis for a major class of elastic vibrating systems