Reduced-order model feedback control design: numerical implementation in a thin shell model

Reduced order models employing the Lagrange and POD reduced basis methods in numerical approximation and feedback control of systems are presented and numerically tested. The system under consideration is a thin cylindrical shell with surface-mounted piezoceramic actua-tors. Donnell-Mushtari equations, modiied to include Kelvin-Voigt damping, are used to model the system dynamics. Basis functions constructed from Fourier polynomials tensored with cubic splines are employed in the Galerkin expansion of the full order model. Reduced basis elements are then formed from full order approximations of the exogenously excited shell taken at diierent time instances. Numerical examples illustrating the features of the reduced basis methods are presented. As a rst step toward investigating the behavior of the methods when implemented in physical systems, the use of reduced order model feedback control gains in the full order model is considered and numerical examples are presented.