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

Reduced-order models employing the Lagrange and popular proper orthogonal decomposition (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 piezoce...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2000-07, Vol.45 (7), p.1312-1324
Main Authors: Banks, H.T., del Rosario, R.C.H., Smith, R.C.
Format: Article
Language:English
Subjects:
Actuators
Approximation
Basis functions
Context modeling
Dynamical systems
Dynamics
Equations
Feedback control
Lagrangian functions
Mathematical analysis
Mathematical models
Military computing
Physics computing
Piezoelectric materials
Reduced order systems
System testing
Thin walled shells
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Summary:Reduced-order models employing the Lagrange and popular proper orthogonal decomposition (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 actuators. Donnell-Mushtari equations, modified 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 different time instances. Numerical examples illustrating the features of the reduced-basis methods are presented. As a first 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.
ISSN:0018-9286
1558-2523
DOI:10.1109/9.867024