Robust Partial Quadratic Eigenvalue Assignment Problem: Spectrum Sensitivity Approach

We propose an optimization approach to the solution of the partial quadratic eigenvalue assignment problem (PQEVAP) for active vibration control design with robustness (RPQEVAP). The proposed cost function is based on the concept of sensitivities over the sum and the product of the closed-loop eigen...

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Bibliographic Details
Published inarXiv.org
Main Authors Araújo, José Mário, Carlos Eduardo Trabuco Dórea, Luiz Marcos Garcia Gonçalves, João Batista da Paz Carvalho, Datta, Biswa Nath
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 05.11.2016
Subjects
Active control
Algorithms
Eigenvalues
Eigenvectors
Operations research
Optimization
Robust control
Robustness (mathematics)
Sensitivity
State feedback
Vibration control
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Summary:We propose an optimization approach to the solution of the partial quadratic eigenvalue assignment problem (PQEVAP) for active vibration control design with robustness (RPQEVAP). The proposed cost function is based on the concept of sensitivities over the sum and the product of the closed-loop eigenvalues, introduced recently in our paper. Explicit gradient formula for the solutions using state feedback and derivative feedback are derived as functions of a free parameter. These formulas are then used to build algorithms to solve RPQEVAP in a numerically efficient way, with no need to compute new eigenvectors, for both state feedback and state-derivative feedback designs. Numerical experiments are carried out in order to demonstrate the effectiveness of the algorithms and to compare the proposed method with other methods in the literature, thus showing its effectiveness.
ISSN:2331-8422