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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2024, Volume 21, Issue 1, Pages 70–80
DOI: https://doi.org/doi.org/10.33048/semi.2024.21.006
(Mi semr1669)
 

Differentical equations, dynamical systems and optimal control

Optimal gyroscopic stabilization of vibrational system: algebraic approach

A. V. Chekhonadskikh

Novosibirsk State Technical University, K Marx av., 20, 630073, Novosibirsk, Russia
Abstract: The paper deals with LTI vibrational systems with positive definite stiffness matrix $K$ and symmetric damping matrix $D$. Gyroscopic stabilization means the existence of gyroscopic forces with a skew-symmetric matrix $G$, such that a closed loop system with damping matrix $D+G$ is asymptotically stable. The feature of characteristic polynomial in the case predetermines such stabilization as a low order control design. Assuming the necessary condition of gyroscopic stabilization is fulfilled, we pose the problem of achieving relative stability maximum using a stabilizer $G$. The stability maximum value is determined by a matrix $D$ trace, but its reachability depends on the coincidence of all pole real parts with the corresponding minimal value, i.e. equality of characteristic and root polynomials. We illustrate a root polynomial technique application to optimal gyroscopic stabilizer design by examples of dimension 3–5.
Keywords: vibrational system, gyroscopic stabilizer, low order control, rightmost poles, relative stability, root polynomial.
Received March 14, 2023, published February 16, 2024
Document Type: Article
UDC: 681.5.01
MSC: 93C05
Language: English
Citation: A. V. Chekhonadskikh, “Optimal gyroscopic stabilization of vibrational system: algebraic approach”, Sib. Èlektron. Mat. Izv., 21:1 (2024), 70–80
Citation in format AMSBIB
\Bibitem{Che24}
\by A.~V.~Chekhonadskikh
\paper Optimal gyroscopic stabilization of vibrational system: algebraic approach
\jour Sib. \`Elektron. Mat. Izv.
\yr 2024
\vol 21
\issue 1
\pages 70--80
\mathnet{http://mi.mathnet.ru/semr1669}
\crossref{https://doi.org/doi.org/10.33048/semi.2024.21.006}
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