Дифференциальные уравнения, динамические системы и оптимальное управление

Optimal gyroscopic stabilization of vibrational system: algebraic approach

A. V. Chekhonadskikh

Novosibirsk State Technical University, K Marx av., 20, 630073, Novosibirsk, Russia

Аннотация: 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.

Ключевые слова: vibrational system, gyroscopic stabilizer, low order control, rightmost poles, relative stability, root polynomial.

УДК: 681.5.01

MSC: 93C05

Поступила 14 марта 2023 г., опубликована 16 февраля 2024 г.

Язык публикации: английский

DOI: 10.33048/semi.2024.21.006