|
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
Citation:
A. V. Chekhonadskikh, “Optimal gyroscopic stabilization of vibrational system: algebraic approach”, Sib. Èlektron. Mat. Izv., 21:1 (2024), 70–80
Linking options:
https://www.mathnet.ru/eng/semr1669 https://www.mathnet.ru/eng/semr/v21/i1/p70
|
Statistics & downloads: |
Abstract page: | 18 | Full-text PDF : | 11 |
|