OPTIMAL GYROSCOPIC STABILIZATION OF VIBRATIONAL SYSTEM: ALGEBRAIC APPROACH

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 force 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 nesessary 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 is connected with system pole locations
according to critical root diagrams. We illustrate root diagrams and
root polynomials techniques to an optimal gyroscopic stabilizer design
by examples of dimension 3–5.