Multi-input partial pole placement for distributed parameter gyroscopic systems

Presents a solution to the partial eigenvalue assignment problem of an undamped gyroscopic distributed parameters system. The partial eigenvalue assignment problem is the problem of reassigning by feedback a few bad eigenvalues of the open-loop operator pencil while leaving the remaining infinite number of eigenvalues unchanged. The distinctive practical features of our solution are (i) it requires solution of only a small finite dimensional linear algebraic system and knowledge of only a small finite number of eigenvalues and eigenvectors of the infinite dimensional open-loop operator pencil, (ii) no spill-over occurs; that is, the remaining infinite number of eigenvalues and eigenvectors that are required to remain invariant will remain in their places and, (iii) it is obtained completely in a distributed parameter setting and no discretization to second-order system of differential equations is invoked so that vital inherent properties of the original system are fully preserved. Because of the above mentioned practical features, the proposed solution is readily applicable to stabilize or to combat the effects of dangerous vibrations in a large structure.