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Feedback Control in Distributed Parameter Gyroscopic Systems: A Solution of the Partial Eigenvalue A

Abstract This paper presents a novel solution to the partial eigenvalue assignment problem of an undamped gyroscopic distributed parameter system. The partial eigenvalue assignment problem is the problem of reassigning by feedback a few undesired 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 the 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 discretisation 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 stabilise or to combat the effects of excessive vibrations in a large structure.