Computational methods for feedback control in damped gyroscopic second-order systems

Abstract

Two new computationally viable algorithms are proposed for partial pole-placement and eigenstructure assignment in damped gyroscopic matrix second-order systems. The algorithms can be implemented with only a partial knowledge of the spectrum and the corresponding eigenvectors of the associated open-loop quadratic matrix pencil. Mathematical results are proved to guarantee that there will be no-spillover effects; that is, it is shown mathematically that the large-number of eigenvalues and eigenvectors that need to remain unchanged will not be effected by feedback. Furthermore, the algorithms work directly in second-order setting allowing them to exploit structures such as sparsity, band, symmetry etc. These practical features of the algorithms make them ideally suited for real-life applications such as control and stabilization of large flexible space structures.