An algorithm for the partial multi-input pole assignment problem of a second-order control system

In this paper, we present a new algorithm for the multi-input pole assignment problem of a control system modeled by a system of second-order differential equations. Specifically, given the damped symmetric definite second-order control system M d(2)/dt(2) v + C d/dt v + Kv = o, and a set {mu(k)}(2p)(k=1) of 2p numbers, closed under complex conjugation, the algorithm finds matrices F and G such that the spectrum of the closed-loop pencil (P) over cap(lambda) = lambda(2)M + (C - BFT) + (K - BG(T)) contains the set {mu(k)}(2p)(k=1) and the complementary part of the spectrum has non-positive real part; that is, no spillover occurs. The algorithm does not require explicit knowledge of the eigenvalues and eigenvectors of the associated open-loop quadratic pencil. This is in sharp contrast with the traditional approach [6], [1]. It is composed of numerically effective tools of matrix computations such as the Cholesky-factorization, singular value decomposition, and solutions of linear systems. The paper is a sequel of the recent work on nonmodal and partial-modal approaches for the control problems of second-order control systems: [4], [2], and [5].