Complete parametric approach for eigenstructure assignment in a class of second-order linear systems

This note deals with eigenstructure assignment in the second-order linear system q double over dot - Aq over dot - Cq = Bu using the proportional-plus-derivative feedback controller it = K(0)q + K(1)q over dot. Under the controllability condition of the matrix pair [A B]. very simple. general. and complete parametric expressions in direct closed forms for both the closed-loop eigenvector matrix and the feedback gains are established in terms of the closed-loop eigenvalues and a group of parameter vectors. The main computations are two sets of elementary matrix transformations. which can be replaced by a series of singular value decompositions when the closed-loop eigenvalues are chosen a Priori. The approach utilizes directly the original system data A, B and C, and involves manipulations on only, n-dimensional matrices. An example illustrates the effect of the proposed approach. (C) 2002 Elsevier Science Ltd. All rights reserved.