Class Of Second-order Linear Systems Research Articles

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 ̈ −A q ̇ −Cq=Bu using the proportional-plus-derivative feedback controller u=K 0q+K 1 q ̇ . 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.

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

This paper deals with eigenstructure assignment in the second-order linear systems using proportional plus derivative feedback controllers. Under the controllability condition of the matrix pair [A B], veiy simple, general, and complete parametric expressions in direct closed forms for both the closed-loop eigenvector matrix and the proportional and derivative feedback gains are proposed. The approach utilises 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.