Complete parametric approach for eigenstructure assignment in a class of second-order linear systems. (English) Zbl 1009.93036

Duan, Guang-Ren; Liu, Guo-Ping

Automatica 38, No. 4, 725-729 (2002).

This paper considers eigenstructure assignment via proportional-plus-derivative feedback control in a class of second-order linear systems in the form of \(\ddot q- A\dot q- Cq= Bu\). Under the controllability condition of the matrix pair \([A,B]\), simple complete parametric expressions for both the closed-loop eigenvector matrices and the feedback gain matrices are established in terms of the closed-loop eigenvalues and a group of parameter vectors. Both the closed-loop eigenvalues and the group of parameters can be properly chosen to produce a closed-loop system with some additional desired specifications. The main computations involved are the Smith form reductions of two polynomial matrices, or two sets of singular value decompositions when the closed-loop eigenvalues are known a priori. A third-order illustrative example is presented.

Reviewer: Petko Hr.Petkov (Sofia)

MSC:

93B55	Pole and zero placement problems
93B60	Eigenvalue problems

Keywords:

second-order systems; eigenstructure assignment; proportional-plus-derivative controllers; closed-loop eigenvector; closed-loop eigenvalues; Smith form reductions; singular value decompositions

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