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| Two parametric approaches for eigenstructure assignment in second-order linear systems |
| Guangren DUAN |
| (Center for Control Theory and Guidance Technology, Harbin Institute of Technology, P.O. Box 416, Harbin Heilongjiang 150001, China) |
| Abstract: |
| This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback . It is shown that the problem is closely related to a type of so-called second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effectiveness of the proposed approaches. |
| Key words: Second-order linear systems Eigenstructure assignment Proportional plus derivative feedback Parametric solutions Singular value decomposition Right factorization |
