Geodesic
Eigenstructure assignment by proportional-plus-derivative feedback for second-order linear control systems
Kybernetika, Tome 41 (2005) no. 5, pp. 661-676 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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This paper introduces a complete parametric approach for solving the eigenstructure assignment problem using proportional-plus-derivative feedback for second-order linear control systems. In this work, necessary and sufficient conditions that ensure the solvability for the second-order system are derived. A parametric solution to the feedback gain matrix is introduced that describes the available degrees of freedom offered by the proportional-plus-derivative feedback in selecting the associated eigenvectors from an admissible class. These freedoms can be utilized to improve robustness of the closed-loop system. The main advantage of the described approach is that the problem is tackled directly in the second-order form without transformation into the first-order form and without mass matrix inversion and the computation is numerically stable as it uses only the singular value decomposition and simple matrix transformation. Numerical examples are included to show the effectiveness of the proposed approach.
This paper introduces a complete parametric approach for solving the eigenstructure assignment problem using proportional-plus-derivative feedback for second-order linear control systems. In this work, necessary and sufficient conditions that ensure the solvability for the second-order system are derived. A parametric solution to the feedback gain matrix is introduced that describes the available degrees of freedom offered by the proportional-plus-derivative feedback in selecting the associated eigenvectors from an admissible class. These freedoms can be utilized to improve robustness of the closed-loop system. The main advantage of the described approach is that the problem is tackled directly in the second-order form without transformation into the first-order form and without mass matrix inversion and the computation is numerically stable as it uses only the singular value decomposition and simple matrix transformation. Numerical examples are included to show the effectiveness of the proposed approach.
Classification : 93B55, 93C35, 93D15
Keywords: eigenstructure assignment; second-order systems; proportional- plus-derivative feedback; feedback stabilization; parameterization 
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     title = {Eigenstructure assignment by proportional-plus-derivative feedback for second-order linear control systems},
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Abdelaziz, Taha H. S.; Valášek, Michael. Eigenstructure assignment by proportional-plus-derivative feedback for second-order linear control systems. Kybernetika, Tome 41 (2005) no. 5, pp. 661-676. http://geodesic.mathdoc.fr/item/KYB_2005_41_5_a6/

[1] Balas M. J.: Trends in large space structure control theory: fondest hopes, wildest dreams. IEEE Trans. Automat. Control 27 (1982), 522–535 | DOI | Zbl

[2] Bhaya A., Desoer C.: On the design of large flexible space structures (LFSS). IEEE Trans. Automat. Control 30 (1985), 1118–1120 | DOI | Zbl

[3] Chu E. K.: Pole assignment for second-order systems. Mechanical System & Signal Processing 16 (2002), 1, 39–59 | DOI | Zbl

[4] Chu E. K., Datta B. N.: Numerically robust pole assignment for second-order systems. Internat. J. Control 64 (1996), 4, 1113–1127 | DOI | MR | Zbl

[5] Diweker A. M., Yedavalli R. K: Stability of matrix second-order systems: new conditions and perspectives. IEEE Trans. Automat. Control 44 (1999), 9, 1773–1777 | DOI | MR

[6] Duan G. R., Liu G. P.: Complete parametric approach for eigenstructure assignment in a class of second order system. Automatica 38 (2002), 725–729 | DOI | MR

[7] Henrion D., Šebek, M., Kučera V.: Robust pole placement for second-order systems: an LMI approach. In: Proc. IFAC Symposium on Robust Control Design, Milan, Italy, 2003

[8] Y. Y. Kim, Kim H. S., Junkins J. L.: Eigenstructure assignment algorithm for mechanical second-order systems. J. Guidance 22 (1999), 5, 729–731 | DOI

[9] Laub A. J., Arnold W. F.: Controllability and observability criteria for multivariable linear second-order models. IEEE Trans. Automat. Control 29 (1984), 163–165 | DOI | MR | Zbl