Eigenvalue Assignment in Second order systems Using Sylvester equations: Approach

Elmer R. L. Villarreal, Andres O. Salazar, Thiago F. do Nascimento, Lucas D. da Silva, Walter M. Rodrigues

Resumo


Second-order systems are those whose models can be written by a second-order differen-tial equation. That is, they are those that have two poles. The present article proposes an approach to solve the output feedback control with eigenvalues for second-order systems using Sylvester equa-tions. The matrices are prescribed in advance and depend greatly on the controllability conditions,being assigned the system’s observability eigenvalues. Furthermore, the real-value spectral decom-position T (λ) is explored to establish conditions so that the feedback gain matrices do not overflow over the eigenvalue assignment. However, it should be noted that the proposed algorithms may present complex computational problems. Two theorems were presented using Sylvester equations.The algorithms were implemented based on Sylvester equations, and examples were presented with their conclusions.


Palavras-chave


Sylvester equations;Eigenvalue assignment;Output feedback control;Second order system.

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Referências


A. Bhaya and C. Desoer. “On the design of large flexible space structures (LFSS)”. In: IEEE Transactions on Automatic Control AC30 (1985), pp. 1118–1120. doi: 10.1016/0024- 3795(93)90467-3.

E. K. Chu and B. N. Datta. “Numerically robust pole assignment for second-order systems”. In: International Journal of Control 64(4) (1996), pp. 1113–1127. doi: 10.1080/ 00207179608921677.

B. N. Datta, W. W. Lin, and J. N. Wang. “Robust and minimum gain partial pole assignment in vibrating structures with aerodynamics effects”. In: Proceedings IEEE Conf. Decision Control 1 (2003), pp. 2358–2363. doi: 10.1109/CDC.2003.1272971.

E. R. L. Villarreal, J. A. V. Ruiz, and E. M. Hemerly. “Static Output Feedback Stabilization using Invariant Subspaces and Sylvester Equations”. In: TEMA Tend. Mat. Apl. Comput 10 (1) (2009), pp. 99–110. doi: 10.5540/tema.2009.010.01.0099.

E. R. L. Villarreal, A. O. Salazar, and P. V. F. Vieira. “Approach to partial eigenvalue assignment using Sylvester equation in system-second order”. In: 2021 IEEE International Conference on Automation/XXIV Congress of the Chilean Association of Automatic Control (ICA-ACCA) 1 (2021), pp. 1–6. doi: 10.1109/ICAACCA51523.2021.9465267.

E. R. L. Villarreal et al. “Impulse elimination for singular second-order system: approach”. In: 2021 IEEE International Conference on Automation/XXIV Congress of the Chilean Association of Automatic Control (ICA-ACCA) 1 (2021), pp. 1–6. doi: 10. 1109/ICAACCA51523.2021.9465327.

A. G. Wu et al. “Solving the generalized Sylvester matrix equation AV+BW=EVF via a Kronecker map”. In: Applied Mathematics Letters 21 (10) (2008), pp. 1069–1073. doi: 10.1016/j.aml.2007.12.004.

J. Zhang, Y. Yuan, and H. Liu. “An Approach to Partial Quadratic Eigenvalue Assignment of Damped Vibration Systems Using Static Output Feedback”. In: International Journal of Structural Stability and Dynamics 18(1) (2018), pp. 1–18. doi: 10 . 1142 / S0219455418500128.




DOI: https://doi.org/10.5540/03.2022.009.01.0249

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