ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Control of Spectrum of Second-order Matrix System with Dynamic Output Feedback

Author(s):

Evgenii Alexandrovich Perepelkin

Saint-Petersburg State University of Aerospace Instrumentation
professor, doctor of technical sciences

eap@list.ru

Abstract:

The control problem of the spectrum of a linear matrix second-order system with one-input and multi-output feedback in the form of a first-order dynamic compensator is solved. Necessary and sufficient conditions for the existence of a solution to the problem are considered and an algorithm for calculating the feedback parameters is described. A numerical example is given. A feature of the proposed approach is that the compensator contains only one first-order equation, in contrast to classical observers and full- and reduced-order dynamic compensators.

Keywords

References:

  1. Polyak B. T. Shcherbakov P. S. Hard problems in linear control theory: possible approaches to their solution. Autom. Remote Control. 66(5), 2005, pp. 681-718
  2. Eremenko A., Gabrielov A. Pole placement by static output feedback for generic linear systems. SIAM J. Control Optim. 41(1), 2002, pp. 303-312
  3. Sontag E. Mathematical Control Theory: Deterministic Finite Dimensional Systems. Springer-Verlag, 1998
  4. Chu E. K. Pole assignment for second-order systems. Mechanical Systems and Signal Processing. 16(1), 2002. pp. 39-59
  5. Henrion D., Sebek M., Kucera V. Robust pole placement for second-order systems: An LMI approach. Kybernetika. 41(1), 2005, pp. 1-14
  6. Abdelaziz T. H. S. Robust pole placement for second-order linear systems using velocity-plus-acceleration feedback. IET Control Theor. Appl. 7(14), 2013, pp. 1843-1856
  7. Abdelaziz T. H. S. Robust pole assignment using velocity-acceleration feedback for second-order dynamical systems with singular mass matrix. ISA Trans. 57, 2015, pp. 71-84
  8. Zhang J., Ouyang H., Zhang Y., Ye J. Partial quadratic eigenvalue assignment in vibrating systems using acceleration and velocity feedback. Inverse Problems in Science and Engineering. 23(3), 2015, pp. 479-497
  9. Perepelkin E. A. Pole assignment problem for a second-order system. Diff. Equat. 53, 2017, pp. 1524-1527
  10. Perepelkin E. A. Pole assignment for second-order system by acceleration feedback. Vestnik Tomskogo gosudarstvennogo universiteta. Upravlenie vychislitelnaja tehnika i informatika [Tomsk State University Journal of Control and Computer Science]. 44, 2018, pp. 25-30. (In Russ. )
  11. Bernstein D. S. Matrix Mathematics: Theory, Facts, and Formulas. Princeton University Press, 2009

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