MODAL CONTROLLABILITY OF ONE TWO-DIMENSIONAL DELAYED SYSTEM IN A SPECIAL CASE

UDC 517.977

 

Yakimenka Andrei Aliaksandravich – PhD (Physics and Mathematics), Associate Professor, Assistant Professor, the Department of Higher Mathematics. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: yakimenko@belstu.by

 

DOI: https://doi.org/ 10.52065/2520-6141-2024-284-1.

Key words: retarded systems, modal control, regulators, feedback control, delay.

For citation: Yakimenka A. A. Modal controllability of one two-dimensional delayed system in a special case. Proceedings of BSTU, issue 3, Physics and Mathematics. Informatics, 2024, no. 2 (284), pp. 5–9 (In Russian). DOI: 10.52065/2520-6141-2024-284-1.

Abstract

The publication considers the solution of the modal controllability problem for a two-dimensional stationary dynamic system with a retarded argument with one input and two commensurate delays in one special case. The definition of the modal control problem for the system under study is given. The modal control problem is one of the main problems of control theory. Such a problem has been well studied for systems without delay. For systems with a retarded argument and neutral type systems, the solution of the modal control problem is much more complicated. This is due to the fact that the state space of such systems is usually infinite-dimensional. The article obtains a solution to the problem for certain values of the parameters of the system with delay under study. Feedback-type controllers are also obtained that solve the modal control problem for the system under study. These controllers are found in the frequency domain as elementary functions of the system coefficients. Below are the rules according to which the obtained controllers pass from the frequency domain to feedback-type controllers for the system under study. An illustrative example of solving the modal control problem for the system under study is given. A list of literature is given in which the modal control problem is solved for other delayed systems and neutral type systems.

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References

  1. Marchenko V. M. On problem of modal control in linear systems with delay. Doklady Akademii nauk BSSR [Reports of the BSSR Academy of Science], 1978, no. 5, pp. 401–404 (In Russian).
  2. Yakimenka A. A. Modal control for one delayed system. Trudy BGTU [Proceedings of BSTU], 2013, no. 6: Physics and Mathematics. Informatics, pp. 3–7 (In Russian).
  3. Yakimenka A. A. Modal control for one neutral type system. Trudy BGTU [Proceedings of BSTU], 2016, no. 6: Physics and Mathematics. Informatics, pp. 18–21 (In Russian).
  4. Yakimenka A. A. Modal control for one neutral type system in general cyclic case. Trudy BGTU [Proceedings of BSTU], issue 3, Physics and Mathematics. Informatics, 2017, no. 2 (200), pp. 25–27 (In Russian).
  5. Yakimenka A. A. Modal control for one neutral type system in general cyclic case with double roots. Trudy BGTU [Proceedings of BSTU], issue 3, Physics and Mathematics. Informatics, 2018, no. 1 (206), pp. 5–8 (In Russian).
  6. Yakimenka A. A. Modal controllability of one two-dimensional delayed system. Proceedings of BSTU, issue 3, Physics and Mathematics. Informatics, 2023, no. 1 (266), pp. 15–19. DOI: 10.52065/2520- 6141-2023-266-1-3 (In Russian).
  7. Yakimenka A. A. Modal controllability of one two-dimensional delayed system in the case of multiple roots. Trudy BGTU [Proceedings of BSTU], issue 3, Physics and Mathematics. Informatics, 2023, no. 2 (272), pp. 18–22. DOI: 10.52065/2520-6141-2023-272-2-3 (In Russian).

 17.04.2024