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

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

About History Editorial Page Addresses Scope Editorial Staff Submission Review For Authors Publication Ethics Issues Русская версия

Synthesis of Control Providing Various Dynamic Properties of Free and Forced Motion of a Multidimensional System

Author(s):

Nikolay Evgenievich Zubov

Doctor of Technical Sciences, Professor, Professor of Department of Automatic Control Systems,
Dean of Rocket and Space Techniques Faculty
Bauman Moscow State Technical University (Bauman MSTU),
Professor of Postgraduate Studies
S.P. Korolev Rocket and Space Corporation “Energia” (S.P. Korolev RSC “Energia”)

Nik.Zubov@gmail.com

Vladimir Nikolaevich Ryabchenko

Doctor of Technical Sciences, Associate Professor,
Professor of Department of Automatic Control Systems,
Bauman MSTU

RyabchenkoVN@yandex.ru

Alexey Vladimirovich Lapin

Candidate of Technical Sciences,
Associate Professor of Department of Automatic Control Systems at Bauman MSTU,
engineer at State Research Institute of Aviation Systems (GosNIIAS)

AlexeyPoeme@yandex.ru

Irek Minyrakhmanovich Galiaskarov

Candidate of Technical Sciences
chief engineer at the Centre of Engineering and Management of Construction of
the Unified Energy System (CEMC UES)

Irek_Galiaskarov@mail.ru

Abstract:

A feedback control law with a precompensator is considered for a multidimensional dynamical system. A special feature of the control synthesis is that the transfer matrix of the precompensator is rectangular or its determinant is equal to zero. Thus, the problem of irregular causal control laws synthesis is considered. The paper describes a control synthesis method that provides various spectral contents (dynamic properties) of a linear dynamical system at free and forced motion. To find a solution we apply the system embedding technology. The improvement of embedding technology methods is shown: by means of irregular control laws we provide various spectra of free and forced components in the state or output vectors of a dynamical system. Theorems on the synthesis of irregular control of a dynamic system by output and on physical realizability of the control law by means of a precompensator are formulated. Methodic examples of the synthesis are given.

Keywords

References:

  1. Bukov, V. N., Goryunov, S. V., and Ryabchenko V. N. Analiz i Sintez Matrichnykh Lineinykh Sistem. Sravneniye Podkhodov [Analysis and Synthesis of Matrix Linear Systems. Comparing Approaches]. Avtomatika i Telemekhanika, iss. 11, p. 3-43, 2000. (In Russian)
  2. Osetinskii, N. I. Obzor Nekotorykh Rezul’tatov i Metodov v Sovremennoi Teorii Lineinykh Sistem [A Review of Some Results and Methods in the Modern Theory of Linear Systems]. Matematicheskiye Metody v Teorii Sistem, p. 328-379, 1989. (In Russian)
  3. Tannenbaum, A. Invariance and System Theory: Algebraic and Geometric Aspects. Lecture Notes in Mathematics. New-York: Springer-Verlag, 1981
  4. Aling, A., and Schumacher, J. M. A Nine Fold Canonical Decomposition for Linear System. Int. J. Control, iss. 39, p. 779-805, 1984
  5. Morse, A. S. Structural Invariants of Linear Multivariable Systems. SIAM J. Control, iss. 11, p. 446-465, 1973
  6. Hautus, M. L. J., and Heymann, H. Linear Feedback Decoupling: Transfer Function Analysis. IEEE Trans. Automat. Control, p. 823-832, 1983
  7. Lin, Ch. -An, and Hsien, T. -Fu. Decoupling Controller Design for Linear Multivariable Plants. IEEE Trans. Automat. Control, vol. 36, iss. 4, p. 485-489, 1991
  8. Kucera, V., and Toledo, E. C. A Review of Stable Exact Model Matching by State Feedback. 22nd Mediterranean Conf. on Control and Automat., p. 85-90, 2014
  9. Toledo, E. C., and Leon, R. J. J. Feedback Decoupling of Linear Multivariable Systems. IEEE Latin America Trans., vol. 13, iss. 8, p. 2529-2537, 2015
  10. Commault, C., Lafay, J. F., and Malabre, M. Structure of Linear Systems. Geometric and Transfer Matrix Approaches. Kybernetika, vol. 27, iss. 3, p. 170-185, 1991
  11. Ryabchenko, V. N. Embedding of Systems. Irregular Control Laws. Autom. Remote Control, vol. 62, iss. 7, p. 1192-1203, 2001
  12. Misrikhanov M. Sh., and Ryabchenko V. N. Kauzal’nyye i Antikauzal’nyye Diskretnyye Dinamicheskiye Sistemy [Causal and Anticausal Discrete Dynamic Systems]. Vestnik IGEU, iss. 6, p. 120-127, 2004. (In Russian)
  13. Zubov, N. E., Mikrin, E. A., and Ryabchenko, V. N. Matrichnye Metody v Teorii i Praktike Sistem Avtomaticheskogo Upravleniya Letatel’nykh Apparatov [Matrix Methods in Theory and Practice of Flying Vehicles Automatic Control Systems]. Moscow, Bauman MSTU Publ., 2016. 666 p. (In Russian)
  14. Cohn, P. M. Free Rings and their Relations. London: Academic Press, 1985. 588 p
  15. Malcolmson P. A Prime Matrix Ideal Yields a Skew Field. J. London Math. Soc., vol. 18, iss. 2, p. 221-233, 1978
  16. Malcolmson, P. Weakly Finite Matrix Localization. J. London Math. Soc., vol. 48, iss. 1, p. 31-38, 1993
  17. Bukov, V. N., and Ryabchenko, V. N. Vlojeniye System. Promatritsy [System Embedding. Pro-Matrices]. Avtomatika I Telemekhanika, iss. 4, p. 20-33, 2000. (In Russian)
  18. Bronnikov, A. M., Bukov, V. N., Ryabchenko, V. N., and Zubov, N. E. Algebraic Singularities of Dynamic Systems Associated with Zero Divisors of their Transfer Matrices. J. Comput. Syst. Sci. Int., vol. 43, iss. 3, p. 351-359, 2004
  19. Zubov, N. E., Misrikhanov, M. Sh., and Ryabchenko, V. N. Postkompensatsiya v Zadachakh Upravleniya Dvijeniyem Letatel’nykh Apparatov [Post-Compensation in the Tasks of Controlling the Flying Vehicles Motion]. Korolev: RSC “Energia” Publ., 2015. 132 p. (In Russian)
  20. Mikrin, E. A., Zubov, N. E., Lapin, A. V., Ryabchenko, V. N. Analytical formula of calculating a controller for linear SIMO-system. Differencialnie Uravnenia i Protsesy Upravlenia, 2020, (1), p. 1-11
  21. Mikrin, E. A., Ryabchenko, V. N., Zubov, N. E., Lapin, A. V. Analysis and synthesis of dynamic MIMO-system based on band matrices of special type. Differencialnie Uravnenia i Protsesy Upravlenia, 2020, (2), p. 1-14
  22. Zubov, N. E., Lapin, A. V., Ryabchenko, V. N. On relation between modal controllability of dynamic MIMO-system by output and a type of matrices with desirable spectra. Differencialnie Uravnenia i Protsesy Upravlenia, 2021, (2), p. 1-12

Full text (pdf)