Extremal values of differential equations with application to control systems

• Autorzy: Górecki Henryk , Zaczyk Mieczysław

Identyfikatory

DOI

10.24425/bpasts.2021.136041

• Języki publikacji: EN

Abstrakty

EN

In the paper, maximal values xe(τ) of the solutions x(t) of the linear differential equations excited by the Dirac delta function are determined. The analytical solutions of the equations and also the maximal positive values of these solutions are obtained. The analytical formulae enable the design of the system with prescribed properties. The complementary case to the earlier paper is presented. In an earlier paper it was assumed that the roots si are different, and now we consider the case when s1=s2=...=sn.

Słowa kluczowe

EN

extremal values; characteristic equation; transfer function; Dirac's impulse; multiple root

PL

wartości ekstremalne; równanie charakterystyczne; funkcja transferu; impuls Diraca

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2021
• Tom: Vol. 69, nr 1
• Strony: art. no. e136041
• Opis fizyczny: Bibliogr. 16 poz., rys.

Twórcy

autor

Górecki Henryk

• AGH University of Science and Technology, Department of Automatics and robotics, Al. Mickiewicza 30, 30-059 Kraków, Poland

autor

Zaczyk Mieczysław

• AGH University of Science and Technology, Department of Automatics and robotics, Al. Mickiewicza 30, 30-059 Kraków, Poland

Bibliografia

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• [3] H. Górecki and M. Zaczyk: “Design of the oscillatory systems with the extremal dynamic properties”, Bull. Pol. Ac.: Tech. 62(2), 241‒253 (2014).
• [4] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
• [5] K.L. Moore and S.P. Bhattacharyya, “A technique for choosing zero locations for minimal overshoot”, Proceedings of the 28th IEEE Conference on Decision and Control, Tampa, FL, USA 2, 1989, pp. 1230‒1233.
• [6] H. Górecki and M. Zaczyk, “Positive extremal values and solutions of the exponential equations with application to automatics”, Bull. Pol. Ac.: Tech. 68(3), 585‒591 (2020).
• [7] H. Górecki and M. Zaczyk, “Extremal dynamic errors in linear dynamic systems”, Bull. Pol. Ac.: Tech. 58(1), 99‒105 (2010).
• [8] H. Górecki and S. Białas, “Relations between roots and coefficients of the transcendental equations”, Bull. Pol. Ac.: Tech. 58(4), 631‒634 (2010).
• [9] H. Górecki and M. Zaczyk, “Design of systems with extremal dynamic properties”, Bull. Pol. Ac.: Tech. 61(3), 563‒567 (2013).
• [10] S. Białas and H. Górecki, “Generalization of Vieta’s formulae to the fractional polynomials, and generalizations the method of GraeffeLobactievsky”, Bull. Pol. Ac.: Tech. 58(4), 625‒629 (2010).
• [11] T. Kaczorek, “A new method for determination of positive realizations of linear continuous-time systems”, Bull. Pol. Ac.: Tech. 66(5), (2018).
• [12] T. Kaczorek, “Global stability of nonlinear feedback systems with positive descriptor linear part”, Bull. Pol. Ac.: Tech. 67(1), 45‒51 (2019).
• [13] T. Kaczorek, “Stability of interval positive continuous-time linear systems”, Bull. Pol. Ac.: Tech. 66(1), 31‒35 (2018).
• [14] J. Osiowski, An outline of operator calculus. Theory and applications in electrical engineering, WNT, Warszawa, 1965 [in Polish].
• [15] H. Górecki, Optimization and Control of Dynamic Systems, Springer, 2018.
• [16] D.C. Kurtz, “Condition for all the roots of a polynomial to be real”, The American Mathematical Monthly 99(3), 259‒263 (1992).

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).