Analytic solutions of transcendental equations with application to automatics

• Autorzy: Górecki H. , Zaczyk M.

Identyfikatory

DOI

10.1515/acsc-2016-0027

• Języki publikacji: EN

Abstrakty

EN

In the paper the extremal dynamic error x(τ) and the moment of time τ are considered. The extremal value of dynamic error gives information about accuracy of the system. The time τ gives information about velocity of transient. The analytical formulae enable design of the system with prescribed properties. These formulae are calculated due to the assumption that x(τ) is a function of the roots s₁, ..., s_n of the characteristic equation.

Słowa kluczowe

EN

extremal problems; characteristic equation; transmittance

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2016
• Tom: Vol. 26, no. 4
• Strony: 497--513
• Opis fizyczny: Bibliogr. 12 poz., rys., wykr., wzory

Twórcy

autor

Górecki H.

• AGH University of Science and Technology, Department of Automatics and Biomedical Engineering, Al. Mickiewicza 30, 30-059 Krakow, Poland

autor

Zaczyk M.

• AGH University of Science and Technology, Department of Automatics and Biomedical Engineering, Al. Mickiewicza 30, 30-059 Krakow, Poland

Bibliografia

• [1] H. Górecki and A. Turowicz: Optimum transient problem in linear automatic control system. Proc. of the 1st IFAC Congress, Moscow, pp.59-61, Published by Butterworths London, (1960).
• [2] H. Górecki and M. Zaczyk: Decomposition method and its application to the extremal problems. Archives of Control Sciences, 26(1) (2016), 49-67.
• [3] H. Górecki: Analytic solution of transcendental equations. Int. J. Applied Mathematics and Computer Science, 20(4), (2010), 671-677.
• [4] H. Górecki and M. Zaczyk: Design of systems with extremal dynamic properties. Bulletin of the Polish Academy of Sciences, Technical Sciences, 61(3), (2013), 563-567.
• [5] H. Górecki: Algebraic condition for decomposition of large-scale linear dynamic systems. Int. J. Applied Mathematics and Computer Science, 19(1), (2009), 107-111.
• [6] H. Górecki and M. Zaczyk: Design of the oscillatory systems with the extremal dynamic properties. Bulletin of the Polish Academy of Sciences, Technical Sciences, 62(2), (2014), 241-253.
• [7] T. Kaczorek: Theory of control. PWN, Warsaw (1977), (in Polish).
• [8] H. Kobayashi: Output overshoot and pole-zero configuration. Proc. 12th IFAC Congress, Sydney, 3 (1993), 73-76.
• [9] H. Kobayashi and E. Shimemura: Some properties of optimal regulators and their applications. Int. J. Control, 33(4), (1981), 587-599.
• [10] W. Mitkowski: Stability of Dynamical Systems. PWN, Warsaw (1991), (in Polish).
• [11] I. Koźniewska: Recurent Equations. PWN, Warsaw (1972), (in Polish).
• [12] M. Ziółko: Modeling of Wave Phenomena. AGH, University Press, Krakow (2000), (in Polish).