Design of the oscillatory systems with the extremal dynamic properties

• Autorzy: Górecki H. , Zaczyk M.

Identyfikatory

DOI

10.2478/bpasts-2014-0024

• Języki publikacji: EN

Abstrakty

EN

In this article the problem of determination of such coefficients a1, a2, ..., an and eigenvalues s1, s2, ..., sn of the characteristic equation which yield required extremal values of the solution x(t) at the extremal value τ of time is solved. The extremal values of x(τ ) and τ are treated as functions of the roots s1, s2, ..., sn. The analytical formulae enable us to design the systems with prescribed dynamic properties. For solution of the problem the properties of symmetrical equations are used. The method is illustrated by an example of the equation of 4-th degree. The regions of the different kinds of the roots: real, with one pair of complex and two pairs of complex roots are illustrated. A practical problem is shown.

Słowa kluczowe

EN

extremal dynamic properties; oscillatory systems; symmetrical equations; regions of the roots

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2014
• Tom: Vol. 62, nr 2
• Strony: 241--253
• Opis fizyczny: Bibliogr. 12 poz., tab., wykr.

Twórcy

autor

Górecki H.

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

autor

Zaczyk M.

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

Bibliografia

• [1] H. Górecki and A. Turowicz, “Optimum transient problem in linear automatic control systems”, Automatic and Remote Control, Proc. 1st IFAC Congress V.I., 59–61 (1965).
• [2] H. Górecki and A. Turowicz, “About some linear adaptive control systems”, Atti del IX Convegno dell’Automazione e Strumentazione tenutosi a Milano 1, 103–123 (1966).
• [3] A. Mostowski and M. Stark, Higher Algebra, Part 2, pp. 82–85 PWN, Warsaw, 1954, (in Polish).
• [4] H. Górecki and M. Zaczyk, “Design of systems with extremal dynamic properties”, Bull. Pol. Ac.: Tech. 61 (3), 563–569 (2013).
• [5] W. Byrski, Observation and Control in Dynamic Systems, UWN-D AGH, Kraków, 2007, (in Polish).
• [6] T. Kaczorek, “Design of single-input system for specified poles an zeros using gain elements”, Control Principles 2 (4), CDROM (1972).
• [7] H. Górecki and S. Białas, “Relations between roots and coefficients of the transcendental equations”, Bull. Pol. Ac.: Tech. 58 (4), 631–634 (2010).
• [8] B. Sikora and J. Klamka, “On constrained stochastic controllability of dynamical systems with multiple delays in control”, Bull. Pol. Ac.: Tech. 60 (2), 301–306 (2012).
• [9] J. Klamka, “Stochastic controllability of linear systems with delay in controlBull. Pol. Ac.: Tech. 55 (1), 23–29 (2007).
• [10] J. Klamka, “Controllability of dynamical systems”, Proc. XXX Int. Conf. SPETO-2007 1, CD-ROM (2007).
• [11] H. Górecki and M. Zaczyk, “Extremal dynamic errors in linear dynamic systems”, Bull. Pol. Ac.: Tech. 58 (1), 99–105 (2010).
• [12] H. Górecki, Optimization and Control of Dynamic Systems, UWND AGH, pp. 378–382 UWN-D AGH, Kraków, 2006, (in Polish)