A new method for analytic determination of extremum of the transients in linear systems

• Autorzy: Górecki H.
• Języki publikacji: EN

Abstrakty

EN

The relation between extremal values of the error and the coefficients of its differential equations is one of the central problems of control systems in chemical industry, because extremal values of the error sometimes cause serious damages to the environment or to the system itself. Analytical formulae for the determination of these values are known only for the second-order systems. In this paper a method which permits to determine extremal values of the error in higher-order systems is proposed.

Słowa kluczowe

EN

transcendental equations; extremal dynamic error; linear stationary system; parametric optimization; analytic formulae; discriminants of exponential functions; Vandermonde's determinant; Viete's formulae; process control

PL

równanie przestępne; układ stacjonarny liniowy; optymalizacja parametryczna; formułka obliczeniowa; wyróżnik funkcji wykładniczej; wyznacznik Vandermondesa; wzór Vietesa

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2004
• Tom: Vol. 33, no 2
• Strony: 275--295
• Opis fizyczny: Bibliogr. 14 poz., rys.

Twórcy

autor

Górecki H.

• University of Technology A.G.H., al.Mickiewicza 30, B1, rm-305, PL-30-059 Cracow, Poland,

Bibliografia

• Górecki, H. (1965) Overshootings in linear and nonlinear control systems. (in Polish) Archive of Automatics and Telemechanics X (2), 95-102.
• Górecki, H. (1966a) About some linear adaptive control systems. Proc. IX. Int. Convention on Automation and Instrumentation, FAST, Milano,Italy, 103-123.
• Górecki, H. (1966b) Extreme values of transients in linear and nonlinear control systems. Proc. 3rd IFAC Congress, London, Book 2, Session XXIII,1, G1-G4.
• Górecki, H. (1966c) Overshoots in linear control systems. Archives of Control Sciences 5 XLI, (3-4).
• Górecki, H. (1993) Optymalizacja systemów dynamicznych (Optimization of dynamical systems; in Polish). WNT, Warszawa.
• Górecki, H. (2000) An electric network chain with feedbacks.Control and Cybernetics 29 (1).
• Górecki, H. and Turowicz, A. (1965) Optimum transient problem in linear automatic control systems. Automatic and Remote Control, Proc. 1st IFAC Congress, Moscow, V.I, 59-61.
• Górecki, H. and Turowicz, A. (1966a) Extremal transients in linear automatic control systems, (in Polish). Scientific Bulletins of the University of Mining and Metallurgy, Automatics 1 (112), 11-67.
• Górecki, H. and Turowicz, A. (1966b) On the extremal transient processesin linear systems. Bulletin de l’Academie Polonaise des Sciences, Serie des Sciences Math., Astr. et Phys. XIV (11), 609-613.
• Górecki, H. and Turowicz, A. (1968) Determination of the dependence of the maximal deviation of the controlled quantity and the time of deviationon the parameters in linear control systems (in Russian). Avtomatika iTelemekhanika (6), 179-181.
• Meerow, N.W.W. (1956) Vvedeniye v dinamiku avtomaticheskego regulirovaniya elektricheskikh mashin (Introduction into the dynamics of automatic control of electric machines; in Russian). I.A.N. SSSR, Moskva.
• Sę̧dziwy, S. (1967) Extremal transient problems in linear systems. Bulletinde I’Academie Polonaise des Sciences, Serie des Sciences Math., Astr. et Phys. XV (8), 557-561.
• Sę̧dziwy, S. (1969) On extremal transient in linear systems. Bulletin deI’Academie Polonaise des Sciences, Serie des Sciences Math., Astr. et Phys. XVII (3), 141-145.
• Zaczyk, M. (1997) Overshoots in 2-nd class of linear control systems. Archivesof Control Sciences 6 XLII (3-4).