Optimum approximation of high-order systems by low-order model with respect to the minimax objective function

• Autorzy: Layer E.

Warianty tytułu

PL

Optymalna aproksymacja systemów wysokiego rzędu za pomocą modelu rzędu niskiego ze względu na minimax założonego kryterium błędu

• Języki publikacji: EN

Abstrakty

EN

The paper presents a method of low-order optimum model determination for high-order systems, which minimises the maximum value of the objective function for a given order of a model. The method consists of two parts. In the first part an input signal is determined that maximises the assumed objective function defined on the difference between the system and model responses. In the second part, the optimisation of the low-order model parameters is performed, achieving a minimum value of the objective function for the input signal determined earlier. The main advantage of this method is that by using signals that maximise the assumed objective function during the optimisation process, the minimised value is made independent of the dynamic signals, which could occur at the input of the real system. As an example of the application of this method the optimum second-order model of a six-order system obtained for two different input signals and integral-square-error criterion as an objective function. In the case of the first signal there was only one constraint concerning its magnitude applied, whereas the other signal was matched to the dynamic behaviour of the high-order system, and two constraints on the magnitude and the rate of change were imposed.

PL

Artykuł przedstawia metodę wyznaczania optymalnego modelu niskiego rzędu odwzorowującego system rzędu wysokiego w sensie minimax założonego kryterium błęu. Metoda składa się z dwóch etapów. W pierwszym wyznacza się sygnał maksymalizujący założone kryterium błędu definiowanego na różnicy odpowiedzi modelu i systemu, natomiast w drugim etapie, za pomocą uprzednio wyznaczonego sygnału, optymalizuje się parametry modelu niskiego rzędu na minimum wartości przyjętego kryterium. Zaleta przedstawionej metody polega na tym, że zminimalizowana przez optymalny model maksymalna wartość błędu jest obowiązująca dla sygnałów o dowolnym kształcie, a zatem dla wszystkich sygnałów, które mogłyby się pojawić na wejściu systemu rzeczywistego. W przykładzie zastosowania omówionej metody przedstawiono wyniki optymalizacji modelu rzędu drugiego odwzorowującego system rzędu szóstego przy założeniu kwadratowo-całkowego kryterium błędu oraz dwóch klas sygnałów: - ograniczonych w amplitudzie oraz - ograniczonych w amplitudzie i prędkości narastania.

Słowa kluczowe

PL

optymalizacja; modele uproszczone; model dynamiczny; błąd; sygnały

• Wydawca: Polish Academy of Sciences, Committee on Electrical Engineering
• Czasopismo: Archives of Electrical Engineering
• Rocznik: 2002
• Tom: Vol. 51, nr 4
• Strony: 451--464
• Opis fizyczny: Bibliogr. 33 poz., rys.

Twórcy

autor

Layer E.

• Faculty of Electrical and Computer Engineering, Cracow University of Technology

Bibliografia

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