Numerical Analysis of Stability of the Variable Parameters, Fractional Order Transfer Functions

eng Article in English DOI: 10.14313/PAR_260/17

send Krzysztof Oprzędkiewicz AGH University, al. A. Mickiewicza 30, 30-059 Krakow, Poland

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Abstract

In the paper the numerical analysis of the practical stability of the new, variable parameters, fractional order transfer function models is addressed. The considered transfer functions are constructed using discrete, variable parameters FOBD approximation. This implies that only sufficient unstability or equivalently necessary stability conditions can be given. They do not assure full and unique information about stability. The considered algorithm uses interval approach and Monte Carlo method. The application of interval analysis allows to quickly detect unstability at vertices of tested area. The proposed algorithm allows to check the stability of predefined range of parameters as well as to estimate of stability areas.

Keywords

FOBD approximation, fractional order transfer function, Monte Carlo Method, stability, time-variant system

Numeryczna analiza stabilności transmitancji ułamkowego rzędu o zmiennych parametrach

Streszczenie

W artykule zaprezentowano numeryczną analizę praktycznej stabilności nowych modeli transmitancyjnych niecałkowitego rzędu o zmiennych parametrach. Rozważane transmitancje są budowane z wykorzystaniem aproksymacji FOBD o zmiennych parametrach. Postać transmitancji implikuje możliwość podania tylko dostatecznych warunków niestabilności lub równoważnie koniecznych warunków stabilności. To nie zapewnia pełnej i jednoznacznej informacji o stabilności. Proponowany algorytm numeryczny bazuje na podejściu przedziałowym i metodzie Monte Carlo. Podejście przedziałowe pozwala na szybkie wykrycie niestabilności na wierzchołkach testowanego obszaru. Proponowany algorytm pozwala na sprawdzenie stabilności w zadanym zakresie oraz na oszacowanie obszarów stabilności na płaszczyźnie parametrów modelu.

Słowa kluczowe

aproksymacja FOBD, metoda Monte Carlo, stabilność, system niestacjonarny, transmitancja ułamkowego rzędu

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