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Dwupunktowe metody identyfikacji modeli FOLPD używanych do aproksymacji dynamiki układów wieloinercyjnych

Byrski Jędrzej

Elektronika : konstrukcje, technologie, zastosowania

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2023

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Vol. 64, Nr 6

32--37

PL

W artykule zostaną przedstawione nowe proste wzory szybkiego wyznaczania stałej czasowej T i opóźnienia czasowego τ modelu FOLPD (First Order Lag Plus Delay). Takie modele są bardzo przydatne do szybkiej oceny dynamiki wieloinercyjnych systemów wysokiego rzędu. Rozpatrzone zostaną dwa przypadki. W pierwszym, zidentyfikowany model FOLPD powinien aproksymować dynamikę dowolnego nieznanego układu wieloinercyjnego. W drugim przypadku zostaną zidentyfikowane parametry takiego modelu FOLPD, który będzie dobrze przybliżał układ inercyjny drugiego rzędu o znanych stałych czasowych T₁, T₂. W obu przypadkach identyfikacja modelu FOLPD będzie wynikać z najlepszego dwupunktowego dopasowania odpowiedzi skokowych jakiegoś systemu i modelu FOLPD. W pierwszym przypadku przedstawione zostaną dwie tabele dla znanych jak i dla nowych formuł identyfikacyjnych na T i τ. W drugim przypadku zostaną podane gotowe wzory analityczne na T i τ w funkcji znanych stałych czasowych T₁ i T₂, bez konieczności aktywnych eksperymentów.

EN

In the paper the new simple formulas for the fast determination of the time constant T and the time delay τ of the First Order Lag Plus Delay (FOLPD) model will be presented. Such models are very useful for quick evaluation of the high-order multi-inertial systems dynamics. Two cases will be considered. In the first, the identified FOLPD model should approximate the dynamics of an unknown multi-inertial system. In the second case, the parameters of FOLPD model will be identified, which will well approximate the second-order inertial system with known time constants T₁, T₂ In both cases, the identification of the FOLPD model will result from the best two-point fit of the step responses of some system and the FOLPD model. In the first case, two tables will be present- ed for known and for new identification formulas for T and τ In the second case, ready-made analytical formulas for T and τ as a function of the known time constants T₁ and T₂ will be given, which will eliminate the need of performing active experiments.

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State estimators and observers for continuous and discrete linear systems. Part 2. Integral observers for exact state reconstruction

Byrski Jędrzej, Byrski Witold

Science, Technology and Innovation

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2019

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Vol. 5, no. 2

23--33

EN

In the paper, the exact state observers will be presented. The state estimators and observers can be used in technical processes for many purposes like the fault detection and diagnosis, the implementation of the state controllers, and soft reconstruction of inaccessible for measurements variables of the system. As the standard, for continuous systems the differential estimators of Kalman filter or Luenberger type observer are commonly used. However, if the initial conditions of the real state are unknown, both estimators guarantee only an asymptotic quality of the real state tracking. The paper presents another type of the state observers, which for continuous system have the structure given by two integral operators. Based on measurements of the system input and output signals on some predefined finite time interval T, they can reconstruct the initial state exactly. In on-line version, the exact state reconstruction is performed continuously for every t, based on special procedure executed within two moving windows of width T, on sliding time interval [t-T, t].

3

An adaptive identification method based on the modulating functions technique and exact state observers for modeling and simulation of a nonlinear MISO glass melting process

Byrski Witold, Drapała Michał, Byrski Jędrzej

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 4

739--757

EN

The paper presents new concepts of the identification method based on modulating functions and exact state observers with its application for identification of a real continuous-time industrial process. The method enables transformation of a system of differential equations into an algebraic one with the same parameters. Then, these parameters can be estimated using the least-squares approach. The main problem is the nonlinearity of the MISO process and its noticeable transport delays. It requires specific modifications to be introduced into the basic identification algorithm. The main goal of the method is to obtain on-line a temporary linear model of the process around the selected operating point, because fast methods for tuning PID controller parameters for such a model are well known. Hence, a special adaptive identification approach with a moving window is proposed, which involves using on-line registered input and output process data. An optimal identification method for a MISO model assuming decomposition to many inner SISO systems is presented. Additionally, a special version of the modulating functions method, in which both model parameters and unknown delays are identified, is tested on real data sets collected from a glass melting installation.