Wiener Sistemlerinin Gradyan Tabanlı Tanımlaması

Year 2018, Volume: 24 Issue: 8, 1418 - 1424, 29.12.2018

İbrahim Alışkan

Abstract

Tek bir bloktan oluşan sistemlerde geribesleme ile
kontrol ve giriş-çıkış ilişkisinin kurulması klasik kontrolde yaygın olarak
görülmektedir.  Fakat doğal sistemler göz
önüne alındığında çok bloklu yapılar ve bu bloklar içerisinde de lineer olmayan
fonksiyonlar görülür. Bu çalışmanın konusu, giriş işaretinin lineer bloka
uygulandığı ve çıkışın lineer olmayan fonksiyondan alındığı sistem yapısı olan
Wiener tipi sistemlerin tanımlamasıdır. Durum geribeslemenin mümkün olmadığı bu
sistem tipinde tanımlama ile farklı kontrol algoritmalarının kullanımı
mümkündür. Sistem tanımlamada harici girişli otoregresif ağ (ARX)-polinom
kaskad bağlantısı tercihi ile en küçük kareler yöntemi ve eğim bilgileri
sayesinde sistemin giriş-çıkışı arasındaki matematiksel ilişki elde edilmiştir.
Üç farklı örnek sistem üzerinde çalışmalar yapılmış, MATLAB/Simulink ortamında
veri kümeleri elde edilmiş ve yapılan sistem tanımlamalarının başarımı grafikler
ile sunulmuştur.

Keywords

Wiener sistemleri, Sistem tanımlama, Doğrusal olmayan sistemler

Gradient Based Identification of Wiener Systems

Abstract

In
systems consisting of a single block, the establishment of feedback control and
input-output relationship is common in classical control. However, considering
natural systems, there are many block structures and non-linear functions
within these blocks. The subject of this study is the identification of Wiener
type systems, which is the system structure in which the input signal is
applied to the linear block and its output is taken from the nonlinear
function. It is possible to use different control algorithms with
identification in this type of system where state feedback control is not
possible. In system identification, the mathematical relationship between the
input and output of the system has been obtained by the choice of auto
regressive with exogenous inputs (ARX)-polynomial cascade connection with using
the least squares method and gradient information. Three different benchmark
systems have been studied in MATLAB/Simulink and the performances of the
identifications made with the dataset are presented graphically.

Keywords

Wiener systems, System identification, Nonlinear systems.

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