Wiener Sistemlerinin Gradyan Tabanlı Tanımlaması

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.

Anahtar Kelimeler:

Wiener sistemleri, Sistem tanımlama, Doğrusal olmayan sistemler

Gradient Based Identification of Wiener Systems

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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