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.

Wiener Sistemlerinin Gradyan Tabanlý Tanýmlamasý

Tek bir bloktan oluþan sistemlerde geribesleme ile kontrol ve giriþ-çýkýþ iliþkisinin kurulmasý klasik kontrolde yaygýn olarak görülmektedir. Fakat doðal sistemler göz önüne alýndýðýnda çok bloklu yapýlar ve bu bloklar içerisinde de lineer olmayan fonksiyonlar görülür. Bu çalýþmanýn konusu, giriþ iþaretinin lineer bloka uygulandýðý ve çýkýþýn lineer olmayan fonksiyondan alýndýðý sistem yapýsý olan Wiener tipi sistemlerin tanýmlamasýdýr. Durum geribeslemenin mümkün olmadýðý bu sistem tipinde tanýmlama ile farklý kontrol algoritmalarýnýn kullanýmý mümkündür. Sistem tanýmlamada harici giriþli otoregresif að (ARX)-polinom kaskad baðlantýsý tercihi ile en küçük kareler yöntemi ve eðim bilgileri sayesinde sistemin giriþ-çýkýþý arasýndaki matematiksel iliþki elde edilmiþtir. Üç farklý örnek sistem üzerinde çalýþmalar yapýlmýþ, MATLAB/Simulink ortamýnda veri kümeleri elde edilmiþ ve yapýlan sistem tanýmlamalarýnýn baþarýmý grafikler ile sunulmuþtur.