Modeling of first order plus time delay system dynamics with adaptive IIR filters based on gradient descent methods and performance analyses for different time delay cases

Year 2024, Volume: 30 Issue: 2, 202 - 211, 30.04.2024

Nagihan Yağmur , Barış Baykant Alagöz

Abstract

In this study, the modeling of First Order Plus Time Delay (FOPTD) dynamics by using adaptive infinite impulse response (IIR) filter based on Gradient Descent (GD) method, which is frequently used in machine learning applications, has been investigated by the help of the input-output data in the time domain. The First Order Time Delay (FOPTD) dynamic system models are the most basic system model that is used in the modeling of control systems. In the study, the IIR filter coefficients are optimized online by using the GD method for convergence of the IIR filter response to the FOPTD dynamic system model response for the same input signal. The distance of the IIR filter output to the output of the FOPTD dynamic system for the same input is expressed by the instant square error function and, recursive GD solutions of this function are used to minimize output mismatches between FOPTD system model and the proposed adaptive IIR filter. Thus, the convergence of the IIR filter to the input-output dynamics of a FOPTD dynamic system is provided in the time domain by performing recursive filter coefficient solutions that are obtained by the GD method. An application of the adaptive IIR filter solutions in the online modeling of FOPTD systems was carried out in MATLAB-Simulink environment. In the developed simulation environment, the collected signals from the inputs and outputs of the FOPTD dynamic system were used to online optimize the IIR filter coefficients in the GD optimization block. In this simulation environment, the convergence performance of the IIR filter response for the time delay system dynamics of the FOPTD plant model is investigated for different time delay values.

Keywords

System modeling, Nonlinear optimization, Gradient descent method, Adaptive IIR Filter, Dynamic system

Birinci mertebe artı zaman gecikmeli sistem dinamiğinin gradyan iniş yöntemine dayali adaptif IIR filtreler ile modellenmesi ve farkli zaman gecikmeleri durumlari için performans analizleri

Abstract

Bu çalışmada makine öğrenmesi uygulamalarında sıklıkla kullanılan ve popüler bir nümerik optimizasyon yöntemi olan Gradyan İniş (GD) yöntemine dayalı adaptif sonsuz impuls cevabı (IIR) filtresi ile Birinci Mertebe Zaman Gecikmeli (FOPTD) sistem dinamiğinin zaman bölgesinde giriş-çıkış verisi yardımı ile modellemesi incelenmiştir. FOPTD dinamik sistem modelleri kontrol sitemlerinin modellemesinde kullanılan en temel sistem modelidir. Çalışmada, IIR filtre katsayıları, aynı giriş işareti için IIR filtre cevabının FOPTD dinamik sistem modelinin cevabına yakınsaması için GD yöntemi ile online optimize edilmiştir. Aynı giriş için IIR filtre çıkışının, FOPTD dinamik sistemin çıkışına uzaklığı anlık karesel hata fonksiyonu ile ifade edilmiş ve bu fonksiyonun özyinelemeli gradyan iniş çözümleri FOPTD sistem cevabı ile tasarlanan adaptif IIR filtre cevabı arasındaki çıkış uyumsuzluğunu minimize etmek için kullanılmıştır. Böylece, zaman bölgesinde IIR filtrenin bir FOPTD dinamik sistemin giriş-çıkış dinamiğine yakınsaması GD yöntemi ile elde edilen özyinelemeli filtre katsayı çözümleri ile sağlanmıştır. Adaptif IIR filtre çözümlerinin FOPTD sistemlerin online modellemesinde uygulaması MATLAB-Simulink ortamında gerçekleştirilmiş. Geliştirilen simülasyon ortamında FOPTD dinamik sistemin giriş ve çıkışlarından alınan işaretler, GD optimizasyon bloğunda IIR filtre katsayılarının online olarak optimize edilmesinde kullanılmış. Bu simülasyon ortamında IIR filtre cevabının FOPTD plant modelinin zaman gecikmeli sistem dinamiğine yakınsama performansı farklı zaman gecikme değerleri için incelenmiştir.

Keywords

Sistem modelleme, Doğrusal olmayan optimizasyon, Gradyan iniş yöntemi, Adaptif IIR filtre, Dinamik sistem

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