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

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 inputoutput 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.