FOPDT Model fitting to an nth-Order All Pole NMP Processes by an Optimal Method

Abstract

Abstract - The aim of this paper is to present a method to approximate the nth-order all pole systems with a zero by the widely used first-order plus dead-time (FOPDT) model in s-plane. To establish this method, impulse response approach is used .This method is applicable for s-shaped functions. The main novelty of the present method is the closeness of the approximated transfer function to the process model. That is the square of the 2-norm of the error signal between the impulse responses of the system and the presented model that is chosen as an index function. By globally minimizing this index function, three nonlinear equations are obtained in terms of the parameters of FOPDT model. Then these equations are analyzed and proved that always have unique solution to the FOPDT model parameters. Finally, by solving the nonlinear equations the optimal values of FOPDT model parameters are achieved. Numerical example is included to present the advantage of the presented method. The proposed research uses optimal method to approximate the nth-order all pole systems by the far-reaching used general form of the first-order plus dead time (FOPDT) model. This proposed investigation has described the structure of optimal FOPDT model, which is analytically modeled for a several industrial processes. The method is based on fitting to special form of transfer function in optimal manner. To compare the performance of the method of this paper and two another, impulse response approach is pr