A New Fractional Reduced-Order Model-Inspired System Identification Method for Dynamical Systems

Abstract

This paper presents a new method for identifying dynamical systems to get fractionalreduced-order models based on the process reaction curve. This proposal uses information collected from the process. It can be applied to processes with an S-shaped step response that can be considered with fractional behavior and a fractional order range of α ∈ [0.5, 1.0]. The proposed approach combines obtaining model fractional order using asymptotic properties of the Mittag-Leffler function with time-based parameter estimation by considering two arbitrary points on the process reaction curve. The improvement in terms of accuracy of the identified FFOPDT model is obtained due to a more accurate estimation of α parameter. This method is characterized by its effectiveness and simplicity of implementation, which are key aspects when applying at an industrial level. Several examples are used to illustrate the effectiveness and simplicity of the proposed method compared to other well-established methods and other approaches based on the process reaction curve. Finally, it is also implemented on microprocessor-based hardware to demonstrate the applicability of the proposed method to identify the fractional model of a thermal process.INDEX TERMS fractional-order systems, process identification, fractional first-order plus dead-time model.

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“…For the fractional approximate model, the method , is used to obtain the parameters of the FFOPDT model: G F ( s ) ≅ 1.112 e − 220.974 s 150.8 s 0.9742 + 1 …”

“…For the fractional approximate model, the method 49 , 50 is used to obtain the parameters of the FFOPDT model: …”

“…There are other recent identification procedures that are also based on the process reaction curve. The approach proposed in ref 50 is based on the asymptotic property of the Mittag-Leffler function and the hybrid approach described in ref 51 combines methods based on the optimization of one variable with the estimation of the remaining model parameters by analytical methods.…”