This paper presents a new method for identifying dynamical systems to get fractional-reduced-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 in [0.5, 1.0]. The proposed approach combines obtaining the fractional order of the model 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.
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