Influence of the Selection of Reaction Curve’s Representative Points on the Accuracy of the Identified Fractional-Order Model

In this paper, a general procedure for identifying a fractional first-order plus dead-time (FFOPDT) model is presented. This procedure is based on fitting three arbitrary points on the process reaction curve, where process information is obtained from a simple open-loop test. A simplification of the general identification procedure is also considered, where only points symmetrically located on the reaction curve are selected. The proposed symmetrical procedure has been applied to the following sets of representative points: (5–50–95%), (10–50–90%), (15–50–85%), (20–50–80%), (25–50–75%), and (30–50–70%). Analytical expressions of the corresponding FFOPDT model parameters for these sets of symmetrical points have been obtained. In order to show the effectiveness and applicability of this procedure for the identification of fractional-order models and to get insight into the influence of selection of the set of symmetrical points on the accuracy of the identified model, some numerical examples are proposed. This identification procedure gives good results in comparison with other integer- and fractional-order identification methods. Finally, some conclusions and final remarks are offered in this context.