A new analytical procedure for identifying fractional first-order plus dead-time (FFOPDT) models has recently been proposed. The technique is applicable to systems with S-shaped step responses and involves selecting three specific points on the process response curve for parameter estimation. In a simplified version of the method, the points are symmetrically positioned as \(x_1 = x\%\) , \(x_2 = 50\%\) , and \(x_3 = (100 - x)\%\) , with \(0< x < 50\%\) , requiring only the optimal position of one point, x, given that the others are set automatically. This study explores the effect of adjusting the value of \(x_2\) in the representative points (x- \(x_2\) - \((100-x)\%)\) , while preserving symmetry around the center of the interval. Simulations provide insights into the influence of \(x_2\) for more accurate estimation, revealing that the accuracy of the identified FFOPDT model is highly sensitive to the position of \(x_2\) , and an optimal value is proposed to enhance precision. Experimental validation on a thermal-based prototype deployed on a microprocessor confirms the technique’s applicability. This approach provides new insights into selecting the central point \(x_2\) and its implications for industrial applications.
