Improving a reaction curve-based analytical identification technique for fractional models

Abstract 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 x₁ = x\% x 1 = x %, x₂ = 50\% x 2 = 50 %, and x₃ = (100 - x) \% x 3 = (100 - x) %, with 0 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 x₂ x 2 in the representative points (x - x₂ x 2 - (100-x) \%) (100 - x) %), while preserving symmetry around the center of the interval. Simulations provide insights into the influence of x₂ x 2 for more accurate estimation, revealing that the accuracy of the identified FFOPDT model is highly sensitive to the position of x₂ 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 x₂ x 2 and its implications for industrial applications.