A unified procedure for the identification of reduced-order fractional models based on the process reaction curve

This paper introduces a unified analytical method for the identification of fractional reduced-order models, specifically the fractional first-order plus dead time (FFOPDT) and fractional dual-pole plus dead time (FDPPDT) structures, using only three points from the open-loop step response. The method provides explicit parameter-estimation formulas that eliminate the need for iterative optimization, reducing computational effort while preserving the simplicity of traditional reaction-curve techniques. Numerical simulations demonstrate superior accuracy and robustness compared to existing analytical and hybrid techniques, especially for overdamped and S-shaped responses typical of thermal and chemical processes. The method is validated for fractional orders within the range $ \alpha \in [0.5, 1.0] $, covering the most relevant dynamics observed in practice. Laboratory experiments on a thermal system confirm the model's applicability under real-world conditions, including measurement noise, limited sensor resolution, and hardware constraints. Because the workflow aligns with standard industrial identification practices and does not require specialized knowledge of fractional calculus, it provides a practical means to incorporate fractional-order modeling into proportional-integral-derivative (PID)-based process control.