A General Identification Procedure for Reduced-Order Fractional Models Based on the Process Reaction Curve

Recent advances in fractional calculus and computation have enabled the development of more accurate and flexible models for industrial process dynamics. Among these, the Fractional First-Order Plus Dead-Time (FFOPDT) and Fractional Dual-Pole Plus Dead-Time (FDPPDT) models have shown notable performance in representing systems with overdamped step responses. This work introduces a unified analytical identification procedure for both models, derived from the process reaction curve obtained through a simple open-loop step test. The proposed methodology is validated through numerical simulations, and the results demonstrate that it achieves comparable or superior performance to existing methods, with the added benefits of analytical simplicity and computational efficiency, making it suitable for industrial applications.