Revisiting Chien-Hrones-Reswick Method for an Analytical Solution
Abstract
This study presents an analytical method for tuning PI controllers in First-Order with Time Delay (FOTD) systems, leveraging the Lambert W function. The Lambert W function enables exact pole placement, yielding analytical expressions for PI gains. The proposed approach identifies a critical condition that achieves a step response without overshoot with minimum settling time, while also providing explicit tuning rules for systems where controlled overshoot is specified. The method demonstrates strong agreement with established empirical Chien-Hrones-Reswick tuning rules for both non-overshooting and overshooting cases, bridging the gap between theoretical analysis and empirical results.
Cite
@article{arxiv.2507.06352,
title = {Revisiting Chien-Hrones-Reswick Method for an Analytical Solution},
author = {Senol Gulgonul},
journal= {arXiv preprint arXiv:2507.06352},
year = {2026}
}
Comments
7 pages, 3 figures, 1 table. This work is licensed under CC BY-NC-ND 4.0. For commercial licensing, contact the author