2025/07/08 by Gulgonul, Senol
#FOS: Electrical engineering #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2507.06352
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.