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arXiv · 2507.06352

Revisiting Chien-Hrones-Reswick Method for an Analytical Solution

Senol Gulgonul
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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.

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Senol Gulgonul. 2025-07-08. Revisiting Chien-Hrones-Reswick Method for an Analytical Solution. https://doi.org/10.1002/adc2.70041

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