Revisiting Chien-Hrones-Reswick Method for an Analytical Solution

TL;DR

This paper introduces an analytical PI tuning method for FOTD systems using the Lambert W function, providing explicit formulas and conditions for optimal step response without overshoot, aligning well with traditional empirical rules.

Contribution

It offers a novel analytical approach for PI controller tuning in FOTD systems, bridging theoretical solutions with empirical tuning rules.

Findings

Exact pole placement using Lambert W function

Critical condition for non-overshooting step response

Strong agreement with Chien-Hrones-Reswick tuning rules

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.