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Language: English

Conflict of Interest: In relation to this article, we declare that there is no conflict of interest.

Publication history: Received July 16, 2025
Revised October 12, 2025
Accepted December 10, 2025
Available online March 25, 2026

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/bync/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Analytical Solution of Optimal Filter Design for Internal Model Control for First and Second Order Dead-Time Processes

Neha Agarwal Rodrigue Tchamna Joonho Park Chanin Panjapornpon Minkyu Kim^† Moonyong Lee^†

School of Chemical Engineering , Yeungnam University ¹University Transportation Research Center , The City College of New York ²Dow Chemical , Houston ³Department of Chemical Engineering, Center of Excellence on Petrochemicals and Materials Technology , Kasetsart University

mk_kim@ynu.ac.kr, mynlee@yu.ac.kr

Korean Journal of Chemical Engineering, March 2026, 43(4), 1027-1042(16)
https://doi.org/10.1007/s11814-025-00621-y

Abstract

This work presents a systematic path towards the analytical design of the optimal parameters of a two parameter second

order Internal Model Control (IMC) fi lter for the fi rst-order plus dead- time and the second-order plus dead-time processes.

The IMC parameters are designed to minimize the control objective function comprising of weighted sum of (1) error

between the process variable and set point, and (2) rate of change of the manipulated variable. The proposed IMC controller

design yields the analytical expression of best/optimal value of the IMC controller parameters in terms of process

parameters without any trial and error.

Keywords

Optimal IMC control · Analytical design approach · Dead time process · FOPDT process · SOPDT process