PID tuning method based on IMC for inverse-response second-order plus dead time processes

Duby Castellanos-Cárdenas, Fabio Castrillón, Rafael E. Vásquez, Carlos Smith

    Research output: Contribution to journalArticlepeer-review

    2 Scopus citations


    This work addresses a set of tuning rules for PID controllers based on Internal Model Control (IMC) for inverse-response second-order systems with dead time. The transfer function, and some time-response characteristics for such systems are first described. Then, the IMC-based methodology is developed by using an optimization objective function that mixes performance and robustness. A correlation that minimizes the objective function and that allows the user to compute the controller's tuning parameter is found. The obtained expressions are mathematically simple, which facilitate their application in a ten-step systematic methodology. Finally, the proposed tuning method is compared to other well-known tuning rules that have been reported in literature, for a wide range of parameters of the process. The performance achieved with the proposed method is very good not only for disturbance rejection but for set-point tracking, when considering a wide-range of parameters of the process' transfer function.

    Original languageEnglish
    Article number1626
    Issue number9
    StatePublished - Sep 2020

    Bibliographical note

    Funding Information:
    Funding: This research was funded by Universidad Pontificia Bolivariana and Universidad de Medellín.

    Publisher Copyright:
    © 2020 by the authors.


    • Internal model control
    • Inverse response
    • PID tuning
    • Process control
    • Second order plus dead time)


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