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“On Tuning PI Controllers for Integrating Plus Time Delay Systems”

Authors: David Di Ruscio,
Affiliation: Telemark University College
Reference: 2010, Vol 31, No 4, pp. 145-164.

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Keywords: PI controller, tuning, integrating system, time delay, maximum time delay error, frequency analysis

Abstract: Some analytical results concerning PI controller tuning based on integrator plus time delay models are worked out and presented. A method for obtaining PI controller parameters, Kp=alpha/(k*tau), and, Ti=beta*tau, which ensures a given prescribed maximum time delay error, dtau_max, to time delay, tau, ratio parameter delta=d au_max/tau, is presented. The corner stone in this method, is a method product parameter, c=alpha*beta. Analytical relations between the PI controller parameters, Ti, and, Kp, and the time delay error parameter, delta, is presented, and we propose the setting, beta=c/a*(delta+1), and, alpha=a/(delta+1), which gives, Ti=c/a*(delta+1)*tau, and Kp=a/((delta+1)*k*tau), where the parameter, a, is constant in the method product parameter, c=alpha*beta. It also turns out that the integral time, Ti, is linear in, delta, and the proportional gain, Kp, inversely proportional to, delta+1. For the original Ziegler Nichols (ZN) method this parameter is approximately, c=2.38, and the presented method may e.g., be used to obtain new modified ZN parameters with increased robustness margins, also documented in the paper.

PDF PDF (636 Kb)        DOI: 10.4173/mic.2010.4.3

DOI forward links to this article:
  [1] David Di Ruscio (2013), doi:10.4173/mic.2013.3.2
  [2] S. Alcántara, R. Vilanova and C. Pedret (2013), doi:10.1016/j.jprocont.2013.01.003
  [3] Finn Haugen, Rune Bakke and Bernt Lie (2013), doi:10.4173/mic.2013.3.1
  [4] Jietae Lee, Wonhui Cho and Thomas F. Edgar (2013), doi:10.1021/ie4009919
  [5] David Di Ruscio (2012), doi:10.4173/mic.2012.2.1
  [6] Henrik Niemann and Robert Miklos (2014), doi:10.1088/1742-6596/570/1/012001
  [7] Miguel A. Davo and Alfonso Banos (2012), doi:10.1109/ETFA.2012.6489761
  [8] Pedro Mercader and Alfonso Banos (2014), doi:10.1109/ETFA.2014.7005115
  [9] Alfonso Banos, Felix Perez and Joaquin Cervera (2014), doi:10.1109/TII.2013.2273434
  [10] Christer Dalen, David Di Ruscio and Roar Nilsen (2015), doi:10.4173/mic.2015.3.5
  [11] Peter Mark Benes, Miroslav Erben, Martin Vesely, Ondrej Liska and Ivo Bukovsky (2016), doi:10.4018/978-1-5225-0063-6.ch002
  [12] Chriss Grimholt and Sigurd Skogestad (2012), doi:10.3182/20120328-3-IT-3014.00003
  [13] David Di Ruscio and Christer Dalen (2017), doi:10.4173/mic.2017.2.4
  [14] Srinibash Swain and Partha Sarathi Khuntia (2017), doi:10.21833/ijaas.2017.08.020
  [15] R. Vilanova, C. Pedret and S. Alcantara (2017), doi:10.1109/CarpathianCC.2017.7970469
  [16] Christer Dalen and David Di Ruscio (2017), doi:10.4173/mic.2017.4.3
  [17] Christer Dalen and David Di Ruscio (2018), doi:10.3390/a11060086
  [18] Chriss Grimholt and Sigurd Skogestad (2018), doi:10.1016/j.jprocont.2018.06.011
  [19] Christer Dalen and David Di Ruscio (2019), doi:10.4173/mic.2019.4.2

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  title={{On Tuning PI Controllers for Integrating Plus Time Delay Systems}},
  author={Di Ruscio, David},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}


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