**Page description appears here**

“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.

     Valid XHTML 1.0 Strict

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

[1] Åström, K. Hägglund, T. (1995). PID Controllers: Theory, Design, and Tuning, Instrument Society of America.
[2] Åström, K. Hägglund, T. (2004). Consider IMC Tuning to Improve Controller Performance, Journal of Process Control, 1.14:635--650.
[3] Balchen, J.G. (1990). Rational Transfer Function Approximations to Transport Delay, Modeling, Identification and Control, 1.3:127--140 doi:10.4173/mic.1990.3.1
[4] Chidambaram, M. Sree, R.P. (2003). A Simple method of tuning PID controllers for integrating/dead-time processes, Computers and Chemical Engineering, 27(27):211--215 doi:10.1016/S0098-1354(02)00178-3
[5] Chien, I.L. Fruehauf, P.S. (1990). Consider IMC Tuning to Improve Controller Performance, Chem. Eng. Progress, Oct:33--41.
[6] Haugen, F. (2010). Comparing PI Tuning Methods in a Real Benchmark Temperature Control System, Modeling, Identification and Control, 3.3:79--91 doi:10.4173/mic.2010.3.1
[7] Seborg, D., Edgar, T.F., Mellichamp, D.A. (1989). Process Dynamics and Control, John Wiley and Sons.
[8] Shamsuzzoha, M., Skogestad, S., Halvorsen, I.J. (2010). On-line pi controller tuning using closed-loop setpoint response, In IFAC Conference of Chemical Processes.DYCOPS, Leuven, Belgium, July.
[9] Skogestad, S. (2001). Probably the best simple pid tuning rules in the world, In AIChE Annual Meeting, Reno, Nevada, Nov.
[10] Skogestad, S. (2003). Simple analytic rules for model reduction and PID controller tuning, Journal of Process Control, 13(13):291--309 doi:10.1016/S0959-1524(02)00062-8
[11] Skogestad, S. (2004). Simple analytic rules for model reduction and PID controller tuning, Modeling, Identification and Control, 2.2:85--120 doi:10.4173/mic.2004.2.2
[12] Tyreus, B.D. Luyben, W.L. (1992). Tuning PI Controllers for Integrator/Dead Time Processes, Ind. Eng. Chem., 3.31:2625--2628.
[13] Ziegler, J. Nichols, N.B. (1942). Optimum settings for automatic controllers, Trans. of the A.S.M.E., 6.64:759--768.

  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}


May 2016: MIC reaches 2000 DOI Forward Links. The first 1000 took 34 years, the next 1000 took 2.5 years.

July 2015: MIC's new impact factor is now 0.778. The number of papers published in 2014 was 21 compared to 15 in 2013, which partially explains the small decrease in impact factor.

Aug 2014: For the 3rd year in a row MIC's impact factor increases. It is now 0.826.

Dec 2013: New database-driven web-design enabling extended statistics. Article number 500 is published and MIC reaches 1000 DOI Forward Links.

Jan 2012: Follow MIC on your smartphone by using the RSS feed.


July 2011: MIC passes 1000 ISI Web of Science citations.

Mar 2010: MIC is now indexed by DOAJ and has received the Sparc Seal seal for open access journals.

Dec 2009: A MIC group is created at LinkedIn and Twitter.

Oct 2009: MIC is now fully updated in ISI Web of Knowledge.