“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.

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
[20] Fahd Alharbi (2020), doi:10.1080/03772063.2020.1756932
[21] Violaine Dalmas, Gerard Robert, Gildas Besancon and Didier Georges (2018), doi:10.1109/CDC.2018.8619438
[22] Isah A. Jimoh, Ibrahim B. Kucukdemiral, Geraint Bevan and Patience E. Orukpe (2020), doi:10.1109/MED48518.2020.9183056
[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}