A Graphical Approach to Design Digital PI Controller for Integrator Plus Dead-Time Processes


(*) Corresponding author


Authors' affiliations


DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)

Abstract


The aim of this paper is to present a novel graphical method to design the digital PI controller for integrator plus dead time (IPDT) model which is suitable for many processes. To start with the process and controller transfer functions are transformed from s-domain to z-domain and then the open-loop transfer function is obtained in z-domain. Then the parameters to design the controller are determined. As we need to design the digital controller in frequency domain a bilinear transformation of z-domain to w-domain is used. Let us determine the stability region by combination the traditional D-partition technique and graphical technique in the controller parameters plane. Then sketch the loci of constant stability margins, such as the gain and phase margins, gain and phase crossover frequencies and Smith’s vector margin in the parameter space. Also, it will be proven that by varying the coefficients of PI controller one can achieve the gain crossover frequency in the interval [0, ωA max] and the phase crossover frequency in the interval [0, ωB max), where ωA max and ωB max are determined by the parameters of process. By sketching the two loci of indices and obtaining their intersection point, one can approach to desired closed-loop systems specifications. Finally some examples are given to demonstrate the effectiveness of the proposed method.
Copyright © 2013 Praise Worthy Prize - All rights reserved.

Keywords


Digital PI Controller; Bilinear Transformation; Industrial Processes Plus Dead Time; Frequency Domain; Phase and Gain Margin; Phase and Gain Crossover Frequency; Smith’s Vector Margin

Full Text:

PDF


References


K. J. Astromand, T. Hagglund, “Automatic Tuning Of PID controllers,” Instrument society of America,1998.

J. G. Ziegler, and N. B. Nichols, “Optimum Settings for automatic controllers,’’ Trans. ASME, vol. 64, pp. 759-768, 1942.

D. Chen, and D. E. Seborg, “PI/PID controller design based on direct synthesis and disturbance rejection,‘’ Ind. Eng. Chem. Process Des. Dev., vol. 25, pp. 4807-4822, 2002.

W. K. Ho, C. C. Hangand J. H. Zhou, “Performance and gain and phase margins of well-Known PItuning formulas,’’ IEEE Transactions on Control Systems Technology, vol. 3, No. 2, pp. 245-248, 1995.

C. A. Smith and A. B. Corripio, “Principles and Practice of Automatic Process control,’’ New York: Wiley, 1985.

F. G.Shinskey,“'Process Control System: Application, Design and Tuning,’’ 3rd Ed. New York:McGraw –Hill Book Co, 1985.

M. Zhuang, D. P. Atherton, “Automatic tuning of optimum PID controllers,’’ IEE Proc-D, vol. 140, No. 3, pp. 216-224, 1993.

A.O’dwyer, “PI and PID controller tuning rules: an overview and personal perspective,’’ ISSC, 2006.

R. PadmaSree, M. N. Srinivas and M.Chidambaram,“Asimple method of tuning PID controllers for stable and unstable FOPDT systems,’’ Computers and Chemical Engineering, vol. 24, No. 11, pp. 2201-2218, 2004.

L. M. Eriksson andM.Johansson “PIDcontroller tuning rules for varying time-delay systems,’’ in proceedings of the American control conference, pp. 619-625, July 2007.

H. Shu and Y. Pi,“PID neural networks for time-delay systems,’’ Computer and Chemical Engineering , vol. 24, no. 2-7, pp. 859-862, 2000.

H. Shu, X. Guo, and H.Shu,“PID neural networks in multi variable systems,’’ in proceedings of the IEEE international symposium on Intelligent Control, pp. 440-444, 2002.

C. Hwang and J. H. Hawng,“Stabilization unstable processes of first order plus dead time using PID controllers,’’ IEE Proceedings:control theory and applications, vol. 151, no. 1,pp. 89-94, 2004.

J.Mckay, “The D-partition method applied to systems with Dead time and distributed lag, Meas. Control, vol. 3, no. 10, pp. 293-297, 1970.

R. Toscano,“Asimple robust PI/PID controller design via numerical optimization approach,’’Journal of process ccontrol, vol. 15, no. 1, pp.81-88, 2005.

Jan Jantzen, “Tuning of fuzzy PID controllers,’’Technical University of Denmark, Department of Automation, Bldg 326, Dk-2800 Lyngby, DENMARK Tech. report no 98-H 871 (fpid), 30 Sep 1998.

C. H. Lee, andC. C. Teng,“Calculation of PID controller parameters by using a fuzzy neural network,’’ ISA Trans, vol. 42, pp. 391-400, 2003.

I.L.Chein, and P. S. Fruehauf,“Consider IMC tuning to improve performance,’’ Chem. Eng. Prog, vol. 89, pp. 33-41, 1990.

M. Friman, and K.V.Walker,“Auto tuning of multi loop control systems,’’ Ind. Eng. Chem. Res, vol. 33, pp. 1708-1717, 1994.

L. Wang and W.RCluett,“Tuning PID controllers for integrating processes,’’ Proc. IEE-Pt. D, vol. 148, pp.180, 2001.

L. Wang and W. R. Cluett, “From Plant Data to Process Control:Ideas for Process Identification and PID Design, Taylor and Francis, London, 2000.

W. Krajewski, A. Lepschy, S. Miani and U. Viaro,“Frequency-domain approach to robust PI control,’’ Journal of the Franklin Institute, vol. 342, pp. 674-687, 2005.

M. SAM FADALI,“Digital Control Engineering, Analysis and Design”.


Refbacks

  • There are currently no refbacks.



Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize