Performance enhancement of IMC-PID controller design for stable and unstable second-order time delay processes

Abstract

An IMC-PID controller was proposed for unstable second-order time delay system which shows the characteristics of inverse response (RHP zero). A plot of M_s versus λ was suggested to calculate the suitable tuning parameter λ, which provides a trade-off between performance and robustness. Six different forms of process models were selected from literature to show the applicability of the present method. Performance of controller was calculated by ITAE and total variation TV and compared with recently published tuning rules. Undesirable overshoot was removed by using a set-point weighting parameter. Robustness was tested by introducing a perturbation into the various model parameters and closed-loop results show that the designed controller is robust in the case of model uncertainty. The proposed method shows an overall better closed-loop response as compared to other recently reported methods.

Keywords

maximum sensitivity / internal model control / unstable process / set-point weighting / integral of time-weighted absolute error

References

[1] BoukhalfaG, BelkacemS, ChikhiA, BenaggouneS. Genetic algorithm and particle swarm optimization tuned fuzzy PID controller on direct torque control of dual star induction motor [J]. Journal of Central South University, 2019, 26(7): 1886-1896

[2] PandaR C, YuC C, HuangH P. PID tuning rules for sopdt systems: Review and some new results [J]. ISA Transactions, 2004, 43(2): 283-295

[3] SreeR P, ChidambaramMControl of unstable systems [R], 2006, Oxford, UK, Alpha Science Int’l Ltd.

[4] NikitaS, LeeM. Control of a wastewater treatment plant using relay auto-tuning [J]. Korean Journal of Chemical Engineering, 2019, 36(4): 505-512

[5] KhanO, MadhuranthakamC M R, DouglasP, LauH, SunJ, FarrellP. Optimized PID controller for an industrial biological fermentation process [J]. Journal of Process Control, 2018, 71: 75-89

[6] ZieglerJ G, NicholsN B. Optimum settings for automatic controllers [J]. Trans ASME, 1942, 64(11): 759-765

[7] Cohen, CoonG. Theoretical consideration of retarded control [J]. Trans ASME, 1953, 75: 827-834

[8] ChenD, SeborgD E. PI/PID controller design based on direct synthesis and disturbance rejection [J]. Industrial & Engineering Chemistry Research, 2002, 41(19): 4807-4822

[9] SEBORG D E, MELLICHAMP D A, EDGAR T F, DOYLE III F J. Process dynamics and control [M]. John Wiley & Sons, 2010.

[10] RaoA S, RaoV, ChidambaramM. Direct synthesis-based controller design for integrating processes with time delay [J]. Journal of the Franklin Institute, 2009, 346(1): 38-56

[11] ChienI L. Consider IMC tuning to improve controller performance [J]. Chem Eng Prog, 1990, 86: 33-41

[12] RiveraD E, MorariM, SkogestadS. Internal model control: PID controller design [J]. Industrial & Engineering Chemistry Process Design and Development, 1986, 25(1): 252-265

[13] SkogestadS. Simple analytic rules for model reduction and Pid controller tuning [J]. Journal of Process Control, 2003, 13(4): 291-309

[14] WangQ, LuC, PanW. IMC PID controller tuning for stable and unstable processes with time delay [J]. Chemical Engineering Research and Design, 2016, 105: 120-129

[15] GarciaC E, MorariM. Internal model control. A unifying review and some new results [J]. Industrial & Engineering Chemistry Process Design and Development, 1982, 21(2): 308-323

[16] GarpingerO, HägglundT, ÅströmK J. Performance and robustness trade-offs in PID control [J]. Journal of Process Control, 2014, 24(5): 568-577

[17] ShamsuzzohaM, LeeM. IMC-PID controller design for improved disturbance rejection of time-delayed processes [J]. Industrial & Engineering Chemistry Research, 2007, 46(7): 2077-2091

[18] ShamsuzzohaM, LeeM. Design of advanced PID controller for enhanced disturbance rejection of second-order processes with time delay [J]. AIChE Journal, 2008, 54(6): 1526-1536

[19] TchamnaR, QyyumM A, ZahoorM, KamgaC, KwokE, LeeM. Analytical design of constraint handling optimal two parameter internal model control for dead-time processes [J]. Korean Journal of Chemical Engineering, 2019, 36(3): 356-367

[20] MorariM, ZafiriouERobust Process Control [M], 1989, New Jersey, Prentice-Hall Inc.

[21] ZhaoZ C, LiuZ Y, ZhangJ G. IMC-PID tuning method based on sensitivity specification for process with time-delay [J]. Journal of Central South University of Technology, 2011, 18(4): 1153-1160

[22] DenizF N, TanN, HamamciS E, KayaI. Stability region analysis in smith predictor configurations using a Pi controller [J]. Transactions of the Institute of Measurement and Control, 2015, 37(5): 606-614

[23] KwonW H, RyuK H, HwangJ A, KimK H, LeeJ H, SungS W. Development of batch proportional-integral-derivative controller [J]. Korean Journal of Chemical Engineering, 2018, 35(6): 1240-1246

[24] DarwishN M. PID controller design in the frequency domain for time-delay systems using direct method [J]. Transactions of the Institute of Measurement and Control, 2018, 40(3): 940-950

[25] BegumK G, RaoA S, RadhakrishnanT. Maximum sensitivity based analytical tuning rules for PID controllers for unstable dead time processes [J]. Chemical Engineering Research and Design, 2016, 109: 593-606

[26] ArrietaO, VilanovaR. Simple servo/regulation proportional—integral—derivative (PID) tuning rules for arbitrary M S-Based robustness achievement [J]. Industrial & Engineering Chemistry Research, 2012, 51(6): 2666-2674

[27] ChuMinghui, XuChi, ChuJizheng. Graphic IMC-PID tuning based on maximum sensitivity for uncertain systems. Transactions of the Institute of Measurement and Control, 2018, 41(8): 2196-2204

[28] BegumK G, RadhakrishnanT, RaoA S, ChidambaramM. IMC based PID controller tuning of series cascade unstable systems [J]. IFAC-Papers Online, 2016, 49(1): 795-800

[29] DasariPurushottama Rao, AlladiLavanya, Seshagiri RaoA., YooChangKyoo. Enhanced design of cascade control systems for unstable processes with time delay. Journal of Process Control, 2016, 45: 43-54

[30] BegumK G, RaoA S, RadhakrishnanT. Enhanced IMC based PID controller design for non-minimum phase (Nmp) integrating processes with time delays [J]. ISA Transactions, 2017, 68: 223-234

[31] BegumK G, RaoA S, RadhakrishnanT. Optimal controller synthesis for second order time delay systems with at least one RHP pole [J]. ISA Transactions, 2018, 73: 181-188

[32] ShamsuzzohaM. Robust PID controller design for time delay processes with peak of maximum sensitivity criteria [J]. Journal of Central South University, 2014, 21(10): 3777-3786

[33] MataušekM R, RibićA I. Control of stable, integrating and unstable processes by the modified smith predictor [J]. Journal of Process Control, 2012, 22(1): 338-343

[34] KumarM, PrasadD, GiriB S, SinghR S. Temperature control of fermentation bioreactor for ethanol production using IMC-PID controller [J]. Biotechnology Reports, 2019, 22: e00319

[35] AlfaroV M, VilanovaR, ArrietaO. Maximum sensitivity based robust tuning for two-degree-of-freedom proportional-integral controllers [J]. Industrial & Engineering Chemistry Research, 2010, 49(11): 5415-5423

[36] AnushaA, RaoA S. Design and analysis of IMC based PID controller for unstable systems for enhanced closed loop performance [J]. IFAC Proceedings Volumes, 2012, 45(3): 41-46

[37] ÅströmK J, HägglundTPID controllers: Theory, design, and tuning [M], 1995, Research Triangle Park, NC, Instrument Society of America

[38] UmaS, ChidambaramM, RaoA S. Set point weighted modified smith predictor with PID filter controllers for non-minimum-phase (NMP) integrating processes [J]. Chemical Engineering Research and Design, 2010, 88(56): 592-601

[39] ChoW, LeeJ, EdgarT F. Simple analytic proportional-integral-derivative (PID) controller tuning rules for unstable processes [J]. Industrial & Engineering Chemistry Research, 2013, 53(13): 5048-5054

[40] KumarD S, SreeR P. Tuning of Imc based PID controllers for integrating systems with time delay [J]. ISA Transactions, 2016, 63242-255

[41] ShamsuzzohaM. A unified approach for proportional-integral-derivative controller design for time delay processes [J]. Korean Journal of Chemical Engineering, 2015, 32(4): 583-596