Robust PID controller design for time delay processes with peak of maximum sensitivity criteria

Abstract

The motivation of this work is to obtain single PI/PID tuning formula for different types of processes with enhanced disturbance rejection performance. The proposed tuning formula consistently gives better performance in comparison to several well-known methods at the same degree of robustness for stable, integrating and unstable processes. For the selection of the closed-loop time constant (τ_c), a guideline is provided over a broad range of time-delay/time-constant ratios on the basis of the peak of maximum sensitivity (M_s). An analysis has been performed for the uncertainty margin with the different process parameters for the robust controller design. It gives the guideline of the M_s-value settings for the PI controller designs based on the process parameters uncertainty. Furthermore, a relationship has been developed between M_s-value and uncertainty margin with the different process parameters (k, τ and θ). Simulation study has been conducted for the broad class of processes and the controllers are tuned to have the same degree of robustness by measuring the maximum sensitivity, M_s, in order to obtain a reasonable comparison.

Keywords

PI/PID controller tuning / internal model control (IMC) method / unstable delay process / integrating delay process / disturbance rejection

References

[1] KanoM, OgawaM. The state of art in chemical process control in Japan: Good practice and questionnaire survey [J]. Journal of Process Control, 2010, 20: 969-982

[2] RiveraD, MorariM, SkogestadS. Internal model control. 4. PID controller design [J]. Ind Eng Chem Process Des Dev, 1986, 25: 252-265

[3] LeeY, ParkS, LeeM, BrosilowC. PID controller tuning for desired closed-loop responses for SI/SO systems [J]. AIChE, 1998, 44: 106-115

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

[5] ShamsuzzohaM, LeeM. IMC-PID controller design for improved disturbance rejection of time-delayed processes [J]. Ind Eng Chem Res, 2007, 46: 2077-2091

[6] SmithC L, CorripioA B, MartinJ. Controller tuning from simple process models [J]. Instrum Technol, 1975, 22(12): 39

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

[8] MorariM, ZafiriouERobust process control [M], 1989, New Jersey, Prentice-Hall Englewood Cliffs: 85-111

[9] LeeY, LeeJ, ParkS. PID controller tuning for integrating and unstable processes with time delay [J]. Chemical Engineering Science, 2000, 55: 3481-3493

[10] YangX, WangQ, HangC, LinC. IMC-based control system design for unstable processes [J]. Industrial and Engineering Chemistry Research, 2002, 41: 4288-4294

[11] WangY, CaiW. Advanced proportional-integral-derivative tuning for integrating and unstable processes with gain and phase margin specifications [J]. Industrial and Engineering Chemistry Research, 2002, 41: 2910-2914

[12] TanW, MarquezH, ChenT. IMC design for unstable processes with time delays [J]. Journal of Process Control, 2003, 13: 203-213

[13] LiuT, ZhangW, GuD. Analytical design of two-degree-of-freedom control scheme for open-loop unstable process with time delay [J]. Journal of Process Control, 2005, 15: 559-572

[14] JungC S, SongH K, HyunC J. A direct synthesis tuning method of unstable first-order-plus-time-delay processes [J]. Journal of Process Control, 1999, 9: 265-269

[15] MajhiS, AthertonD. Obtaining controller parameters for a new smith predictor using autotuning [J]. Automatica, 2000, 36: 1651-1658

[16] KwakH, SungS, LeeI B, ParkJ. Modified smith predictor with a new structure for unstable processes [J]. Industrial and Engineering Chemistry Research, 1999, 38: 405-411

[17] ZhangW, GuD, WangW, XuX. Quantitative performance design of a modified smith predictor for unstable processes with time delay [J]. Industrial and Engineering Chemistry Research, 2004, 43: 56-62

[18] TyreusB, LuybenW. Tuning PI controllers for integrator/dead time processes [J]. Ind Eng Chem Res, 19922625-2628

[19] ShamsuzzohaM, LeeM. Analytical design of enhanced PID-filter controller for integrating and first order unstable processes with time delay [J]. Chemical Engineering Science, 2, 2008, 63: 2717-2731

[20] AlcantaraS, VilanovaR, PedretC. PID control in terms of robustness/performance and servo/regulator trade-offs: A unifying approach to balanced autotuning [J]. Journal of Process Control, 2013, 23: 527-542

[21] LeeJ, ChoW, EdgarT F. Simple analytic PID controller tuning rules revisited [J]. Industrial & Engineering Chemistry Research, 2014, 53: 5038-5047

[22] ChoW, LeeL, EdgarT. Simple analytic proportional-integral-derivative (PID) controller tuning rules for unstable processes [J]. Industrial & Engineering Chemistry Research, 2014, 53: 5048-5054

[23] TorricoB C, CavalcanteM U, BragaA P, Normey-ricoJ E, AlbuquerqueA A. Simple tuning rules for dead-time compensation of stable, integrative, and unstable first-order dead-time processes [J]. Industrial & Engineering Chemistry Research, 2013, 52: 11646-11654

[24] AlfaroV M, VilanovaR. Optimal robust tuning for 1DoF PI/PID control unifying FOPDT/SOPDT models [C]. IFAC Conference on Advances in PID Control PID’12, Brescia (Italy): IFAC, 2012

[25] JinQ B, LiuQ. IMC-PID design based on model matching approach and closed-loop shaping [J]. ISA Transactions, 2014, 53: 462-473

[26] JinQ B, LiuQ. Analytical IMC-PID design in terms of performance/robustnesstradeoff for integrating processes: From 2-Dof to 1-Dof [J]. Journal of Process Control, 2014, 24: 22-32

[27] JenJ C, LinS W. Robust Proportional-integral-derivative controller design for stable/integrating processes with inverse response and time delay [J]. Ind Eng Chem Res, 2012, 51: 2652-2665

[28] ArrietaO, VilanovaR. Simple servo/regulation proportional-integral-derivative (PID) tuning rules for arbitrary Ms-based robustness achievement [J]. Ind Eng Chem Res, 2012, 51: 2666-2674

[29] Normey-RicoJ E, GuzmánJ L. Unified PID tuning approach for stable, integrative, and unstable dead-time processes [J]. Ind Eng Chem Res, 2013, 52: 16811-16819

[30] ZieglerJ G, NicholsN B. Optimum settings for automatic controllers [J]. Trans ASME, 1942, 64: 759-768

[31] ShamsuzzohaM, SkogestadS. The setpoint overshoot method: A simple and fast closed-loop approach for PID tuning [J]. Journal of Process Control, 2010, 20: 1220-1234

[32] HuW, XiaoG. Analytical proportional-integral (PI) controller tuning using closed-loop setpoint response [J]. Ind Eng Chem Res, 20112461-2466

[33] ShamsuzzohaM. Closed-loop PI/PID controller tuning for stable and integrating process with time delay [J]. Ind Eng Chem Res, 2013, 52: 12973-12992