IMC-PID tuning method based on sensitivity specification for process with time-delay

Abstract

To overcome the deficiencies addressed in the conventional PID control and improve the dynamic performance and robustness of the system, a simple design and parameters tuning approach of internal model control-PID (IMC-PID) controller was proposed for the first order plus time-delay (FOPTD) process and the second order plus time-delay (SOPTD) process. By approximating the time-delay term of the process model with the first-order Taylor series, the expressions for IMC-PID controller parameters were derived, and they had only one adjustable parameter λ which was directly related to the dynamic performance and robustness of the system. Moreover, an analytical approach of selecting λ was given based on the maximum sensitivity M_s. Then, the robust tuning of the system could be achieved according to the value of M_s. In addition, the proposed method could be extended to the integrator plus time-delay (IPTD) process and the first order delay integrating (FODI) process. Simulation studies were carried out on various processes with time-delay, and the results show that the proposed method could provide a better dynamic performance of both the set-point tracking and disturbance rejection and robustness against parameters perturbation.

Keywords

process with time-delay / integrating process / internal model control-PID / robustness / sensitivity / parameters tuning

References

[1] DuanX.-g., LiH.-x., DengHua.. Effective tuning method for fuzzy PID with internal model control [J]. Industrial and Engineering Chemistry Research, 2008, 47(21): 8317-8323

[2] DwyerA. O.Handbook of PI and PID controller tuning rules [M], 2006, London, Imperial College Press: 18-520

[3] OliveiraV. A., CossiL. V., TeixeiraM. C. M., SilvaA. M. F.. Synthesis of PID controllers for a class of time delay systems [J]. Automatica, 2009, 45(7): 1778-1782

[4] MalwatkarG. M., SonawaneS. H., WaghmareL. M.. Tuning PID controllers for higher-order oscillatory systems with improved performance [J]. ISA Transactions, 2009, 48(3): 347-353

[5] RongH.-g., ZhengH., LiZ.-q., XiaY.-xiang.. Tuning of fuzzy PID controller for Smith predictor [J]. Journal of Central South University of Technology, 2010, 17(3): 566-571

[6] UmaS., ChidambaramM., RaoS. A.. 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(5): 592-601

[7] UmaS., ChidambaramM., RaoS. A.. Enhanced control of integrating cascade processes with time delays using modified Smith predictor [J]. Chemical Engineering Science, 2010, 65(3): 1065-1075

[8] OuL.-l., GuD.-y., ZhangW.-dong.. Optimal tuning method of PID controller based on gain margin and phase margin [J]. Control Theory and Applications, 2007, 24(5): 837-841

[9] CvejnJ.. Sub-optimal PID controller settings for FOPDT systems with long dead time [J]. Journal of Process Control, 2009, 19(9): 1486-1495

[10] ShamsuzzohaM., LeeM.. An enhanced performance PID filter controller for first order time delay processes [J]. Journal of Chemical Engineering of Japan, 2007, 40(6): 501-510

[11] ShamsuzzohaM., LeeM.. Design of advanced PID controller for enhanced disturbance rejection of second-order processes with time delay [J]. American Institute of Chemical Engineers, 2008, 54(6): 1526-1536

[12] LiuK., ShimizuT., InagakiM., OhkawaA.. New tuning method for IMC controller [J]. Journal of Chemical Engineering of Japan, 1998, 31(3): 320-324

[13] ChenC.-l., HuangH.-p., HsiehC.-tyan.. Tuning of PI/PID controllers based on specification on maximum closed loop amplitude ratio [J]. Journal of Chemical Engineering of Japan, 1999, 32(6): 783-788

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

[15] JonesR. W., ThamM. T.. Maximum sensitivity based PID controller tuning: A survey and comparison [C]. SICE-ICASE International Joint Conference, 2006, New York, IEEE Computer Society: 3258-3263

[16] AliA., MajhiS.. PI/PID controller design based on IMC and percentage overshoot specification to controller set-point change [J]. ISA Transactions, 2009, 48(1): 10-15

[17] WangY.-g., ShaoH.-he.. PID auto-tuner based on sensitivity specification [J]. Chemical Engineering Research and Design, 2000, 78(2): 312-316

[18] PandaR. C., YuC.-c., HuangH.-ping.. PID tuning rules for SOPTD systems: Review and some new result [J]. ISA Transactions, 2004, 43(2): 283-295

[19] LuybenW. L.. Tuning proportional-integral-derivative controllers for integrator/deadtime processes [J]. Industrial and Engineering Chemistry Research, 1996, 35(10): 3480-3483

[20] ChidambaramM., PadmaS. R.. A simple method of tuning PID controllers for integrator/dead-time processes [J]. Computers and Chemical Engineering, 2003, 27(2): 211-215

[21] WangY.-g., CaiW.-Jian.. Advanced proportional-integral-derivative tuning for integrating and unstable processes with gain and phase margin specifications [J]. Industrial and Engineering Chemistry Research, 2002, 41(12): 2910-2914