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A Frequency Domain PID Controller Design Method Using Direct Synthesis Approach

  • Research Article - Chemical Engineering
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Abstract

In this study, the PID controller design method based on direct synthesis approach for achieving the desired set-point or load-disturbance response is proposed. The PID controller is derived using an approximate frequency-response-matching criteria. A simple criterion has been also provided to choose the frequency points for matching of the proposed PID controller with the desired direct synthesis controller. It is a unified approach which deals with broad class of processes including integrating and inverse response, and it is directly applicable to any order of process with time delay. The ideal controller based on the direct synthesis approach has been directly approximated to the PID controller in desired frequency range. Therefore, the proposed method is free from model reduction in high-order process to low-order process and also rational approximation of the time-delay term e −sL. The advantage of method is illustrated through examples taken from the literature and compared with some of the well-known methods.

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References

  1. Astrom K.J., Hagglund T.: PID Controllers Theory Design and Tuning. 2nd edn. Instrument Society of America, Research Triangle Park, North Carolina (1995)

    Google Scholar 

  2. Vilanova R., Visioli A.: PID Control in the Third Millennium: Lessons Learned and New Approaches. S. L. Ltd., Ed., London (2012)

    Book  Google Scholar 

  3. Ang K.H., Chong G., Li Y.: PID Control System Analysis, Design, and Technology. IEEE Trans. Control System Tech. 13(4), 559–576 (2005)

    Article  Google Scholar 

  4. Rivera D.E., Morari M., Skogestad S.: Internal model control 4. PID controller design. Ind. Eng. Chem. Process 25, 252–265 (1986)

    Article  Google Scholar 

  5. Li Y., Park S., Lee M., Brosi C.: PID controller tuning for desired closed-loop responses for SI/SO systems. AIChE J. 44(1), 106–115 (1998)

    Article  Google Scholar 

  6. Shamsuzzoha M., Lee M.: IMC–PID controller design for improved disturbance rejection of time-delayed processes. Ind. Eng. Chem. Res. 46, 2077–2091 (2007)

    Article  Google Scholar 

  7. Panda R.C.: Synthesis of PID tuning rule using the desired closed-loop response. Ind. Eng. Chem. Res. 47, 8684–8692 (2008)

    Article  Google Scholar 

  8. Panda R.C.: Synthesis of PID controller for unstable and integrating processes. Chem. Eng. Sci. 64, 2807–2816 (2009)

    Article  Google Scholar 

  9. Shamsuzzoha M., Lee M.: Design of advanced PID controller for enhanced disturbance rejection of second-order processes with time delay. AIChE J. 54(6), 1526–1536 (2008)

    Article  Google Scholar 

  10. Shamsuzzoha M., Lee M.: Analytical design of enhanced PID filter controller for integrating and first order unstable processes with time delay. Chem. Eng. Sci. 63, 2717–2731 (2008)

    Article  Google Scholar 

  11. Vijayan V., Panda R.C.: Design of PID controllers in double feedback loops for SISO systems with set-point filters. ISA Trans. 51, 514–521 (2012)

    Article  Google Scholar 

  12. Wang Q.G., Hang C.C., Yang X.P.: Single-loop controller design via IMC principles. Automatica 37, 2041–2048 (2001)

    Article  MATH  Google Scholar 

  13. Wang L., Barnes T.J.D., Cluett W.R.: New frequency domain design method for PID controllers. IEE Proc. Control Theory Appl. 142(04), 265–271 (1995)

    Article  MATH  Google Scholar 

  14. Wang Q.G., Hang C.C., Bi Q.: A frequency domain controller design method. Trans. Inst. Chem. Eng. 75(Part A), 64–74 (1997)

    Article  Google Scholar 

  15. Seborg D.E., Edgar T.F., Mellichamp D.A.: Process Dynamics and Control. Willey, New York (1989)

    Google Scholar 

  16. Chen D., Seborg D.E.: PI/PID controller design based on direct synthesis and disturbance rejection. Ind. Eng. Chem. Res. 41, 4807–4822 (2002)

    Article  Google Scholar 

  17. Rao A.S., Rao V.S.R., Chidambaram M.: Direct synthesis-based controller design for integrating processes with time delay. J. Franklin Inst. 346, 38–56 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  18. Vanavil, B.; Chaitanya, K.K.; Rao, A.S.: Improved PID controller design for unstable time delay processes based on direct synthesis method and maximum sensitivity. Int. J. Syst. Sci. 46(8), 1349–1366 (2015). doi:10.1080/00207721.2013.822124

  19. Shamsuzzoha M., Skogestad S.: The setpoint overshoot method: a simple and fast closed-loop approach for PID tuning. J. Process Control 20, 1220–1234 (2010)

    Article  Google Scholar 

  20. Hu W., Xiao G.: Analytical proportional–integral (PI) controller tuning using closed-loop setpoint response. Ind. Eng. Chem. Res 2011, 2461–2466 (2011)

    Article  Google Scholar 

  21. Haugen F.: Comparing PI tuning methods in a real benchmark temperature control system. Model. Identif. Control 31, 79–91 (2010)

    Article  Google Scholar 

  22. Shamsuzzoha M.: Closed-loop PI/PID controller tuning for stable and integrating process with time delay. Ind. Eng. Chem. Res 52, 12973–12992 (2013)

    Article  Google Scholar 

  23. Alcantara S., Vilanova R., Pedret C.: PID control in terms of robustness/performance and servo/regulator trade-offs: a unifying approach to balanced autotuning. J. Process Control 23, 527–542 (2013)

    Article  Google Scholar 

  24. Alcantara S., Pedret C., Vilanova R.: On the model matching approach to PID design: analytical perspective for robust Servo/Regulator tradeoff tuning. J. Process Control 20, 596–608 (2010)

    Article  Google Scholar 

  25. Alcantara S., Zhang W., Pedret C., Vilanova R., Skogestad S.: IMC-like analytical H∞ design with S/SP mixed sensitivity consideration: utility in PID tuning guidance. J. Process Control 21, 976–985 (2011)

    Article  Google Scholar 

  26. Alcantara, S.; Vilanova, R.; Pedret, C.; Skogestad, S.: A look into robustness/performance and servo/regulation issues in PI tuning. In: Proceedings of the IFAC Conference on Advances in PID Control PID’12, Brescia(Italy) (2012)

  27. Lee J., Cho W., Edgar T.F.: Simple analytic PID controller tuning rules revisited. Ind. Eng. Chem. Res. 52, 12973–12992 (2013)

    Article  Google Scholar 

  28. Torrico B.C., Cavalcante M.U., Braga A.P., Normey-Rico J.E., Albuquerque A.A.: Simple tuning rules for dead-time compensation of stable, integrative, and unstable first-order dead-time processes. Ind. Eng. Chem. Res. 52, 11646–11654 (2013)

    Article  Google Scholar 

  29. Ravi V.R., Thyagarajan T.: Adaptive decentralized PI controller for two conical tank interacting level system. Arab. J. Sci. Eng. 39, 8433–8451 (2014)

    Article  MathSciNet  Google Scholar 

  30. Milne-Thomson L.M.: The Calculus of Finite Differences. Macmillan, London (1960)

    Google Scholar 

  31. Pal J.: An algorithm method for the simplification of linear dynamic scalar systems. Int. J. Control 43(1), 257–269 (1986)

    Article  MATH  Google Scholar 

  32. Pan S., Pal J.: Reduced order modelling of discrete-time systems. Appl. Math. Model. 19, 133–138 (1995)

    Article  MATH  Google Scholar 

  33. Skogestad S.: Simple analytic rules for model reduction and PID controller tuning. J. Process Control 13, 291–309 (2003)

    Article  Google Scholar 

  34. Jeng J.-C., Lin S.-W.: Robust proportional–integral–derivative controller design for stable/integrating processes with inverse response and time delay. Ind. Eng. Chem. Res. 51, 2652–2665 (2012)

    Article  Google Scholar 

  35. Chen, P.; Zhang, W.; Zhu, L.: Design and tuning method of PID controller for A class of inverse response processes. In: Proceedings of the 2006 American Control Conference, Minneapolis, Minnesota, USA, 2006

  36. Ho W.K., Hang C.C., Cao L.S.: Tuning of PID controllers based on gain and phase margin specification. Automatica 31(3), 497–502 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  37. Ali A., Majhi S.: PID controller tuning for integrating processes. ISA Trans. 49, 70–78 (2010)

    Article  Google Scholar 

  38. Chidambaram M., Sree R.P.: A simple method of tuning of PID controller for integrating/dead time processes. Comput. Chem. Eng. 27, 211–215 (2003)

    Article  Google Scholar 

  39. Shamsuzzoha M., Lee M.: PID controller design for integrating processes with time delay. Korean J. Chem. Eng. 25(4), 637–645 (2008)

    Article  Google Scholar 

  40. Gu D., Ou L., Wang P., Zhang W.: Relay feedback autotuning method for integrating processes with inverse response and time delay. Ind. Eng. Chem. Res. 45, 3119–3132 (2006)

    Article  Google Scholar 

  41. Yang X., Xu B., Chiu M.S.: PID controller design directly from plant data. Ind. Eng. Chem. Res. 50, 1352–1359 (2011)

    Article  Google Scholar 

  42. Zhang W., Xi Y., Yang G., Xu X.: Design PID controllers for desired time-domain or frequency-domain response. ISA Trans. 41, 511–520 (2002)

    Article  Google Scholar 

  43. Shamsuzzoha, M.: A unified approach for proportional–integral–derivative controller design for time delay processes. Korean J. Chem. Eng. doi:10.1007/s11814-014-0237-6

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Authors and Affiliations

  1. Department of Electrical Engineering, Indian School of Mines, Dhanbad, 826004, India

    Md Nishat Anwar & Somnath Pan

  2. Department of Chemical Engineering, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    M. Shamsuzzoha

Authors
  1. Md Nishat Anwar
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  2. M. Shamsuzzoha
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  3. Somnath Pan
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Correspondence to M. Shamsuzzoha.

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Anwar, M.N., Shamsuzzoha, M. & Pan, S. A Frequency Domain PID Controller Design Method Using Direct Synthesis Approach. Arab J Sci Eng 40, 995–1004 (2015). https://doi.org/10.1007/s13369-015-1582-4

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  • DOI: https://doi.org/10.1007/s13369-015-1582-4

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