Multiloop Control of Multivariable Processes

  • Tao LiuEmail author
  • Furong Gao
Part of the Advances in Industrial Control book series (AIC)


A number of criteria have been explored for analyzing cross interaction in multivariable systems (see Bristol (1966), McAvoy (1983), Jensen et al. (1986), Huang et al. (1994, 2003), Shinskey (1996), Lee and Edgar (2004), Salgado and Conley (2004), Skogestad and Postlethwaite (2005), and He et al. (2009)). Among these criteria, relative gain array (RGA) and singular value decomposition (SVD) have been widely recognized in practice, which are briefly introduced as follows.


  1. Åström KJ, Hägglund T (1995) PID controller: theory, design, and tuning, 2nd edn. ISA Society of America, Research Triangle ParkGoogle Scholar
  2. Bristol EH (1966) On a new measure of interaction for multivariable process control. IEEE Trans Autom Control 11(1):133–134CrossRefGoogle Scholar
  3. Campo PJ, Morari M (1994) Achievable closed-loop properties of systems under decentralized control: involving the steady-state gain. IEEE Trans Autom Control 39(3):932–943MathSciNetzbMATHCrossRefGoogle Scholar
  4. Cha S, Chun D, Lee J (2002) Two-step IMC-PID method for multiloop control system design. Ind Eng Chem Res 41(12):3037–3041CrossRefGoogle Scholar
  5. Chen D, Seborg DE (2002) Multiloop PI/PID controller design based on Gershgorin bands. IEE Process Control Theory Appl 149(1):68–73CrossRefGoogle Scholar
  6. Chen D, Seborg DE (2003) Design of decentralized PI control systems based on Nyquist stability analysis. J Process Control 13(1):27–39CrossRefGoogle Scholar
  7. Chien IL, Huang HP, Yang JC (1999) A simple multiloop tuning method for PID controllers with no proportional kick. Ind Eng Chem Res 38(4):1456–1468CrossRefGoogle Scholar
  8. Chiu MS, Arkun Y (1992) A methodology for sequential design of robust decentralized control systems. Automatica 28(5):997–1002MathSciNetzbMATHCrossRefGoogle Scholar
  9. Cui H, Jacobsen EW (2002) Performance limitations in decentralized control. J Process Control 12:485–494CrossRefGoogle Scholar
  10. Desbiens A, Pomerleau A, Hodouin D (1996) Frequency based tuning of SISO controllers for two-by-two processes. IEE Proccess Control Theory Appl 143(1):49–56MathSciNetzbMATHCrossRefGoogle Scholar
  11. Gündes AN, Özgüler AB (2002) Two-channel decentralized integral-action controller design. IEEE Trans Autom Control 47(12):2084–2088CrossRefGoogle Scholar
  12. Halevi Y, Palmor ZJ, Efrati T (1997) Automatic tuning of decentralized PID controllers for MIMO processes. J Process Control 7(2):119–128CrossRefGoogle Scholar
  13. He MJ, Cai WJ, Ni W, Xie L-H (2009) RNGA based control system configuration for multivariable processes. J Process Control 19:1036–1042CrossRefGoogle Scholar
  14. Ho WK, Lee TH, Gan OP (1997) Tuning of multiloop proportional-integral-derivative controllers based on gain and phase margin specification. Ind Eng Chem Res 36:2231–2238CrossRefGoogle Scholar
  15. Hovd M, Skogestad S (1993) Improved independent design of robust decentralized controllers. J Process Control 3:43–51CrossRefGoogle Scholar
  16. Huang HP, Ohshima M, Hashimoto L (1994) Dynamic interaction and multiloop control system design. J Process Control 4(1):15–22CrossRefGoogle Scholar
  17. Huang HP, Jeng JC, Chiang CH, Pan W (2003) A direct method for multi-loop PI/PID controller design. J Process Control 13(8):769–786CrossRefGoogle Scholar
  18. Jensen N, Fisher DG, Shah SL (1986) Interaction analysis in multivariable control systems. AICHE J 32(6):959–970CrossRefGoogle Scholar
  19. Jung J, Choi JY, Lee J (1999) One-parameter method for a multiloop control system design. Ind Eng Chem Res 38:1580–1588CrossRefGoogle Scholar
  20. Lee J, Cho W, Edgar TF (1998) Multiloop PI controller tuning for interacting multivariable processes. Comput Chem Eng 22(11):1711–1723CrossRefGoogle Scholar
  21. Lee J, Edgar TF (2000) Phase conditions for stability of multi-loop control systems. Comput Chem Eng 23:1623–1630CrossRefGoogle Scholar
  22. Lee J, Edgar TF (2004) Dynamic interaction measures for decentralized control of multivariable processes. Ind Eng Chem Res 43(2):283–287CrossRefGoogle Scholar
  23. Liu T, Zhang W, Gu DY (2005) Analytical multiloop PI/PID controller design for two-by-two processes with time delays. Ind Eng Chem Res 44(6):1832–1841CrossRefGoogle Scholar
  24. Loh AP, Hang CC, Quek CK, Vasnani VU (1993) Autotuning of multiloop proportional-integral controllers using relay feedback. Ind Eng Chem Res 32(6):1102–1107CrossRefGoogle Scholar
  25. Luyben WL (1986) Simple method for tuning SISO controllers in multivariable systems. Ind Eng Chem Process Des Dev 25:654–660CrossRefGoogle Scholar
  26. Luyben WL (1990) Process modeling, simulation, and control for chemical engineers. McGraw Hill, New YorkGoogle Scholar
  27. McAvoy TJ (1983) Interaction analysis. ISA Society of America, Research Triangle ParkzbMATHGoogle Scholar
  28. Morari M, Zafiriou E (1989) Robust process control. Prentice Hall, Englewood CliffGoogle Scholar
  29. Ogunnaike BA, Ray WH (1994) Process dynamics, modeling, and control. Oxford University Press, New YorkGoogle Scholar
  30. Palmor ZJ, Halevi Y, Krasney N (1995) Automatic tuning of decentralized PID controllers for TITO processes. Automatica 31(7):1001–1010zbMATHCrossRefGoogle Scholar
  31. Salgado ME, Conley A (2004) MIMO interaction measure and controller structure selection. Int J Control 77(4):367–383MathSciNetzbMATHCrossRefGoogle Scholar
  32. Seborg DE, Edgar TF, Mellichamp DA (2004) Process dynamics and control, 2nd edn. Wiley, HobokenGoogle Scholar
  33. Shen SH, Yu CC (1994) Use of relay-feedback test for automatic tuning of multivariable systems. AICHE J 40(4):627–646CrossRefGoogle Scholar
  34. Shinskey FG (1996) Process control system, 4th edn. McGraw Hill, New YorkGoogle Scholar
  35. Skogestad S, Postlethwaite I (2005) Multivariable feedback control: analysis and design, 2nd edn. Wiley, ChichesterGoogle Scholar
  36. Wang QG, Lee TH, Zhang Y (1998) Mutiloop version of the modified Ziegler-Nichols method for two input two output processes. Ind Eng Chem Res 37:4725–4733CrossRefGoogle Scholar
  37. Wang QG, Zou B, Lee TH (1997) Auto-tuning of multivariable PID controllers from decentralized relay feedback. Automatica 33(3):319–330MathSciNetzbMATHCrossRefGoogle Scholar
  38. Wood RK, Berry MW (1973) Terminal composition control of binary distillation column. Chem Eng Sci 28(10):1707–1717Google Scholar
  39. Zhang Y, Wang QG, Åström KJ (2002) Dominant pole placement for multi-loop control systems. Automatica 38(7):1213–1220zbMATHCrossRefGoogle Scholar
  40. Zhou KM, Doyle JC, Glover K (1996) Robust and optimal control. Prentice Hall, Englewood CliffzbMATHGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.RWTH Aachen UniversityAachenGermany
  2. 2.Hong Kong University of Science and TechnologyKowloonHong Kong SAR

Personalised recommendations