RGA Analysis of Dynamic Process Models Under Uncertainty

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 236)


The aim of this paper is to gain insights into how process dynamics can affect control configuration decision based on relative gain array (RGA) analysis in the face of model uncertainty. Analytical expressions for worst-case bounds of uncertainty in steady-state and dynamic RGA are derived for two inputs two outputs (TITO) plant models. A simulation example which has been used in several prior studies is considered here to demonstrate the results. The obtained bounds of uncertainty in RGA provide valuable information pertaining to the necessity of robustness and accuracy in the model of decentralized multivariable systems.


Relative gain array Parametric uncertainty Control configuration selection Worst-case bounds Multivariable plants 


  1. 1.
    Bristol, E.H.: On a new measure of interactions for multivariable process control. IEEE Trans. Autom. Control AC-11, 133–134 (1966)Google Scholar
  2. 2.
    Niederlinski, A.: A heuristic approach to the deisgn of linear multivariable interacting control systems. Automatica 7, 691–701 (1971)CrossRefMATHGoogle Scholar
  3. 3.
    Skogestad, S., Postlethwaite, I.: Multivariable feedback control: analysis and design. Wiley, Chichester (2005)Google Scholar
  4. 4.
    McAvoy, T.J.: Interaction Analysis. Instrument Society of America, Research Triangle Park (1983a)Google Scholar
  5. 5.
    Shinskey, F.G.: Distillation Control, 2nd edn. McGraw-Hill, New York (1984)Google Scholar
  6. 6.
    Grosdidier, P., Morari, M., Holt, B.R.: Closed-loop properties from steady-state gain information. Ind. Eng. Chem. Fundam. 24, 221–235 (1985)CrossRefGoogle Scholar
  7. 7.
    Yu, C.C., Luyben, W.L.: Robustness with respect to integral controllability. Ind. Eng. Chem. Res. 26, 1043–1045 (1987)CrossRefGoogle Scholar
  8. 8.
    Skogestad, S., Morari, M.: Implications of large rga elements on control performance. Ind. Eng. Chem. Res. 26, 2323–2330 (1987)CrossRefGoogle Scholar
  9. 9.
    Chiu, M.S., Arkun, Y.: A new result on relative gain array, niederlinski index and decentralized stability condition: 2x2 plant cases. Automatica 27, 419–421 (1991)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Hovd, M., Skogestad, S.: Simple frequency-dependent tools for control system analysis, structure selection and design. Automatica 28, 989–996 (1992)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Chen, J., Freudenberg, J.S., Nett, C.N.: The role of the condition number and the relative gain array in robustness analysis. Automatica 30, 1029–1035 (1994)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Zhu, Z.X., Jutan, A.: Loop decomposition and dynamic interaction analysis of decentralized control systems. Chem. Eng. Sci. 51, 3325–3335 (1996)CrossRefGoogle Scholar
  13. 13.
    Lee, J., Edgar, T.F.: Computational method for decentralized integral controllability of low dimensional processes. Comput. Chem. Eng. 24, 847–852 (2000)CrossRefGoogle Scholar
  14. 14.
    Witcher, M., McAvoy, T.J.: Interacting control systems: steady-state and dynamic measurement of interaction. ISA Trans. 16, 35–44 (1977)Google Scholar
  15. 15.
    Bristol, E.H.: Recent results on interactions in multivariable process control. Presented at 71st Annual AIChE Meeting, Houston, TX (1979)Google Scholar
  16. 16.
    Tung, L., Edgar, T.: Analysis of control-output interactions in dynamic systems. A.I.Ch.E. J. 27, 690–693(1981)Google Scholar
  17. 17.
    Gagnepain, J.P., Seborg, D.E.: Analysis of process interactions with application to multiloop control system design. Ind. Eng. Chem. Pro. Des. Dev. 21, 5–11 (1982)Google Scholar
  18. 18.
    McAvoy, T.J., Arkun, Y., Chen, R., Robinson, D., Schnelle, P.D.: A new approach to defining a dynamic relative gain. Cont. Eng. Pract. 11, 907–914 (2003)CrossRefGoogle Scholar
  19. 19.
    Xiong, Q., Cai, W., He, M.: A practical loop pairing criterion for multivariable processes. J. Process Control 15, 741–747 (2005)CrossRefGoogle Scholar
  20. 20.
    Monshizadeh-Naini, N., Fatehi, A., Khaki-Sedigh, A.: Input-output pairing using effective relative energy array. Ind. Eng. Chem. Res. 48, 7137–7144 (2009)CrossRefGoogle Scholar
  21. 21.
    Grosdidier, P., Morari, M.: Interaction measures for systems under decentralized control. Automatica 22, 309–319 (1986)CrossRefGoogle Scholar

Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.Institute of Engineering and TechnologyJK Laxmipat University (JKLU)JaipurIndia
  2. 2.Chemical Engineering DepartmentBirla Institute of Technology and SciencePilaniIndia

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