“Variable selection for decentralized control”

Authors: Sigurd Skogestad and Manfred Morari,
Affiliation: NTNU, Department of Chemical Engineering and California Institute of Technology
Reference: 1992, Vol 13, No 2, pp. 113-125.

Keywords: DIC, relative gain array (RGA), steady-state, integral control, interactions

Abstract: Decentralized controllers (single-loop controllers applied to multivariable plants) are often preferred in practice because they are robust and relatively simple to understand and to change. The design of such a control system starts with pairing inputs (manipulated variables) and outputs (controlled variables). For a nxn plant there are n! possible pairings, and there is a great need for screening techniques to quickly eliminate undesirable pairings. In this paper we present several tests for eliminating pairings which are not decentralized integral controllable (DIC). A system is DIC if there exists a stabilizing decentralized controller with integral action such that the gains of the individual loops may be reduced independently without introducing instability. Note that the DIC is a property of the plant and the chosen pairings. The tests presented are in terms of different measures of the sign of the steady state gain matrix; including the RGA, the determinant and eigenvalues. The relationship to previously presented results is discussed in detail.

PDF PDF (1039 Kb)        DOI: 10.4173/mic.1992.2.3

DOI forward links to this article:
[1] Miltiadis V. Papalexandris (2004), doi:10.1115/1.1789537
[2] Nima Monshizadeh-Naini, Alireza Fatehi and Ali Kahki-Sedigh (2011), doi:10.1016/j.automatica.2010.10.008
[3] Wolfgang Birk, Miguel Castaño and Andreas Johansson (2014), doi:10.1016/j.conengprac.2013.12.012
[4] Kwang-Ki K. Kim, Sigurd Skogestad, Manfred Morari and Richard D. Braatz (2014), doi:10.1016/j.compchemeng.2014.07.023
[5] Kurt E. Haggblom (2008), doi:10.1109/ACC.2008.4587319
[6] P.J. Campo and M. Morari (1994), doi:10.1109/9.284869
[7] K.E. Haggblom (1997), doi:10.1109/CDC.1997.657774
[8] Ali Reza Mehrabian and Caro Lucas (2006), doi:10.1109/IS.2006.348444
[9] Mostafa Eslami and Amin Nobakhti (2015), doi:10.1109/TAC.2015.2444111
[10] Yi ZHANG, Steven Weidong Su, Andrey Savkin, Branko Celler and Hung Nguyen (2017), doi:10.1021/acs.iecr.7b02165
[11] Miguel Castaño Arranz, Wolfgang Birk and George Nikolakopoulos (2017), doi:10.1016/j.ifacol.2017.08.1536
[12] Kurt E. Haggblom (2017), doi:10.1109/CCTA.2017.8062494
[13] Parijat Bhowmick and Sourav Patra (2018), doi:10.1016/j.automatica.2018.03.053
[14] Ali Khaki-Sedigh and Bijan Moaveni (2009), doi:10.1007/978-3-642-03193-9_4
[15] Ali Khaki-Sedigh and Bijan Moaveni (2009), doi:10.1007/978-3-642-03193-9_2
[16] Julian Hofmann, Lutz Groll and Veit Hagenmeyer (2021), doi:10.1109/PC52310.2021.9447487
References:
[1] BRISTOL, E. H. (1966). On a new measure of interaction for multivariable process control, IEEE Trans. on Automatic Control, 11, 133-134 doi:10.1109/TAC.1966.1098266
[2] DOYLE, J. C. (1982). Analysis of feedback systems with structured uncertainty, IEE Proc..UK, 129, 242-250.
[3] ELAAHI, A. LUYBEN, W. L. (1985). Control of an energy-conservative complex configuration of distillation column for four-component separations, Ind. Eng. Chem, Process Des. Dev., 24, 368-376 doi:10.1021/i200029a025
[4] GROSDIDIER, P., MORARI, M. HOLT, B. R. (1985). Closed-loop properties from steady-state gain information, Ind. Eng. Chem. Fund., 24, 221-235 doi:10.1021/i100018a015
[5] GROSDIDIER, P. MORARI, M. (1986). Interaction measures for systems under decentralized control, Automatica, 22, 309-319 doi:10.1016/0005-1098(86)90029-4
[6] GROSDIDIER, P. MORARI, M. (1987). A computer aided methodology for the design of decentralized controllers, Comput. chem. Engng., 11, 423-433.
[7] MANOUSIOUTHAKIS, V., SAVAGE, R. ARKUN, Y. (1986). Synthesis of decentralized controllers using the concept of block relative gain, AIChE Journal, 32, 991-1003 doi:10.1002/aic.690320609
[8] McAVOY, T. J. (1983). Interaction Analysis - Principles and Applications, Instrument Society of America, Research Triangle Park, NC.
[9] MITARES, G., COLE, J. D., NAUGLE, N. W., PREISIG, H. A. HOLLAND, C. D. (1986). A new criterion for the pairing of control and manipulated variables, AlChE Journal, 32, 1439-1449.
[10] NETT, C. N. SPANG, H. A. III (1987). Control structure design: a missing link in the evolution of modern control theory, Presented at the 1987 American Control Conference, Minneapolis, June 1987.
[11] NIEDERLINSKI, A. (1971). A heuristic approach to the design of linear multivariable control systems, Automatica, 7, 691 doi:10.1016/0005-1098(71)90007-0
[12] SKOGESTAD, S. MORARI, M. (1987). Letter to the Editor, AlChE Journal, 33, 701-702.
[13] SKOGESTAD, S. MORARI, M. (1989). Robust performance of decentralized control systems by independent designs, Automatica, 25, 119-125 doi:10.1016/0005-1098(89)90127-1
[14] YU, C.-C. LUYBEN, W. L. (1986). Design of multiloop SISO controllers in multivariable processes, Ind. Eng. Chem. Process Des. Dev., bf 25, 498-503.


BibTeX:
@article{MIC-1992-2-3,
  title={{Variable selection for decentralized control}},
  author={Skogestad, Sigurd and Morari, Manfred},
  journal={Modeling, Identification and Control},
  volume={13},
  number={2},
  pages={113--125},
  year={1992},
  doi={10.4173/mic.1992.2.3},
  publisher={Norwegian Society of Automatic Control}
};