“Simple frequency-dependent tools for analysis of inherent control limitations”

Authors: Sigurd Skogestad, Morten Hovd and Petter Lundström,
Affiliation: NTNU
Reference: 1991, Vol 12, No 4, pp. 159-177.

Keywords: Dynamic resilience, relative gain array, disturbance rejection, process control

Abstract: By a plant´s inherent control limitations we mean the characteristics of the plant which will cause poor control performance irrespective of what controller is used. Another frequently used term is ´dynamic resilience´ which is the best closed-loop performance achievable using any controller. Since a plant´s dynamic resilience cannot be altered by change of the control algorithm, but only by design modifications, it follows that the term controllability provides a link between process design and process control. In this paper we focus on two aspects of controllability. The plants´ sensitivity to disturbances and the limitations imposed by interactions when using decentralized control. We use simple tools such as the RGA, the PRGA (Performance RGA) and the closely related Closed Loop Disturbance Gain (CLDG). For example, if kth column of the CLDG is large, then this indicates that disturbance k will be difficult to reject. This may pinpoint the need for modifying the process. The PRGA provides a measure of interaction which also includes one-way coupling. In the paper we apply these measures to distillation column control and fluid catalytic cracker (FCC) control.

PDF PDF (865 Kb)        DOI: 10.4173/mic.1991.4.1

DOI forward links to this article:
[1] Zhihong Yuan, Bingzhen Chen and Jinsong Zhao (2011), doi:10.1002/aic.12340
[2] Satish Enagandula and James B. Riggs (2006), doi:10.1016/j.conengprac.2005.03.011
[3] V.J. Pohjola, M.K. Alha and K. Lien (1994), doi:10.1016/B978-0-08-042358-6.50034-9
[4] J.H.A. Ludlage, S. Weiland, A.A. Stoorvogel and T.A.C.P.M. Backx (2003), doi:10.1109/TAC.2003.814108
[5] J.H.A. Ludlage, S. Weiland and A.A. Stoorvogel (1999), doi:10.1109/ACC.1999.786149
[6] V.J. Pohjola, M.K. Alha and K. Lien (1994), doi:10.1016/S1474-6670(17)47985-7
[1] BALCHEN, J. G. (1958). Lecture Notes in Control (Norwegian Institute of Technology (NTH), Norway (in Norwegian), .
[2] BRISTOL, E. H. (1966). On a new measure of interactions for multivariable process control, IEEE Trans. Automat. Control, AC-11, 133-134 doi:10.1109/TAC.1966.1098266
[3] BRISTOL, E. H. (1978). Recent results on interactions in multivariable process control, AlChE Annual Meeting, Chicago.
[4] FRIEDLY, E. H. (1984). Use of the Bristol array in designing noninteracting control loops, A limitation and extension, Ind. Eng. Chem. Process Des. Dev., 23, 469-472 doi:10.1021/i200026a010
[5] GROSDIDIER, P. (1990). Analysis of interaction direction with the singular value decomposition, Computers and Chem. Engng., 14, 687-689 doi:10.1016/0098-1354(90)87037-P
[6] HOLM, M., LUNDSTRÖM, P. SKOGESTAD, S. (1990). Controllability analysis using frequency-dependent tools for interactions and disturbances, AlChE Annual Meeting, Chicago, Paper 312j.
[7] HOVD, M. SKOGESTAD, S. (1992). Use of simple frequency-dependent tools for control system analysis, structure selection and design, Automatica (in press) doi:10.1016/0005-1098(92)90152-6
[8] KURIHARA, H. (1967). Optimal Control of Fluid Catalytic Cracking Processes, MIT Electr. Sys. Lab., report ESL-R-309.
[9] LEE, E. GROVES, F. R., JR. (1985). Mathematical model of the fluidized bed catalytic cracking plant, Trans. Soc. Comp. Sim., 2, 219-236.
[10] McAVOY, T. J. (1983). Interaction Analysis, Instrument Society of America, Research Triangle Park, USA.
[11] MORARI, M. (1983). Design of resilient processing plants - IR Chem, Eng. Sci., 38, 1881-1891 doi:10.1016/0009-2509(83)85044-1
[12] PERKINS, J. D. (1989). Interactions between process design and process control, Preprints IFAC Symposium DYCORD+ 89.Maastricht, NL.
[13] ROSENBROCK, H. H. (1970). State-Space and Multivariahle Theory, Nelson, London.
[14] SEBORG, D. E., EDGAR, T. F. MELLICHAMP, D. A. (1989). Process Dynamics and Control, Wiley, New York.
[15] SHINSKEY, F. G. (1967). Process Control Systems, McGraw-Hill, New York.
[16] SHINSKEY, F. G. (1984). Distillation Control, 2nd Edition.McGraw Hill, New York.
[17] SKOGESTAD, S. HOVD, M. (1990). Use of frequency-dependent RGA for control structure selection, Proc. American Control Conference, San Diego, 2133-2139.
[18] SKOGESTAD, S. LUNDSTRÖM, P. (1990). Mu-optimal LV-control of distillation columns, Computers and Chem. Engng., 14, 401-413 doi:10.1016/0098-1354(90)87016-I
[19] SKOGESTAD, S. MORARI, M. (1987). Effect of disturbance directions on closed loop performance, Ind. Eng. Chem. Res., 26, 2029-2035 doi:10.1021/ie00070a017
[20] SKOGESTAD, S. MORARI, M. (1987). Implications of large RGA elements on control performance, Ind. Eng. Chem. Res., 26, 2323-2330 doi:10.1021/ie00071a025
[21] SKOGESTAD, S., LUNDSTRÖM, P. JACOBSEN, E. W. (1990). Selecting the best distillation control configuration, AlChE Journal, 36, 753-764.
[22] STANLEY, G., MARINO-GALLARRAGA, M., MCAVOY, T. J. (1985). Shortcut operability analysis - 1: The relative disturbance gain, Ind. Eng. Chem. Process Des. Dev., 24, 1181-1188 doi:10.1021/i200031a048
[23] STEPHANOPOULOS, G. (1984). Chemical Process Control, Prentice-Hall, New York.

  title={{Simple frequency-dependent tools for analysis of inherent control limitations}},
  author={Skogestad, Sigurd and Hovd, Morten and Lundström, Petter},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}