Abstract
This note provides a simple process example from chemical engineering which is proposed as a challenge problem for multivariable identification. The process considered is a simple heat-exchanger with two inputs and two outputs. It is strongly interactive and also ill-conditioned. A single slow pole, resulting from the interactions, is dominating all the individual open-loop responses. Attempting to identify a model based on fitting the individual transfer-matrix elements will usually result in a multivariable model which incorrectly has this dominant pole repeated. Such a model, although a reasonable model for the open-loop dynamics, yields a poor prediction of the process behavior under feedback control, in particular when considering partial control.
The note includes a description of the process, a file for generating open-loop “experimental” data and an example demonstrating that classical identification employing an ARMAX-type of model yields a model which is poor for feedback control studies of the process.
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These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Financial support from the Royal Norwegian Council for Scientific and Industrial Research (NTNF) is greatfully acknowledged.
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Abbreviations
- A:
-
heat transfer area (m 2)
- c P :
-
heat capacity (kJ/°Ckg)
- G(s):
-
process transfer-matrix for effect of inputs u
- g ij (s):
-
transfer matrix element i,j
- q C :
-
cold inlet flow (m 3/min)
- q H :
-
hot inlet flow (m 3/min)
- T C :
-
cold outlet temperature (°C)
- T H :
-
hot outlet temperature (°C)
- U:
-
heat transfer coefficient (kJ/m 2 °Cmin)
- V C :
-
liquid volume cold side (m 3)
- V H :
-
liquid volume hot side (m 3)
- τ1 :
-
dominant (largest) process time-constant (min.)
- τ2 :
-
smaller process time-constant (min.)
- s:
-
setpoint change
References
Jacobsen, E.W., P. Lundström and S. Skogestad, “Modelling and Identification for Robust Control of Ill-Conditioned Plants — A Distillation Case Study”, Proc. 1991 American Control Conference, Boston, 242–248, 1991.
Jacobsen, E. W. and S. Skogestad, “Inconsistencies in Dynamic Models for Ill-Conditioned Plants — with Application to Low-Order Models of Distillation Columns”, Submitted to Chem.Eng.Sci.., 1992
Kapoor, N. and T.J. McAvoy, “An Analytical Approach to Approximate Dynamic Modelling of Distillation Towers”, Ind.Eng.Chem.Res., 26, 2473–2482, 1987.
Ljung, L., System Identification Toolbox Version 3.0, MathWorks Inc., 1991.
Skogestad, S. and M. Morari, “Understanding the Dynamic Behavior of Distillation Columns”, Ind. & Eng. Chem. Res, 27, 10, 1848–1862, 1988.
Skogestad, S., M. Morari and J.C. Doyle, “Robust Control of Ill-Conditioned Plants: High-Purity Distillation”, IEEE Trans. Autom. Control, 33, 12, 1092–1105, 1988.
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© 1994 Springer-Verlag
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Jacobsen, E.W., Skogestad, S. (1994). Identification of Ill-conditioned plants — A benchmark problem. In: Smith, R.S., Dahleh, M. (eds) The Modeling of Uncertainty in Control Systems. Lecture Notes in Control and Information Sciences, vol 192. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036269
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DOI: https://doi.org/10.1007/BFb0036269
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