The Relationship between the Condition Number, RGA and Interaction in Multivariable Systems

Aref Shahmansoorian; Sahar Jamebozorg

doi:doi:10.11648/j.acm.20140304.12

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The Relationship between the Condition Number, RGA and Interaction in Multivariable Systems

Aref Shahmansoorian, Sahar Jamebozorg

Published in Applied and Computational Mathematics (Volume 3, Issue 4)

Received: 17 June 2014 Accepted: 8 July 2014 Published: 20 July 2014

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Abstract

One of the most widely used input and output controllability measure is relative gain array (RGA). RGA measures input-output interaction in multi input multi output (MIMO) systems. The other significant measure in use is the smallest singular value of frequency subordinate. The condition number is defined as the ratio between the largest and smallest singular values of a system. In this paper, the relationship of relative gain array (RGA) with condition number and interaction as well as condition number in relation to interaction will be investigated respectively. The results indicate that the parameters under investigation are not always correlated, that is, the two-way relationship is not established between them all the time.

Published in	Applied and Computational Mathematics (Volume 3, Issue 4)
DOI	10.11648/j.acm.20140304.12
Page(s)	121-124
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Relative Gain Array, Condition Number, Interaction, MIMO Systems

References

[1]	D. Kincaid, W. Cheney, Numerical Analysis. Mathematics of Scientific Computing, Third Edition, 2008.
[2]	S. Skogestad and K. Havre., The use of RGA and Condition Number as Robustness Measures,European Symposium on Computer Aided Process Engineering -Part B, vol. 20, pp. 1005- 1010, 1996.
[3]	D.S. Lubinsky, Condition numbers of Hankel matrices for exponential weights, Mathematical Analysis and Applications 314, 266–285, 2006.
[4]	E. Bristol,On a new measure of interaction for multivariable process control, IEEE Transactions on Automatic Control, vol. 11, no. 1, pp. 133-134, 1966.
[5]	P. Grosdidier, M. Morari, B.R. Holt, Closed-loop properties from steady-state gain information, Industrial & engineering chemistry. Fundamentals - ACS, vol. 24, no. 2, pp. 221-235, 1985.
[6]	S. Skogestad, M. Morari, Implications of large RGA elements on control performance, Industrial & engineering chemistry research 26 (11), 2323-2330,1987.
[7]	C. N. Nett, V.Manousiouthakis, Euclidean Condition and Block Relative Gain, Connections, Conjectures, and Clarifications, IEEE Transactions on Automatic Control, vol. 32, no. 5, pp. 405-407, 1987.
[8]	K. Razzaghi, F. Shahraki, A Survey for the Selection of Control Structure for Distillation Columns Based on Steady State Controllability Indexes, Iranian Journal of Chemical Engineering Vol. 6, No. 2 (Spring), 2009.
[9]	Q.Liang, Is the relative gain array a sensitivity measure?, IFAC workshop on interactions between process design and process control, London,UK,pp.133-138,1992.
[10]	S. Skogestad and I. Postlethwaite, Multivariable Feedback Control: Analysis and Design (2nd Edition). UK: Wiley, 2005.
[11]	A. Khaki-Sedigh, B. Moaveni, Control Configuration Selection for Multivariable Plants, LNCIS 391, Springer Verlag, 2009.
[12]	B. Halvarsson, Interaction Analysis in Multivariable Control Systems Applications to Bioreactors for Nitrogen Removal, Phd Thesis, Uppsala University, Sweden,2010.
[13]	M.Mousavi, M.Haeri, Welding current and arc voltage control in a GMAW process using ARMarkov based MPC, Control Engineering Practice, Vol. 19, PP.1408–1422, 2011.
[14]	J.M.Maciejowski, Multivariable Feedback Design, Addison-Wesley, 1989.

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APA Style

Aref Shahmansoorian, Sahar Jamebozorg. (2014). The Relationship between the Condition Number, RGA and Interaction in Multivariable Systems. Applied and Computational Mathematics, 3(4), 121-124. https://doi.org/10.11648/j.acm.20140304.12

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ACS Style

Aref Shahmansoorian; Sahar Jamebozorg. The Relationship between the Condition Number, RGA and Interaction in Multivariable Systems. Appl. Comput. Math. 2014, 3(4), 121-124. doi: 10.11648/j.acm.20140304.12

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AMA Style

Aref Shahmansoorian, Sahar Jamebozorg. The Relationship between the Condition Number, RGA and Interaction in Multivariable Systems. Appl Comput Math. 2014;3(4):121-124. doi: 10.11648/j.acm.20140304.12

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@article{10.11648/j.acm.20140304.12,
  author = {Aref Shahmansoorian and Sahar Jamebozorg},
  title = {The Relationship between the Condition Number, RGA and Interaction in Multivariable Systems},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {4},
  pages = {121-124},
  doi = {10.11648/j.acm.20140304.12},
  url = {https://doi.org/10.11648/j.acm.20140304.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140304.12},
  abstract = {One of the most widely used input and output controllability measure is relative gain array (RGA). RGA measures input-output interaction in multi input multi output (MIMO) systems. The other significant measure in use is the smallest singular value of frequency subordinate. The condition number is defined as the ratio between the largest and smallest singular values of a system. In this paper, the relationship of relative gain array (RGA) with condition number and interaction as well as condition number in relation to interaction will be investigated respectively. The results indicate that the parameters under investigation are not always correlated, that is, the two-way relationship is not established between them all the time.},
 year = {2014}
}

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TY  - JOUR
T1  - The Relationship between the Condition Number, RGA and Interaction in Multivariable Systems
AU  - Aref Shahmansoorian
AU  - Sahar Jamebozorg
Y1  - 2014/07/20
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140304.12
DO  - 10.11648/j.acm.20140304.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 121
EP  - 124
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140304.12
AB  - One of the most widely used input and output controllability measure is relative gain array (RGA). RGA measures input-output interaction in multi input multi output (MIMO) systems. The other significant measure in use is the smallest singular value of frequency subordinate. The condition number is defined as the ratio between the largest and smallest singular values of a system. In this paper, the relationship of relative gain array (RGA) with condition number and interaction as well as condition number in relation to interaction will be investigated respectively. The results indicate that the parameters under investigation are not always correlated, that is, the two-way relationship is not established between them all the time.
VL  - 3
IS  - 4
ER  -

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Author Information

Aref Shahmansoorian

EE Department, Imam Khomeini International University, Qazvin, Iran
Sahar Jamebozorg

EE Department, Imam Khomeini International University, Qazvin, Iran

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APA Style

Aref Shahmansoorian, Sahar Jamebozorg. (2014). The Relationship between the Condition Number, RGA and Interaction in Multivariable Systems. Applied and Computational Mathematics, 3(4), 121-124. https://doi.org/10.11648/j.acm.20140304.12

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ACS Style

Aref Shahmansoorian; Sahar Jamebozorg. The Relationship between the Condition Number, RGA and Interaction in Multivariable Systems. Appl. Comput. Math. 2014, 3(4), 121-124. doi: 10.11648/j.acm.20140304.12

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AMA Style

Aref Shahmansoorian, Sahar Jamebozorg. The Relationship between the Condition Number, RGA and Interaction in Multivariable Systems. Appl Comput Math. 2014;3(4):121-124. doi: 10.11648/j.acm.20140304.12

Copy | Download

@article{10.11648/j.acm.20140304.12,
  author = {Aref Shahmansoorian and Sahar Jamebozorg},
  title = {The Relationship between the Condition Number, RGA and Interaction in Multivariable Systems},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {4},
  pages = {121-124},
  doi = {10.11648/j.acm.20140304.12},
  url = {https://doi.org/10.11648/j.acm.20140304.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140304.12},
  abstract = {One of the most widely used input and output controllability measure is relative gain array (RGA). RGA measures input-output interaction in multi input multi output (MIMO) systems. The other significant measure in use is the smallest singular value of frequency subordinate. The condition number is defined as the ratio between the largest and smallest singular values of a system. In this paper, the relationship of relative gain array (RGA) with condition number and interaction as well as condition number in relation to interaction will be investigated respectively. The results indicate that the parameters under investigation are not always correlated, that is, the two-way relationship is not established between them all the time.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - The Relationship between the Condition Number, RGA and Interaction in Multivariable Systems
AU  - Aref Shahmansoorian
AU  - Sahar Jamebozorg
Y1  - 2014/07/20
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140304.12
DO  - 10.11648/j.acm.20140304.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 121
EP  - 124
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140304.12
AB  - One of the most widely used input and output controllability measure is relative gain array (RGA). RGA measures input-output interaction in multi input multi output (MIMO) systems. The other significant measure in use is the smallest singular value of frequency subordinate. The condition number is defined as the ratio between the largest and smallest singular values of a system. In this paper, the relationship of relative gain array (RGA) with condition number and interaction as well as condition number in relation to interaction will be investigated respectively. The results indicate that the parameters under investigation are not always correlated, that is, the two-way relationship is not established between them all the time.
VL  - 3
IS  - 4
ER  -

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