“Finding feedforward configurations using gramian based interaction measures”

Authors: Fredrik Bengtsson and Torsten Wik,
Affiliation: Chalmers University of Technology
Reference: 2021, Vol 42, No 1, pp. 27-35.

Keywords: Process control, input-output pairing, interaction matrix, control configuration selection, sparse control, feedforward

Abstract: A sparse control structure can be seen as a decentralised controller that is expanded to include feedforward or MIMO blocks. Here, use of the gramian based interaction measures to determine a sparse control structure with feedforward is examined. A modification to the method used today is proposed and it is demonstrated that it results in a considerable improvement. Furthermore, recently proposed modifications to scaling gramian based measures are expanded to also cover sparse control structures. We show that the method that yields the best result is when two different scaling methods are combined, using one to design a decentralized controller and another to find feedforward connections.

PDF PDF (599 Kb)        DOI: 10.4173/mic.2021.1.3

References:
[1] Bengtsson, F. and Wik, T. (2017). A multiple input, multiple output model generator, Technical report, Department of Signals and Systems, Chalmers University of Technology. https://research.chalmers.se/publication/253490.
[2] Bengtsson, F., Wik, T., and Svensson, E. (2020). Resolving issues of scaling for gramian based input-output pairing methods, International Journal of Control. doi:10.1080/00207179.2020.1812725
[3] Birk, W. and Medvedev, A. (2003). A note on gramian-based interaction measures, In Proceedings of European Control Conference (ECC). pages 2625--2630. doi:10.23919/ECC.2003.7086437
[4] Chiang, T.P. and Luyben, W.L. (1988). Comparison of the dynamic performances of three heat-integrated distillation configurations, Industrial & Engineering Chemistry Research. 27(1):99--104. doi:10.1021/ie00073a019
[5] Conley, A. and Salgado, M.E. (2000). Gramian based interaction measure, In Proceedings of the 39th IEEE Conference on Decision and Control, volume5. pages 5020--5022. doi:10.1109/CDC.2001.914730
[6] Fatehi, A. (2011). Automatic pairing of large scale MIMO plants using normalised RGA, International Journal of Modelling, Identification and Control. 14(1-2):37--45. doi:10.1504/IJMIC.2011.042338
[7] Khaki-Sedigh, A. and Moaveni, B. (2009). Control configuration selection for multivariable plants, Springer. doi:10.1007/978-3-642-03193-9
[8] Salgado, M.E. and Conley, A. (2004). MIMO interaction measure and controller structure selection, International Journal of Control. 77(4):367--383. doi:10.1080/0020717042000197631
[9] Shen, Y., Cai, W.-J., and Li, S. (2010). Multivariable process control: Decentralized, decoupling, or sparse? Industrial & Engineering Chemistry Research, 49(2):761--771. doi:10.1021/ie901453z
[10] Sinkhorn, R. and Knopp, P. (1967). Concerning nonnegative matrices and doubly stochastic matrices, Pacific Journal of Mathematics. 21(2):343--348. doi:10.2140/pjm.1967.21.343
[11] Wittenmark, B. and Salgado, M.E. (2002). Hankel-norm based interaction measure for input-output pairing, In Proceedings of the 2002 IFAC World Congress, volume 139. pages 429--434. doi:10.3182/20020721-6-ES-1901.01625


BibTeX:
@article{MIC-2021-1-3,
  title={{Finding feedforward configurations using gramian based interaction measures}},
  author={Bengtsson, Fredrik and Wik, Torsten},
  journal={Modeling, Identification and Control},
  volume={42},
  number={1},
  pages={27--35},
  year={2021},
  doi={10.4173/mic.2021.1.3},
  publisher={Norwegian Society of Automatic Control}
};