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Subspace Identification for Data-Driven Modeling and Quality Control of Batch Processes

  • Prashant MhaskarEmail author
  • Abhinav Garg
  • Brandon Corbett
Chapter
Part of the Advances in Industrial Control book series (AIC)

Abstract

In this Chapter, a novel data-driven, quality modeling and control approach for batch processes is presented. Specifically, subspace identification methods are adapted for use with batch data to identify a state-space model from available process measurements and input moves. The resulting LTI, dynamic, state-space model is shown to be able to describe the transient behavior of finite duration batch processes. Next, the terminal quality is related to the terminal value of the identified states. Finally, the resulting model is applied in a shrinking-horizon, model predictive control scheme to directly control terminal product quality. The theoretical properties of the proposed approach are studied and compared to state-of-the-art latent variable control approaches. The efficacy of the proposed approach is demonstrated through a simulation study of a batch polymethyl methacrylate (PMMA) polymerization reactor. Results for both disturbance rejection and set-point changes (that is, new quality grades) are demonstrated.

References

  1. 1.
    Corbett, B., Macdonald, B., Mhaskar, P.: Model predictive quality control of polymethyl methacrylate. IEEE Trans. Control Syst. Technol. 23, 687–692 (2015)CrossRefGoogle Scholar
  2. 2.
    VanOverschee, P., DeMoor, B.: N4SID - Subspace algorithms for the identification of combined deterministic stochastic-systems. Automatica 30, 75–93 (1994)CrossRefGoogle Scholar
  3. 3.
    Moonen, M., Demoor, B., Vandenberghe, L., Vandewalle, J.: Online and off-line identification of linear state-space models. Int. J. Control 49, 219–232 (1989)CrossRefGoogle Scholar
  4. 4.
    Shi, R., MacGregor, J.: Modeling of dynamic systems using latent variable and subspace methods. J. Chemom. 14, 423–439 (2000). 6th Scandinavian Symposium on Chemometrics, PORSGRUNN, NORWAY, 15–19 AUG 1999Google Scholar
  5. 5.
    Overschee, Pv: Subspace Identification for Linear Systems: Theory, Implementation Applications. Kluwer Academic Publishers, Boston (1996)CrossRefGoogle Scholar
  6. 6.
    Yao, Y., Gao, F.: Subspace identification for two-dimensional dynamic batch process statistical monitoring. Chem. Eng. Sci. 63, 3411–3418 (2008)CrossRefGoogle Scholar
  7. 7.
    Dorsey, A., Lee, J.: Building inferential prediction models of batch processes using subspace identification. J. Process Control 13, 397–406 (2003)CrossRefGoogle Scholar
  8. 8.
    Flores-Cerrillo, J., MacGregor, J.F.: Control of batch product quality by trajectory manipulation using latent variable models. J. Process Control 14, 539–553 (2004)CrossRefGoogle Scholar
  9. 9.
    Kassidas, A., MacGregor, J., Taylor, P.: Synchronization of batch trajectories using dynamic time warping. AIChE J. 44, 864–875 (1998)CrossRefGoogle Scholar
  10. 10.
    Nomikos, P., Macgregor, J.: Multivariate SPC charts for monitoring batch processes. Technometrics 37, 41–59 (1995)CrossRefGoogle Scholar
  11. 11.
    Kourti, T., Nomikos, P., Macgregor, J.: Analysis, monitoring and fault-diagnosis of batch processes using multiblock and multiway PLS. J. Process Control 5, 277–284 (1995). IFAC Symposium on Advanced Control of Chemical Processes (ADCHEM 94), KYOTO, JAPAN, 25–27 MAY 1994Google Scholar
  12. 12.
    Kourti, T., Lee, J., MacGregor, J.F.: Experiences with industrial applications of projection methods for multivariate statistical process control. Comput. Chem. Eng. 20, S745–S750 (1996)CrossRefGoogle Scholar
  13. 13.
    Neogi, D., Schlags, C.: Multivariate statistical analysis of an emulsion batch process. Ind. Eng. Chem. Res. 37, 3971–3979 (1998)CrossRefGoogle Scholar
  14. 14.
    Viberg, M.: Subspace-based methods for the identification of linear time-invariant systems. Automatica 31, 1835–1851 (1995)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Qin, S.J.: An overview of subspace identification. Comput. Chem. Eng. 30, 1502–1513 (2006). 7th International Conference on Chemical Process Control (CPC 7), Lake Louise, Canada, 08–13 Jan 2006CrossRefGoogle Scholar
  16. 16.
    VanOverschee, P., DeMoor, B.: A unifying theorem for three subspace system identification algorithms. Automatica 31, 1853–1864 (1995). 10th IFAC Symposium on System Identification, Copenhagen, Denmark, 04–06 JULY 1994Google Scholar
  17. 17.
    Ekpo, E.E., Mujtaba, I.M.: Evaluation of neural networks-based controllers in batch polymerisation of methyl methacrylate. Neurocomputing 71, 1401–1412 (2008)CrossRefGoogle Scholar
  18. 18.
    Fan, S., Gretton-Watson, S., Steinke, J., Alpay, E.: Polymerisation of methyl methacrylate in a pilot-scale tubular reactor: modelling and experimental studies. Chem. Eng. Sci. 58, 2479–2490 (2003)CrossRefGoogle Scholar
  19. 19.
    Rho, H., Huh, Y., Rhee, H.: Application of adaptive model-predictive control to a batch MMA polymerization reactor. Chem. Eng. Sci. 53, 3729–3739 (1998)CrossRefGoogle Scholar
  20. 20.
    Flores-Cerrillo, J., MacGregor, J.: Latent variable MPC for trajectory tracking in batch processes. J. Process Control 15, 651–663 (2005)CrossRefGoogle Scholar
  21. 21.
    Flores-Cerrillo, J., MacGregor, J.: Iterative learning control for final batch product quality using partial least squares models. Ind. Eng. Chem. Res. 44, 9146–9155 (2005)CrossRefGoogle Scholar
  22. 22.
    Golshan, M., MacGregor, J.F., Bruwer, M.-J., Mhaskar, P.: Latent variable MPC for trajectory tracking in batch processes: role of the model structure. In: Proceedings of the American Control Conference (345 E 47TH ST, New York, NY 10017 USA), vol. 1–6, pp. 4779–4784. IEEE (2009). American Control Conference 2009, St Louis, MO, 10–12 JUNE 2009Google Scholar
  23. 23.
    Golshan, M., MacGregor, J.F., Bruwer, M.-J., Mhaskar, P.: Latent variable model predictive control (LV-MPC) for trajectory tracking in batch processes. J. Process Control 20, 538–550 (2010)CrossRefGoogle Scholar
  24. 24.
    Golshan, M., MacGregor, J.F., Mhaskar, P.: Latent variable model predictive control for trajectory tracking in batch processes: alternative modeling approaches. J. Process Control 21, 1345–1358 (2011)CrossRefGoogle Scholar
  25. 25.
    Nelson, P., Taylor, P., MacGregor, J.: Missing data methods in PCA and PLS: score calculations with incomplete observations. Chemom. Intell. Lab. Syst. 35, 45–65 (1996)CrossRefGoogle Scholar
  26. 26.
    Arteaga, F., Ferrer, A.: Dealing with missing data in MSPC: several methods, different interpretations, some examples. J. Chemom. 16, 408–418 (2002). 7th Scandinavian Symposium on Chemometrics, Copenhagen, Denmark, 19–23 AUGUST 2001Google Scholar
  27. 27.
    Flores-Cerrillo, J., MacGregor, J.F.: Control of particle size distributions in emulsion semibatch polymerization using mid-course correction policies. Ind. Eng. Chem. Res. 41(7), 1805–1814 (2002)CrossRefGoogle Scholar
  28. 28.
    Verhaegen, M.: Application of a subspace model identification technique to identify LTI systems operating in closed-loop. Automatica 29, 1027–1040 (1993)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Katayama, T.: Subspace identification of closed-loop systems. In: SICE 2002: Proceedings of the 41st SICE Annual Conference (345 E 47TH ST, NEW YORK, NY 10017 USA), vol. 1–5, pp. 1517–1520, Soc Instrument & Control Engineers, IEEE (2002). 41st Annual Conference of the Society-of-Instrument-and-Control-Engineers (SICE 2002), OSAKA, JAPAN, 05–07 AUGUST 2002Google Scholar
  30. 30.
    Veen, G., Wingerden, J.-W., Bergamasco, M., Lovera, M., Verhaegen, M.: Closed-loop subspace identification methods: an overview IET. Control Theory Appl. 7, 1339–1358 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Prashant Mhaskar
    • 1
    Email author
  • Abhinav Garg
    • 1
  • Brandon Corbett
    • 1
  1. 1.Department of Chemical EngineeringMcMaster UniversityHamiltonCanada

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