Skip to main content
SpringerLink
Log in

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

  • Chapter
  • First Online:
Modeling and Control of Batch Processes

Part of the book series: Advances in Industrial Control ((AIC))

  • 665 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    ©2015 The MathWorks, Inc. MATLAB and Simulink are registered trademarks of the MathWorks, Inc. See www.mathworks.com/trademarks for a list of additional trademarks. Other product or brand names may be trademarks or registered trademarks of their respective holders.

References

  1. Corbett, B., Macdonald, B., Mhaskar, P.: Model predictive quality control of polymethyl methacrylate. IEEE Trans. Control Syst. Technol. 23, 687–692 (2015)

    Article  Google Scholar 

  2. VanOverschee, P., DeMoor, B.: N4SID - Subspace algorithms for the identification of combined deterministic stochastic-systems. Automatica 30, 75–93 (1994)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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 1999

    Google Scholar 

  5. Overschee, Pv: Subspace Identification for Linear Systems: Theory, Implementation Applications. Kluwer Academic Publishers, Boston (1996)

    Book  Google Scholar 

  6. Yao, Y., Gao, F.: Subspace identification for two-dimensional dynamic batch process statistical monitoring. Chem. Eng. Sci. 63, 3411–3418 (2008)

    Article  Google Scholar 

  7. Dorsey, A., Lee, J.: Building inferential prediction models of batch processes using subspace identification. J. Process Control 13, 397–406 (2003)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  9. Kassidas, A., MacGregor, J., Taylor, P.: Synchronization of batch trajectories using dynamic time warping. AIChE J. 44, 864–875 (1998)

    Article  Google Scholar 

  10. Nomikos, P., Macgregor, J.: Multivariate SPC charts for monitoring batch processes. Technometrics 37, 41–59 (1995)

    Article  Google Scholar 

  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 1994

    Google Scholar 

  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)

    Article  Google Scholar 

  13. Neogi, D., Schlags, C.: Multivariate statistical analysis of an emulsion batch process. Ind. Eng. Chem. Res. 37, 3971–3979 (1998)

    Article  Google Scholar 

  14. Viberg, M.: Subspace-based methods for the identification of linear time-invariant systems. Automatica 31, 1835–1851 (1995)

    Article  MathSciNet  Google Scholar 

  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 2006

    Article  Google Scholar 

  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 1994

    Google Scholar 

  17. Ekpo, E.E., Mujtaba, I.M.: Evaluation of neural networks-based controllers in batch polymerisation of methyl methacrylate. Neurocomputing 71, 1401–1412 (2008)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  20. Flores-Cerrillo, J., MacGregor, J.: Latent variable MPC for trajectory tracking in batch processes. J. Process Control 15, 651–663 (2005)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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 2009

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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 2001

    Google Scholar 

  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)

    Article  Google Scholar 

  28. Verhaegen, M.: Application of a subspace model identification technique to identify LTI systems operating in closed-loop. Automatica 29, 1027–1040 (1993)

    Article  MathSciNet  Google Scholar 

  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 2002

    Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemical Engineering, McMaster University, Hamilton, ON, Canada

    Prashant Mhaskar, Abhinav Garg & Brandon Corbett

Authors
  1. Prashant Mhaskar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abhinav Garg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Brandon Corbett
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Prashant Mhaskar .

Appendices

11.8 Appendix A: Identified PMMA Models

1.1 11.8.1 Dynamic Model (Subspace Identification)

$$ \mathbf {A} = \begin{bmatrix} 0.98516&-0.041768&-0.11588&-0.081012&0.14133&0.027337&0.065944&-0.008974&0.026833\\ -0.053849&0.79861&0.063273&-0.074642&0.41775&0.21953&0.16301&0.074074&0.0076323\\ 0.014815&0.053163&0.98982&0.039297&-0.078398&0.084098&0.075658&-0.01062&-0.015769\\ -0.0084043&-0.029059&0.010815&0.96612&0.11911&-0.033243&0.078468&0.039254&0.0071832\\ -0.005217&-0.019198&0.0048115&-0.011641&0.8878&-0.080295&-0.030649&-0.13453&0.1784\\ -0.001108&-0.0040268&0.00085731&-0.004503&-0.03083&0.93209&-0.038058&-0.12716&0.052801\\ -0.00041708&-0.001586&-0.00040162&-0.00030684&0.1618&0.086359&0.80687&-0.077694&-0.20116\\ -0.006212&-0.022836&0.004279&-0.011486&-0.076859&-0.10873&-0.20005&0.18359&0.014277\\ 0.0037065&0.013566&-0.002334&0.0087541&-0.13833&-0.0099258&0.39496&0.66942&0.4205\\ \end{bmatrix} $$
$$ \varvec{\lambda _A} = \begin{bmatrix} 0.2224\\ 0.56704+0.19029i\\ 0.56704-0.19029i\\ 0.80866\\ 0.86491\\ 0.99958+0.0039544i\\ 0.99958-0.0039544i\\ 0.98534\\ 0.95601\\ \end{bmatrix} $$
$$ \mathbf {B} = \begin{bmatrix} -0.058874\\ -0.20903\\ 0.057585\\ -0.032671\\ -0.020277\\ -0.004307\\ -0.0016209\\ -0.024143\\ 0.014406\\ \end{bmatrix} $$
$$ \mathbf {C} = \begin{bmatrix} -0.26209&-0.97571&0.49382&-0.081618&0.077041&0.15654&0.3934&0.34012&-0.064527\\ 0.003204&0.16186&0.23888&-0.63143&0.010558&-0.1874&-0.030857&0.00037325&-0.01769\\ -0.72052&0.17384&0.02821&0.024757&0.21978&0.045767&0.094573&-0.051717&0.00075872\\ \end{bmatrix} $$

1.2 11.8.2 Quality Model

$$ \mathbf {Q} = \begin{bmatrix} -0.0043689&-0.016241&-0.073542&0.038459\\ 1458.7852&12206.803&21917.8887&-41581.0424\\ 2432.0509&19726.6489&33292.0309&-72136.2077\\ -0.00039146&-0.021493&-0.056014&0.03811\\ \end{bmatrix} $$
$$ \varvec{c_k} = \begin{bmatrix} -5.0845\\ 1985711.0276\\ 3323464.3048\\ 1.3826\\ \end{bmatrix} $$

11.9 Appendix B: Tuning Parameters for Benchmark Control

1.1 11.9.1 PI

$$ k_c = -0.1 $$
$$ \tau _I = 30 $$

1.2 11.9.2 LVMPC

Number of principal components = 5

$$ \mathbf {Q}_1= \begin{bmatrix} 0.01&0&0&0\\ 0&0.01&0&0\\ 0&0&0.01&0\\ 0&0&0&0\\ \end{bmatrix} $$
$$ \mathbf {Q}_2 = \begin{bmatrix} 10&0&0&0&0\\ 0&10&0&0&0\\ 0&0&10&0&0\\ 0&0&0&10&0\\ 0&0&0&0&10\\ \end{bmatrix} $$
$$ \lambda = 100; $$
$$ \left| \Delta t\right| \le 0.5. $$

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Mhaskar, P., Garg, A., Corbett, B. (2019). Subspace Identification for Data-Driven Modeling and Quality Control of Batch Processes. In: Modeling and Control of Batch Processes. Advances in Industrial Control. Springer, Cham. https://doi.org/10.1007/978-3-030-04140-3_11

Download citation

Publish with us

Policies and ethics

Search

Navigation