Skip to main content
SpringerLink
Log in

Model variables identification of a gas turbine using a subspace approach based on input/output data measurements

  • Research Article
  • Published:
Control Theory and Technology Aims and scope Submit manuscript

Abstract

This paper deals with a state model identification of a gas turbine used for gas transport, using a subspace approach of the state space model. This method provides a reliable and robust state representation of the model, taking advantage of its benefits in the control, monitoring, and supervision of this machine. The model for each variable is set so that the state matrices associated with the gas turbine model are determined from their real input/output data. The comparison of the obtained identification results with those of the actual turbine operation serves to validate the proposed model in this work. This numerical algorithm of the subspace identification method is full of information and more accurate in terms of residual modeling error, and expresses a very high level of confidence in the identified turbine system dynamics. Hence, the controllability and observability tests of turbine operation for different input/output variables allowed to validate the real-time operating stability of the turbine.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

References

  1. Benyounes, A., Hafaifa, A., & Guemana, M. (2016). Gas turbine modelling based on fuzzy clustering algorithm using experimental data. Journal of Applied Artificial Intelligence, 30(1), 29–51.

    Article  Google Scholar 

  2. Chaibakhsh, A., & Amirkhani, S. (2018). A simulation model for transient behaviour of heavy-duty gas turbines. Applied Thermal Engineering, 132, 115–127.

    Article  Google Scholar 

  3. Gupta, S., Gupta, R., & Padhee, S. (2020). Stability and weighted sensitivity analysis of robust controller for heat exchanger. Control Theory and Technology, 18, 56–71.

    Article  MathSciNet  Google Scholar 

  4. Asgari, H., Chen, X., Morini, M., Pinelli, M., Sainudiin, R., Spina, P. R., et al. (2016). NARX models for simulation of the start-up operation of a single-shaft gas turbine. Applied Thermal Engineering, 93, 368–376.

    Article  Google Scholar 

  5. Benrahmoune, M., Hafaifa, A., Guemana, M., & Chen, X i a o Qi. (2018). Detection and modeling vibrational behavior of a gas turbine based on dynamic neural networks approach. Journal of Mechanical Engineering, 68(3), 143–166.

    Google Scholar 

  6. Hadroug, N., Hafaifa, A., Batel, N., Abdellah, K., & Chaibet, A. (2018). Active fault tolerant control based on a neuro fuzzy inference system applied to a two shafts gas turbine. Journal of Applied Artificial Intelligence, 32(6), 515–540.

    Article  Google Scholar 

  7. Varanasi, S. K., & Jampana, P. (2020). Nuclear norm subspace identification of continuous time state–space models with missing outputs. Control Engineering Practice, 95, 104239.

    Article  Google Scholar 

  8. Gibanica, M., & Abrahamsson, T. J. S. (2020). Identification of physically realistic state-space models for accurate component synthesis. Mechanical Systems and Signal Processing, 145, 106906.

    Article  Google Scholar 

  9. Liu, T., Hou, J., Qin, S. J., & Wang, W. (2020). Subspace model identification under load disturbance with unknown transient and periodic dynamics. Journal of Process Control, 85, 100–111.

    Article  Google Scholar 

  10. Diaz, J. L. C., Ocampo-Martinez, C., & Olaru, S. (2020). Dual mode control strategy for the energy efficiency of complex and flexible manufacturing systems. Journal of Manufacturing Systems, 56, 104–116.

    Article  Google Scholar 

  11. Giannopoulos, A., & Aider, J.-L. (2020). Prediction of the dynamics of a backward-facing step flow using focused time-delay neural networks and particle image velocimetry data-sets. International Journal of Heat and Fluid Flow, 82, 108533.

    Article  Google Scholar 

  12. Garg, A., Gomes, F. P. C., Mhaskar, P., & Thompson, M. R. (2019). Model predictive control of uni-axial rotational molding process. Computers & Chemical Engineering, 121, 306–316.

    Article  Google Scholar 

  13. Slim, H., Maher, K., & Abdessattar, C. (2014). N4SID and MOESP algorithms to highlight the ill-conditioning into subspace identification. International Journal of Automation and Computing, 11(1), 30–38.

    Article  Google Scholar 

  14. Akçay, H. (2014). Spectral estimation in frequency-domain by subspace techniques. Signal Processing, 101, 204–217.

    Article  Google Scholar 

  15. Scheel, M., Gibanica, M., & Nord, A. (2019). State-space dynamic substructuring with the transmission simulator method. Experimental Techniques, 43, 325–340.

    Article  Google Scholar 

  16. Wiese, A. P., Blom, M. J., Manzie, C., Brear, M. J., & Kitchener, A. (2015). Model reduction and MIMO model predictive control of gas turbine systems. Control Engineering Practice, 45, 194–206.

    Article  Google Scholar 

  17. Sashittal, P., & Bodony, D. J. (2019). Reduced-order control using low-rank dynamic mode decomposition. Theoretical and Computational Fluid Dynamics, 33, 603–623.

    Article  MathSciNet  Google Scholar 

  18. Hadroug, N., Hafaifa, A., Abdellah, K., & Chaibet, A. (2017). Dynamic model linearization of two shafts gas turbine via their input / output data around the equilibrium points. Energy, 120, 488–497.

    Article  Google Scholar 

  19. Benner, P., Himpe, C., & Mitchell, T. (2018). On reduced input-output dynamic mode decomposition. Advances in Computational Mathematics, 44, 1751–1768.

    Article  MathSciNet  Google Scholar 

  20. Favoreel, W., De Moor, B., & Van Overschee, P. (2020). Subspace state space system identification for industrial processes. Journal of Process Control, 10(2/3), 149–155.

    Google Scholar 

  21. Wang, J., Miller, D., Wang, H. W., & Hong, G. (2015). Closed-loop subspace identification algorithm based on correlation function estimates. Science China Information Sciences, 58(3), 1–10.

    MATH  Google Scholar 

  22. Mithun, I. M., Mohan, S., & Bhikkaji, B. (2019). Optimal finite-dimensional spectral densities for the identification of continuous-time MIMO systems. Control Theory and Technology, 17, 276–296.

    Article  MathSciNet  Google Scholar 

  23. Wang, D., Ding, F., & Ximei, L. (2014). Least squares algorithm for an input nonlinear system with a dynamic subspace state space model. Nonlinear Dynamics, 75(1/2), 49–61.

    Article  MathSciNet  Google Scholar 

  24. Hou, J., Liu, T., & Chen, F. (2017). Orthogonal projection-based subspace identification against colored noise. Control Theory and Technology, 15(1), 69–77.

    Article  MathSciNet  Google Scholar 

  25. Simani, S., & Fantuzzi, C. (2006). Dynamic system identification and model-based fault diagnosis of an industrial gas turbine prototype. Mechatronics, 16(6), 341–363.

    Article  Google Scholar 

  26. Manngård, M., Böling, J. M., & Toivonen, H. T. (2017). Subspace identification for MIMO systems in the presence of trends and outliers. Computer Aided Chemical Engineering, 40, 307–312.

    Article  Google Scholar 

  27. Xie, X., Zheng, H., Jonckheere, S., Pluymers, B., & Desmet, W. (2019). A parametric model order reduction technique for inverse viscoelastic material identification. Computers & Structures, 212, 188–198.

    Article  Google Scholar 

  28. Jianyang, Y., Jianing, Y., Chen, F., & Wang, C. (2019). Numerical study of tip leakage flow control in turbine cascades using the DBD plasma model improved by the parameter identification method. Aerospace Science and Technology, 84, 856–864.

    Article  Google Scholar 

  29. Theisen, L. R. S., Niemann, H. H., Santos, I. F., Galeazzi, R., & Blanke, M. (2016). Modelling and identification for control of gas bearings. Mechanical Systems and Signal Processing, 70(71), 1150–1170.

    Article  Google Scholar 

  30. Van Overschee, P., & De Moor, B. (1994). N4SID: subspace algorithms for the identification of combined deterministic-stochastic systems. Automatica, 30(1), 75–93.

    Article  MathSciNet  Google Scholar 

  31. Mohammadi, E., & Montazeri-Gh, M. (2015). A fuzzy-based gas turbine fault detection and identification system for full and part-load performance deterioration. Aerospace Science and Technology, 46, 82–93.

    Article  Google Scholar 

  32. Tan, Y., Zang, C., Zhou, B., Wang, X., & Petrov, E. P. (2018). Identification of crystal orientation for turbine blades with anisotropy materials. Chinese Journal of Aeronautics, 31(2), 410–418.

    Article  Google Scholar 

  33. Simani, S., & Patton, R. J. (2008). Fault diagnosis of an industrial gas turbine prototype using a system identification approach. Control Engineering Practice, 16(7), 769–786.

    Article  Google Scholar 

  34. Wang, J., Ding, B., & Zhang, S. (2020). Multivariable offset-free MPC with steady-state target calculation and its application to a wind tunnel system. ISA Transactions, 97, 317–324.

    Article  Google Scholar 

  35. De, S., Brewick, P. T., Johnson, E. A., & Wojtkiewicz, S. F. (2019). A hybrid probabilistic framework for model validation with application to structural dynamics modeling. Mechanical Systems and Signal Processing, 121, 961–980.

    Article  Google Scholar 

  36. Lin, D. W., & Kung, S.-Y. (1982). Optimal Hankel-norm approximation of continuous-time linear systems. Circuits, Systems and Signal Processing, 1(3/4), 407–431.

    Article  MathSciNet  Google Scholar 

  37. Inoue, M. (2019). Subspace identification with moment matching. Automatica, 99, 22–32.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This paper is the result of the work of estimation and identification of gas turbine variables in real time, and was supported and carried out by the Gas Turbine Joint Research Team with the Applied Automation and Industrial Diagnostics Laboratory, University of Djelfa, Algeria. The authors express their sincere thanks to the General Directorate of Scientific Research and Technological Development (DGRSDT), Algeria.

Author information

Authors and Affiliations

  1. Applied Automation and Industrial Diagnostics Laboratory, Faculty of Science and Technology, University of Djelfa, 17000, Djelfa, Algeria

    Hakim Bagua & Ahmed Hafaifa

  2. Gas Turbine Joint Research Team, University of Djelfa, 17000, Djelfa, Algeria

    Hakim Bagua, Ahmed Hafaifa & Mouloud Guemana

  3. Faculty of Science and Technology, University of Bordj Bou Arreridj, 34000, Bordj Bou Arreridj, Algeria

    Abdelhamid Iratni

Authors
  1. Hakim Bagua
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ahmed Hafaifa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abdelhamid Iratni
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mouloud Guemana
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ahmed Hafaifa.

Appendix

Appendix

\(A_{1} = \left[ {\begin{array}{*{20}c} {0.9390} & {0.0454} & {0.1768{\text{ }}} & {0.0831} & {0.0178} \\ { - 0.0370} & {0.9311} & {0.2384} & { - 0.0003} & {0.0730} \\ { - 0.0402} & { - 0.2204} & {0.7793} & {0.3171} & {0.0855} \\ { - 0.0098} & {0.0664} & { - 0.3825} & {0.8473} & {0.3733} \\ { - 0.0193} & {0.0131} & { - 0.0328} & { - 0.3800} & {0.8987} \\ \end{array} } \right]\), \(A_{2} = \left[ {\begin{array}{*{20}c} {0.1067} & { - 0.2596} & {0.1113{\text{ }}} & {0.0211} & { - 0.3074} \\ { - 0.0464} & {0.0753} & { - 0.0393} & { - 0.1120} & {0.2101} \\ { - 0.3540} & {0.1286} & { - 0.0978} & {0.1224} & { - 0.0616} \\ { - 0.0129} & { - 0.0147} & { - 0.0047} & { - 0.0125} & {0.0025} \\ { - 0.1365} & { - 0.0575} & {0.0544} & {0.1506} & { - 0.0358} \\ \end{array} } \right]\),

\(A_{3} = \left[ {\begin{array}{*{20}c} {0.1676} & { - 0.0738} & {0.0185{\text{ }}} & { - 0.1211} & { - 0.1642} \\ { - 0.1025} & { - 0.0166} & {0.0553} & {0.1006} & {0.1763} \\ { - 0.0906} & {0.0924} & { - 0.0184} & {0.1099} & { - 0.0189} \\ { - 0.0621} & { - 0.0237} & {0.0994} & {0.1164} & {0.0617} \\ { - 0.0144} & { - 0.0013} & {0.1158} & {0.1287} & { - 0.0679} \\ \end{array} } \right]\), \(A_{4} = \left[ {\begin{array}{*{20}c} { - 0.0018} & {0.0108} & {0.1448{\text{ }}} & {0.0255} & {0.0364} \\ { - 0.0134} & { - 0.0039} & { - 0.0202} & { - 0.0194} & {0.0197} \\ { - 0.0098} & {0.0016} & {0.0111} & {0.0181} & { - 0.0793} \\ {0.0013} & { - 0.0138} & {0.0277} & {0.0348} & { - 0.0269} \\ {0.0010} & {0.0081} & {0.0197} & {0.0712} & {0.0033} \\ \end{array} } \right]\),

\(A_{5} = \left[ {\begin{array}{*{20}c} {0.8095} & {0.5461} & { - 0.0105{\text{ }}} & {0.2875} & { - 0.1027} \\ { - 0.0889} & {0.8274} & { - 0.3234} & { - 0.4720} & { - 0.0083} \\ { - 0.1448} & {0.2664} & {0.9558{\text{ }}} & { - 0.0968} & { - 0.2889} \\ { - 0.1208} & {0.0875} & { - 0.0815} & {0.7228} & {0.0227} \\ {0.0125} & {0.1102} & {0.1332} & {0.0756} & {0.9828} \\ \end{array} } \right]\), \(A_{6} = \left[ {\begin{array}{*{20}c} {0.0167} & {0.1870} & { - 0.3005{\text{ }}} & { - 0.2226} & { - 0.1387} \\ {0.1893} & { - 0.0930} & { - 0.2344} & { - 0.4089} & { - 0.0613} \\ {0.0329} & { - 0.0294} & {0.1167{\text{ }}} & { - 0.0752} & { - 0.0201} \\ {0.2420} & { - 0.2494} & {0.2351} & { - 0.1667} & { - 0.0501} \\ { - 0.1437} & {0.1175} & {0.0487} & {0.1930} & { - 0.0943} \\ \end{array} } \right]\),

\(A_{7} = \left[ {\begin{array}{*{20}c} { - 0.0078} & {0.0105} & {0.0257{\text{ }}} & {0.0340} & {0.0033} \\ {0.0020} & { - 0.0097} & {0.0018} & { - 0.0125} & { - 0.0055} \\ { - 0.0012} & {0.0006} & {0.0062{\text{ }}} & { - 0.0114} & {0.0098} \\ {0.0027} & { - 0.0009} & { - 0.0200} & { - 0.0252} & { - 0.0010} \\ {0.0011} & { - 0.0037} & { - 0.0016} & { - 0.0096} & {0.0071} \\ \end{array} } \right]\), \(A_{8} = \left[ {\begin{array}{*{20}c} { - 0.0450} & { - 0.0509} & {0.0147{\text{ }}} & { - 0.1270} & {0.0390} \\ {0.0008} & {0.0135} & {0.0077} & {0.0276} & { - 0.1166} \\ {0.0484} & { - 0.0244} & { - 0.1219{\text{ }}} & { - 0.0918} & {0.0702} \\ {0.0196} & { - 0.0073} & { - 0.1325} & { - 0.0006} & { - 0.1677} \\ {0.0392} & { - 0.0244} & { - 0.0283} & { - 0.0601} & {0.0511} \\ \end{array} } \right]\),

\(A_{9} = \left[ {\begin{array}{*{20}c} {0.2400} & {0.4907} & { - 0.1192{\text{ }}} & { - 0.8564} & { - 0.3882} \\ { - 0.8187} & { - 0.1227} & { - 0.2995} & { - 0.4478} & { - 0.1482} \\ { - 0.0691} & { - 0.4302} & {0.4053{\text{ }}} & {0.2727} & { - 0.5263} \\ { - 0.1843} & {0.5882} & {0.5298} & {0.4170} & { - 0.1806} \\ { - 0.1653} & { - 0.0335} & {0.6396} & { - 0.1156} & {0.5794} \\ \end{array} } \right]\), \(B_{1} = \left[ {\begin{array}{*{20}c} { - 2.7155} & {0.2081} & {0.0072} & { - 0.4548} \\ {2.0230} & {0.2389} & { - 0.0004} & {0.4332} \\ { - 0.1794} & { - 0.1678} & {0.0102} & { - 0.0782} \\ {0.1183} & {0.3796} & {0.0011} & {0.0929} \\ { - 1.9328} & { - 0.1330} & { - 0.0033} & { - 0.1165} \\ \end{array} } \right]\),

\(B_{2} = \left[ {\begin{array}{*{20}c} { - 1.1620} & { - 1.0709} & {0.0186} & { - 0.1266} \\ {2.6272} & {0.7804} & {0.0013} & { - 0.0148} \\ {0.6515} & { - 0.2221} & {0.0133} & { - 0.1161} \\ {2.8482} & {0.7465} & {0.0089} & {0.0628} \\ { - 0.3457} & { - 0.4995} & {0.0032} & {0.0307} \\ \end{array} } \right]\), \(B_{3} = \left[ {\begin{array}{*{20}c} {6.3638} & { - 3.0824} & {0.0241} & {0.1250} \\ {5.4994} & {7.2621} & { - 0.0294} & {0.4442} \\ { - 0.4800} & {4.4795} & { - 0.0247} & {0.1852} \\ {4.7431} & { - 5.0950} & {0.0430} & { - 0.0779} \\ {4.3002} & { - 0.8934} & {0.0222} & {0.0430} \\ \end{array} } \right]\),

\(C_{1} = \left[ {\begin{array}{*{20}c} { - 0.0374} & { - 0.0412} & {0.0024} & { - 0.0072} & {0.0832} \\ { - 0.3338} & { - 0.0988} & {0.3744} & {0.1116} & {0.1736} \\ \end{array} } \right]\), \(C_{2} = \left[ {\begin{array}{*{20}c} { - 0.0151} & {0.0663} & { - 0.0365} & {0.0472} & {0.1893} \\ {0.4273} & { - 0.3592} & {0.1181} & { - 0.3299} & {0.0087} \\ \end{array} } \right]\), \(C_{3} = \left[ {\begin{array}{*{20}c} {0.1103} & { - 0.0106} & { - 0.1571} & { - 0.1889} & {0.1359} \\ {0.1525} & { - 0.1956} & {0.0854} & { - 0.1091} & {0.0361} \\ \end{array} } \right]\).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bagua, H., Hafaifa, A., Iratni, A. et al. Model variables identification of a gas turbine using a subspace approach based on input/output data measurements. Control Theory Technol. 19, 183–196 (2021). https://doi.org/10.1007/s11768-020-00005-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11768-020-00005-z

Keywords

Search

Navigation