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An Improved Consistent Subspace Identification Method Using Parity Space for State-space Models

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  • Control Theory and Applications
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Abstract

In this paper, an alternative consistent subspace identification method using parity space is proposed. The future/past input data and the past output data are used to construct the instrument variable to eliminate the noise effect on consistent estimation. The extended observability matrix and the triangular block-Toeplitz matrix are then retrieved from a parity space of the noise-free matrix using a singular value decomposition based method. The system matrices are finally estimated from the above estimated matrices. The consistency of the proposed method for estimation of the extended observability matrix and the triangular block-Toeplitz matrix is established. Compared with the classical SIMs using parity space like SIMPCA and SIMPCA-Wc, the proposed method generally enhances the estimated model efficiency/accuracy thanks to the use of future input data. Two examples are presented to illustrate the effectiveness and merit of the proposed method.

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References

  1. P. V. Overschee and B. L. De Moor, Subspace Identification for Linear Systems: Theory-implementation-applications, Springer, Berlin, 2012.

    MATH  Google Scholar 

  2. T. Katayama, Subspace Methods for System Identification, Springer, Berlin, 2006.

    MATH  Google Scholar 

  3. S. J. Qin, “An overview of subspace identification,” Computers & Chemical Engineering, vol. 30, no. 10–12, pp. 1502–1513, September 2006.

    Article  Google Scholar 

  4. M. Verhaegen, “Identification of the deterministic part of MIMO state-space models given in innovations form from input-output data,” Automatica, vol. 30, no. 1, pp. 61–74, January 1994.

    Article  MathSciNet  MATH  Google Scholar 

  5. W. E. Larimore, “System identification, reduced-order filtering and modeling via canonical variate analysis,” American Control Conference, pp. 445–451, June 1983.

    Google Scholar 

  6. P. V. Overschee and B. L. De Moor, “N4SID: subspace algorithms for the identification of combined deterministic-stochastic systems,” Automatica, vol. 30, no. 1, pp. 75–93, January 1994.

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Jansson and B. Wahlberg, “On consistency of subspace methods for system identification,” Automatica, vol. 34, no. 12, pp. 1507–1519, December 1998.

    Article  MathSciNet  MATH  Google Scholar 

  8. A. Chiuso and G. Picci, “The asymptotic variance of subspace estimates,” Journal of Econometrics, vol. 118, no. 1–2, pp. 257–291, JanuaryFebruary 2004.

    Article  MathSciNet  MATH  Google Scholar 

  9. D. Bauer, “Estimating ARMAX systems for multivariate time series using the state approach to subspace algorithms,” Journal of Multivariate Analysis, vol. 100, no. 3, pp. 397–421, March 2009.

    Article  MathSciNet  MATH  Google Scholar 

  10. J. Hou, T. Liu, and F. Chen, “Orthogonal projection based subspace identification against colored noise,” Control Theory and Technology, vol. 15, no. 1, pp. 69–77, February 2017.

    Article  MathSciNet  Google Scholar 

  11. W. Li and S. J. Qin, “Consistent dynamic PCA based on errors-in-variables subspace identification,” Journal of Process Control, vol. 11, no. 6, pp. 661–678, December 2001.

    Article  Google Scholar 

  12. J. Wang and S. J. Qin, “A new subspace identification approach based on principal component analysis,” Journal of Process Control, vol. 12, no. 8, pp. 841–855, December 2002.

    Article  Google Scholar 

  13. J. Wang and S. J. Qin, “Closed-loop subspace identification using the parity space,” Automatica, vol. 42, no. 2, pp. 315–320, February 2006.

    Article  MathSciNet  MATH  Google Scholar 

  14. W. Li, H. Raghavan, and S. Shah, “Subspace identification of continuous time models for process fault detection and isolation,” Journal of Process Control, vol. 13, no. 5, pp. 407–421, August 2003.

    Article  Google Scholar 

  15. A. Micchi and G. Pannocchia, “Comparison of input signals in subspace identification of multivariable illconditioned systems,” Journal of Process Control, vol. 18, no. 6, pp. 582–593, July 2008.

    Article  Google Scholar 

  16. H. Yang, S. Li, and K. Li, “Order estimation of multivariable ill-conditioned processes based on PCA method,” Journal of Process Control, vol. 22, no. 7, pp. 1397–1403, August 2012.

    Article  Google Scholar 

  17. Z. Liao, Z. Zhu, S. Liang, C. Peng, and Y. Wang, “Subspace identification for fractional order Hammerstein systems based on instrumental variables,” International Journal of Control, Automation and Systems, vol. 10, no. 5, pp. 947–953, September 2012.

    Article  Google Scholar 

  18. P. Wu, H. P. Pan, J. Ren, and C. Yang, “A new subspace identification approach based on principal component analysis and noise estimation,” Industrial & Engineering Chemistry Research, vol. 54, no. 18, pp. 5106–5114, April 2015.

    Article  Google Scholar 

  19. D. Maurya, A. K. Tangirala, and S. Narasimhan, “Identification of Errors-in-Variables models using dynamic iterative principal component analysis,” Industrial & Engineering Chemistry Research, vol. 57, no. 35, pp. 11939–11954, August 2018.

    Article  Google Scholar 

  20. J. Hou, T. Liu, B. Wahlberg, and M. Jansson, “Subspace Hammerstein model identification under periodic disturbance,” IFAC-PapersOnLine, vol. 51, no. 15, pp. 335–340, July 2018.

    Article  Google Scholar 

  21. S. X. Ding, P. Zhang, A. Naik, E. L. Ding, and B. Huang, “Subspace method aided data-driven design of fault detection and isolation systems,” Journal of Process Control, vol. 19, no. 9, pp. 1496–1510, October 2009.

    Article  Google Scholar 

  22. S. X. Ding, “Data-driven design of monitoring and diagnosis systems for dynamic processes: a review of subspace technique based schemes and some recent results,” Journal of Process Control, vol. 24, no. 2, pp. 431–449, February 2014.

    Article  Google Scholar 

  23. S. Yin, G. Wang, and H. R. Karimi, “Data-driven design of robust fault detection system for wind turbines,” Mechatronics, vol. 24, no. 4, pp. 298–306, June 2014.

    Article  Google Scholar 

  24. S. Yin, S. X. Ding, X. Xie, and H. Luo, “A review on basic data-driven approaches for industrial process monitoring,” IEEE Transactions on Industrial Electronics, vol. 61, no. 11, pp. 6418–6428, November 2014.

    Article  Google Scholar 

  25. S. Yin, S. X. Ding, A. H. Abandan Sari, and H. Hao, “Datadriven monitoring for stochastic systems and its application on batch process,” International Journal of Systems Science, vol. 44, no. 7, pp. 1366–1376, July 2013.

    Article  MathSciNet  MATH  Google Scholar 

  26. K. Peng, M. Wang, and J. Dong, “Event-triggered fault detection framework based on subspace identification method for the networked control systems,” Neurocomputing, vol. 239, no. 24, pp. 257–267, May 2017.

    Article  Google Scholar 

  27. G. Wang and Z. Huang, “Data-driven fault-tolerant control design for wind turbines with robust residual generator,” IET Control Theory & Applications, vol. 9, no. 7, pp. 1173–1179, April 2015.

    Article  Google Scholar 

  28. J. S. Wang and G. H. Yang, “Data-driven output-feedback fault-tolerant compensation control for digital PID control systems with unknown dynamics,” IEEE Transactions on Industrial Electronics, vol. 63, no. 11, pp. 7029–7039, November 2016.

    Article  Google Scholar 

  29. Y.Wang, H. Zhang, S.Wei, D. Zhou, and B. Huang, “Control performance assessment for ILC-controlled batch processes in a 2-D system framework,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 48, no. 9, pp. 1493–1504, September 2017.

    Google Scholar 

  30. J. S. Wang and G. H. Yang, “Data-driven compensation method for sensor drift faults in digital PID systems with unknown dynamics,” Journal of Process Control, vol. 65, pp. 15–33, May 2018.

    Article  Google Scholar 

  31. H. Oku and H. Kimura, “A recursive 4SID from the inputoutput point of view,” Asian Journal of Control, vol. 1, no. 4, pp. 258–269, December 1999.

    Article  Google Scholar 

  32. D. S. Bernstein, Matrix Mathematics, 2nd ed., Princeton University Press, Princeton, 2009.

    Book  MATH  Google Scholar 

  33. V. Filipovic, N. Nedic, and V. Stojanovic, “Robust identification of pneumatic servo actuators in the real situations,” Forschung im Ingenieurwesen, vol. 75, no. 4, pp. 183–196, December 2011.

    Article  Google Scholar 

  34. V. Stojanovic and N. Nedic, “Robust identification of OE model with constrained output using optimal input design,” Journal of the Franklin Institute, vol. 353, no. 2, pp. 576–593, January 2016.

    Article  MathSciNet  MATH  Google Scholar 

  35. V. Stojanovic and N. Nedic, “Joint state and parameter robust estimation of stochastic nonlinear systems,” International Journal of Robust and Nonlinear Control, vol. 26, no. 14, pp. 3058–3074, September 2016.

    Article  MathSciNet  MATH  Google Scholar 

  36. P. V. Overschee and B. L. De Moor, “A unifying theorem for three subspace system identification algorithms,” Automatica, vol. 31, no. 12, pp. 1853–1864, December 1995.

    Article  MathSciNet  MATH  Google Scholar 

  37. T. Liu, B. Huang, and S. J. Qin, “Bias-eliminated subspace model identification under time-varying deterministic type load disturbance,” Journal of Process Control, vol. 25, pp. 41–49, January 2015.

    Article  Google Scholar 

  38. J. Hou, T. Liu, and Q. G. Wang, “Recursive subspace identification subject to relatively slow time-varying load disturbance,” International Journal of Control, vol. 91, no. 3, pp. 648–664, May 2018.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. College of Automation, Chongqing University of Posts and Telecommunications, No. 2 Chongwen Road, Chongqing, China

    Jie Hou, Penghua Li & Zhiqin Zhu

  2. Department of Automation, Wuhan University, No. 299 Bayi Road, Wuhan, Hubei, China

    Fengwei Chen

  3. National Robot Test and Assessment Center (Chongqing), Chongqing Dexin Robot Testing Center Co., Ltd, No. 101 Yunhan Road, Liangjiang New Area, Chongqing, China

    Fei Liu

Authors
  1. Jie Hou
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  2. Fengwei Chen
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  3. Penghua Li
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  4. Zhiqin Zhu
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  5. Fei Liu
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Corresponding author

Correspondence to Jie Hou.

Additional information

Recommended by Associate Editor Yongping Pan under the direction of Editor Jay H. Lee. This research was supported by the National Natural Science Foundation of China under Grant 61803061, 61703347, and 61703311; Science and Technology Research Program of Chongqing Municipal Education Commission grant KJQN201800603; the Chongqing Natural Science Foundation Grant cstc2018jcyjAX0167; the Common Key Technology Innovation Special of Key Industries of Chongqing science and Technology Commission under Grant cstc2017zdcy-zdyfX0067; the Artificial Intelligence Technology Innovation Significant Theme Special Project of Chongqing science and Technology Commission under Grant cstc2017rgzn-zdyfX0014 and cstc2017rgzn-zdyfX0035.

Jie Hou received his Ph.D. degree in Control Theory and Control engineering from Dalian University of Technology in 2018. His research interests include process modelling and system identification.

Fengwei Chen received his Ph.D. degree from Universite de Lorraine in 2014. His research interests include system identification and signal processing.

Penghua Li received his Ph.D. degree in Control Theory and Control engineering from Chongqing University in 2012. His research interest includes fault diagnosis.

Zhiqin Zhu received his Ph.D. degree in Control Theory and Control engineering from Chongqing University in 2017. His research interests include image processing and identification.

Fei Liu received his Ph.D. degree in Control theory and Control engineering from Chongqing University in 2015. His research interests include intelligent mobile robot control, navigation, robot testing and assessment.

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Hou, J., Chen, F., Li, P. et al. An Improved Consistent Subspace Identification Method Using Parity Space for State-space Models. Int. J. Control Autom. Syst. 17, 1167–1176 (2019). https://doi.org/10.1007/s12555-018-0499-6

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  • DOI: https://doi.org/10.1007/s12555-018-0499-6

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