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Subspace identification for closed-loop 2-D separable-in-denominator systems

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Abstract

Identification for closed-loop two-dimensional (2-D) causal, recursive, and separable-in-denominator (CRSD) systems in the Roesser form is discussed in this study. For closed-loop 2-D CRSD systems, under feedback control condition, there exists some correlation between the unknown disturbances and future inputs which offers the fundamental limitation for utilizing standard open-loop 2-D CRSD systems subspace identification methods. In other words, the existing open-loop subspace approaches will result in biased estimates of plant parameters from closed-loop data. In this study, based on orthogonal projection and principal component analysis, novel 2-D CRSD subspace identification methods are developed, which are applicable to both open-loop and closed-loop data. Additionally, the whiteness external excitation case is discussed and subsequently modified instrument variables are adopted to improve the proposed subspace algorithm. An illustrative example of the injection molding process and several numerical examples are used to validate consistency and efficiency of the proposed subspace approaches for 2-D CRSD systems.

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References

  • Bauer, D. (2005). Asymptotic properties of subspace estimators. Automatica, 41, 359–376.

    Article  MathSciNet  MATH  Google Scholar 

  • Chiuso, A. (2007). The role of vector autoregressive modeling in predictor-based subspace identification. Automatica, 43, 1034–1048.

    Article  MathSciNet  MATH  Google Scholar 

  • Chiuso, A., & Picci, G. (2005). Consistency analysis of some closed-loop subspace identification methods. Automatica, 41(3), 377–391.

    Article  MathSciNet  MATH  Google Scholar 

  • Favoreel, W., De Moor, B., & Van Overschee, P. (2000). Subspace state space system identification for industrial processes. Journal of Process Control, 10(2), 149–155.

    Article  Google Scholar 

  • Gustafsson, T. (2002). Subspace-based system identification: Weighting and pre-filtering of instruments. Automatica, 38(3), 433–443.

    Article  MathSciNet  MATH  Google Scholar 

  • Hinamoto, T. (1980). Realizations of a state-space model from two-dimensional input-output map. IEEE Transactions on Circuits and Systems, 27(1), 36–44.

    Article  MathSciNet  MATH  Google Scholar 

  • Hong, X., Lai, X., & Zhao, R. (2016). A fast design algorithm for elliptic-error and phase-error constrained LS 2-D FIR filters. Multidimensional Systems and Signal Processing, 27(2), 477–491.

    Article  MATH  Google Scholar 

  • Huang, B., Ding, S. X., & Qin, S. J. (2005). Closed-loop subspace identification: An orthogonal projection approach. Journal of Process Control, 15(1), 53–66.

    Article  Google Scholar 

  • Huang, B., & Kadali, R. (2008). Dynamic modeling, predictive control and performance monitoring: A data-driven subspace approach. Berlin: Springer.

    MATH  Google Scholar 

  • Jansson, M. (2003). Subspace identification and ARX modeling. In Proceedings of the 13th IFAC SYSID symposium.

  • Kaczorek, T. (1985). Two-dimensional linear systems. Berlin: Springer.

    MATH  Google Scholar 

  • Katayama, T. (2006). Subspace methods for system identification. Berlin: Springer.

    MATH  Google Scholar 

  • Katayama, T., & Tanaka, H. (2007). An approach to closed-loop subspace identification by orthogonal decomposition. Automatica, 43(9), 1623–1630.

    Article  MathSciNet  MATH  Google Scholar 

  • Lashgari, B., Silverman, L. M., & Abramatic, J. F. (1983). Approximation of 2-D separable in denominator filters. IEEE Transactions on Circuits and Systems, 30(2), 107–121.

    Article  MathSciNet  MATH  Google Scholar 

  • Lin, W. L., Qin, S. J., & Ljung, L. (2004). On consistency of closed-loop subspace identification with innovation estimation. In 2004 43rd IEEE conference on decision and control (pp. 2195–2200).

  • Liu, J. (2013). Observer-based higher order sliding mode control of power factor in three-phase AC/DC converter for hybrid electric vehicle applications. International Journal of Control, 87(6), 1117–1130.

    Article  MathSciNet  MATH  Google Scholar 

  • Liu, J., Laghrouche, S., Harmouche, M., & Wack, M. (2014). Adaptive-gain second-order sliding mode observer design for switching power converters. Control Engineering Practice, 30, 124–131.

    Article  Google Scholar 

  • Liu, T. (2012). A bias-eliminated subspace identification method for errors-in-variables systems. In International symposium on advanced control of chemical processes (ADCHEM) (pp. 10–13).

  • Liu, T., Shao, C., & Wang, X. Z. (2013). Consistency analysis of orthogonal projection based closed-loop subspace identification methods. In European Control Conference (ECC) (pp.1428–1432).

  • Ljung, L., & McKelvey, T. (1996). Subspace identification from closed loop data. Signal Processing, 52(2), 209–215.

    Article  MATH  Google Scholar 

  • Nam, S. C., Abe, M., & Kawamata, M. (2007). GA-based design of 2D state-space digital filters with linear phase characteristics. Journal of Circuits, Systems, and Computers, 16(02), 287–303.

    Article  Google Scholar 

  • Pal, D., & Pillai, H. K. (2014). On restrictions of nD systems to 1-D subspaces. Multidimensional Systems and Signal Processing, 25(1), 115–144.

    Article  MathSciNet  MATH  Google Scholar 

  • Qin, S. J. (2006). An overview of subspace identification. Computers & Chemical Engineering, 30(10), 1502–1513.

    Article  Google Scholar 

  • Qin, S. J., & Ljung, L. (2003). Closed-loop subspace identification with innovation estimation. In Proceedings of the 13th IFAC SYSID symposium (pp. 887–892).

  • Ramos, J. (1994). A subspace algorithm for identifying 2-D separable in denominator filters. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 41(1), 63–67.

    Article  MATH  Google Scholar 

  • Ramos, J. A., Alenany, A., Shang, H., & dos Santos, P. J. L. (2011). Subspace algorithms for identifying separable-in-denominator two-dimensional systems with deterministic inputs. IET Control Theory & Applications, 5(15), 1748–1765.

    Article  MathSciNet  Google Scholar 

  • Roesser, R. P. (1975). A discrete state-space model for linear image processing. IEEE Transactions on Automatic Control, 20(1), 1–10.

    Article  MathSciNet  MATH  Google Scholar 

  • Ruscio, D. (2009). Closed and open loop subspace system identification of the Kalman filter. Modeling, Identification and Control, 30(2), 71–86.

    Article  Google Scholar 

  • Shi, J., Gao, F., & Wu, T. J. (2005). Robust design of integrated feedback and iterative learning control of a batch process based on a 2D Roesser system. Journal of Process Control, 15(8), 907–924.

    Article  Google Scholar 

  • Shyu, J. J., Pei, S. C., Huang, Y. D., & Chen, Y. S. (2014). A new structure and design method for variable fractional-delay 2-D FIR digital filters. Multidimensional Systems and Signal Processing, 25(3), 511–529.

    Article  Google Scholar 

  • Söderström, T. (2007). Errors-in-variables methods in system identification. Automatica, 43(6), 939–958.

    Article  MathSciNet  MATH  Google Scholar 

  • Treasure, R., Sreeram, V., & Ngan, K. N. (2004). Balanced identification and model reduction of a separable denominator 2-D system. In 5th Asian control conference (pp. 2048–2052).

  • van der Veen, G., van Wingerden, J. W., Bergamasco, M., Lovera, M., & Verhaegen, M. (2013). Closed-loop subspace identification methods: An overview. IET Control Theory & Applications, 7(10), 1339–1358.

    Article  MathSciNet  Google Scholar 

  • Van Overschee, P., & De Moor, B. (1995). A unifying theorem for three subspace system identification algorithms. Automatica, 31(12), 1853–1864.

    Article  MathSciNet  MATH  Google Scholar 

  • Wang, D., Zilouchian, A., & Bai, Y. (2005). An algorithm for balanced approximation and model reduction of 2-D separable-in-denominator filters. Multidimensional Systems and Signal Processing, 16(4), 439–461.

    Article  MathSciNet  MATH  Google Scholar 

  • Wang, J., & Qin, S. J. (2002). A new subspace identification approach based on principal component analysis. Journal of Process Control, 12(8), 841–855.

    Article  Google Scholar 

  • Wang, J., & Qin, S. J. (2006). Closed-loop subspace identification using the parity space. Automatica, 42(2), 315–320.

    Article  MathSciNet  MATH  Google Scholar 

  • Wang, L., Mo, S., Qu, H., Zhou, D., & Gao, F. (2013). H\(\infty \) design of 2D controller for batch processes with uncertainties and interval time-varying delays. Control Engineering Practice, 20(10), 1321–1333.

    Article  Google Scholar 

  • Wu, L., Shi, P., Gao, H., & Wang, C. (2008). H\(\infty \) filtering for 2D Markovian jump systems. Automatica, 44(7), 1849–1858.

    Article  MathSciNet  MATH  Google Scholar 

  • Xiao, C., Sreeram, V., Liu, W.Q., & Venetsanopoulos, A.N. (1997). Identification and model reduction of 2-D systems via the extended impulse response Gramians. In American control conference (pp. 3567–3571).

  • Yang, R., Xie, L., & Zhang, C. (2006). H-2 and mixed H-2/H-infinity control of two-dimensional systems in Roesser model. Automatica, 42, 1507–1514.

    Article  MATH  Google Scholar 

  • Zhao, Y., Liebgott, H., & Cachard, C. (2015). Comparison of the existing tool localisation methods on two-dimensional ultrasound images and their tracking results. IET Control Theory & Applications, 9(7), 1124–1134.

    Article  Google Scholar 

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Acknowledgments

This study was supported by the National Natural Science Foundation of China under Grant 61374099 and the Program for New Century Excellent Talents in University under Grant NCET-13-0652.

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Correspondence to Youqing Wang.

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Cheng, J., Fang, M. & Wang, Y. Subspace identification for closed-loop 2-D separable-in-denominator systems. Multidim Syst Sign Process 28, 1499–1521 (2017). https://doi.org/10.1007/s11045-016-0427-y

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  • DOI: https://doi.org/10.1007/s11045-016-0427-y

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