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Volume 10 Issue 12
Dec.  2023

IEEE/CAA Journal of Automatica Sinica

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K. Li, H. Luo, Y. C. Jiang, D. J. Tang, and  H. Y. Yang,  “Subspace identification for closed-loop systems with unknown deterministic disturbances,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 12, pp. 2248–2257, Dec. 2023. doi: 10.1109/JAS.2023.123330
Citation: K. Li, H. Luo, Y. C. Jiang, D. J. Tang, and  H. Y. Yang,  “Subspace identification for closed-loop systems with unknown deterministic disturbances,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 12, pp. 2248–2257, Dec. 2023. doi: 10.1109/JAS.2023.123330

Subspace Identification for Closed-Loop Systems With Unknown Deterministic Disturbances

doi: 10.1109/JAS.2023.123330
Funds:  This work was partially supported by National Key Research and Development Program of China (2019YFC1510902), National Natural Science Foundation of China (62073104), Natural Science Foundation of Heilongjiang Province (LH2022F024), and China Postdoctoral Science Foundation (2022M710965)
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  • This paper presents a subspace identification method for closed-loop systems with unknown deterministic disturbances. To deal with the unknown deterministic disturbances, two strategies are implemented to construct the row space that can be used to approximately represent the unknown deterministic disturbances using the trigonometric functions or Bernstein polynomials depending on whether the disturbance frequencies are known. For closed-loop identification, CCF-N4SID is extended to the case with unknown deterministic disturbances using the oblique projection. In addition, a proper Bernstein polynomial order can be determined using the Akaike information criterion (AIC) or the Bayesian information criterion (BIC). Numerical simulation results demonstrate the effectiveness of the proposed identification method for both periodic and aperiodic deterministic disturbances.


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  • [1]
    V. Stojanovic and N. Nedic, “Robust identification of OE model with constrained output using optimal input design,” J. Franklin I., vol. 353, no. 2, pp. 576–593, Jan. 2016. doi: 10.1016/j.jfranklin.2015.12.007
    M. Dai, Y. He, and X. Yang, “Continuous-time system identification with nuclear norm minimization and GPMF-based subspace method,” IEEE/CAA J. Autom. Sinica, vol. 3, no. 2, pp. 184–191, Apr. 2016. doi: 10.1109/JAS.2016.7451106
    K. Zhu, C. Yu, and Y. Wan, “Recursive least squares identification with variable-direction forgetting via oblique projection decomposition,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 3, pp. 547–555, Mar. 2022. doi: 10.1109/JAS.2021.1004362
    Y. Jiang, S. Yin, and O. Kaynak, “Optimized design of parity relation-based residual generator for fault detection: Data-driven approaches,” IEEE Trans. Ind. Informat., vol. 17, no. 2, pp. 1449–1458, Feb. 2021. doi: 10.1109/TII.2020.2987840
    S. Yin, J. J. Rodriguez-Andina, and Y. Jiang, “Real-time monitoring and control of industrial cyberphysical systems: With integrated plant-wide monitoring and control framework,” IEEE Ind. Electron. Mag., vol. 13, no. 4, pp. 38–47, Dec. 2019. doi: 10.1109/MIE.2019.2938025
    P. Cheng, H. Wang, V. Stojanovic, S. He, K. Shi, X. Luan, F. Liu, and C. Sun, “Asynchronous fault detection observer for 2-D Markov jump systems,” IEEE Trans. Cybern., vol. 52, no. 12, pp. 13623–13634, 2022.
    C. Yu, L. Ljung, A. Wills, and M. Verhaegen, “Constrained subspace method for the identification of structured state-space models (COSMOS),” IEEE Trans. Autom. Control, vol. 65, no. 10, pp. 4201–4214, Oct. 2020. doi: 10.1109/TAC.2019.2957703
    B. Cox and R. Toth, “Linear parameter-varying subspace identification: A unified framework,” Automatica, vol. 123, p. 109296, Jan. 2021. doi: 10.1016/j.automatica.2020.109296
    C. Yu, J. Chen, and M. Verhaegen, “Subspace identification of individual systems in a large-scale heterogeneous network,” Automatica, vol. 109, p. 108517, Aug. 2019. doi: 10.1016/j.automatica.2019.108517
    L. Zhang, D. Zhou, M. Zhong, and Y. Wang, “Improved closed-loop subspace identification based on principal component analysis and prior information,” J. Process Control, vol. 80, pp. 235–246, Aug. 2019. doi: 10.1016/j.jprocont.2019.06.001
    W. Lin, S. J. Qin, and L. Ljung, “Comparisons of subspace identification methods for systems operating on closed-loop,” IFAC Proceedings Volumes, vol. 38, no. 1, pp. 494–499, 2005. doi: 10.3182/20050703-6-CZ-1902.00083
    A. Chiuso and G. Picci, “Consistency analysis of some closed-loop subspace identification methods,” Automatica, vol. 41, no. 3, pp. 377–391, Mar. 2005. doi: 10.1016/j.automatica.2004.10.015
    B. Huang, S. X. Ding, and S. Qin, “Closed-loop subspace identification: An orthogonal projection approach,” J. Process Control, vol. 15, no. 1, pp. 53–66, Feb. 2005. doi: 10.1016/j.jprocont.2004.04.007
    M. Verhaegen and A. Hansson, “N2SID: Nuclear norm subspace identification of innovation models,” Automatica, vol. 72, pp. 57–63, Oct. 2016. doi: 10.1016/j.automatica.2016.05.021
    K. Li, H. Luo, S. Yin, and O. Kaynak, “A novel bias-eliminated subspace identification approach for closed-loop systems,” IEEE Trans. Ind. Electron., vol. 68, no. 6, pp. 5197–5205, Jun. 2021. doi: 10.1109/TIE.2020.2989717
    H. Luo, K. Li, O. Kaynak, S. Yin, M. Huo, and H. Zhao, “A robust data-driven fault detection approach for rolling mills with unknown roll eccentricity,” IEEE Trans. Control Syst. Technol., vol. 28, no. 6, pp. 2641–2648, Nov. 2020. doi: 10.1109/TCST.2019.2942799
    I. Houtzager, J. van Wingerden, and M. Verhaegen, “Rejection of periodic wind disturbances on a smart rotor test section using lifted repetitive control,” IEEE Trans. Control Syst. Technol., vol. 21, no. 2, pp. 347–359, Mar. 2013. doi: 10.1109/TCST.2011.2181171
    M. O. Gebraad, J. van Wingerden, A. Fleming, and A. D. Wright, “LPV identification of wind turbine rotor vibrational dynamics using periodic disturbance basis functions,” IEEE Trans. Control Syst. Technol., vol. 21, no. 4, pp. 1183–1190, Jul. 2013. doi: 10.1109/TCST.2013.2257775
    G. van der Veen, J. van Wingerden, and M. Verhaegen, “Closed-loop MOESP subspace model identification with parametrisable disturbances,” in Proc. 49th IEEE Conf. Decision and Control, Dec. 2010, pp. 2813–2818.
    T. Liu, B. Huang, and S. J. Qin, “Bias-eliminated subspace model identification under time-varying deterministic type load disturbance,” J. Process Control, vol. 25, pp. 41–49, Jan. 2015. doi: 10.1016/j.jprocont.2014.10.008
    T. Liu, J. Hou, S. J. Qin, and W. Wang, “Subspace model identification under load disturbance with unknown transient and periodic dynamics,” J. Process Control, vol. 85, pp. 100–111, Dec. 2020. doi: 10.1016/j.jprocont.2019.08.005
    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, Oct. 2018. doi: 10.1016/j.ifacol.2018.09.157
    S. Zhang, J. Hou, J. Du, and T. Liu, “Recursive subspace identification of Hammerstein-type nonlinear systems under slow time-varying load disturbance,” in Proc. Chinese Automation Congress, Nov. 2018, pp. 870–874.
    Y. Shin, “Modified Bernstein polynomials and their connectionist interpretation,” in Proc. IEEE World Congr. Int. Conf. Neural Networks, Jun. 1994, vol.3, pp. 1433–1438.
    H. Luo, K. Li, M. Huo, S. Yin, and O. Kaynak, “A data-driven process monitoring approach with disturbance decoupling,” in Proc. IEEE 7th Data Driven Control and Learning Systems Conf., May 2018, pp. 569–574.


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    • This paper presents a subspace identification method for closed-loop systems with unknown deterministic disturbances under standard feedback control
    • The influence of unknown deterministic disturbances can be alleviated via the projection onto the constructed row space, which can easily adapt to aperiodic deterministic disturbances with unknown frequencies using the row space constructed by Bernstein polynomials
    • A proper Bernstein polynomial order is determined to approximate the unknown deterministic disturbances


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