Abstract
A novel subspace identification method based on correlation function which estimates a state-space system dynamics of unknown plant operating in closed-loop experimental condition is proposed in this paper. It is shown that the cross-correlation function of the output and external input signals are equal to the cross-correlation function of the input and external signals filtered through the system dynamics since noise signal has no correlation with the external input. The proposed algorithm is developed to obtain unbiased estimates of system matrices based on time-shifted invariance of the correlation function estimates. Later the algorithm is compared to other popular subspace methods in the simulation study and the results show the effectiveness of our method in the presence of colored noise and low signal-to-noise ratios.
Similar content being viewed by others
References
Qin S J. An overview of subspace identification. Comput Chem Eng, 2006, 30: 1502–1513
Cheng D Z. Advances in automation and control research in China. Sci China Ser-F: Inf Sci, 2009, 52: 1954–1963
Katayama T, Tanakab H. An approach to closed-loop subspace identification by orthogonal decomposition. Automatica, 2007, 43: 1623–1630
van Der Veen G, van Wingerden J W. Closed-loop subspace identification methods: an overview. IET Control Theory Appl, 2013, 7: 1339–1358
Houtzager I, van Wingerden J W, Verhaegen M. Recursive predictor-based subspace identification with application to the real-time closed-loop tracking of flutter. IEEE Trans Control Syst Technol, 2012, 20: 934–949
Liu T, Shao C, Wang X Z. Consistency analysis of orthogonal projection based closed-loop subspace identification methods. In: Proceedings of the 12th European Control Conference, Zürich, 2013. 1428–1432
Chiuso A. On the asymptotic properties of closed-loop CCA-type subspace algorithms: equivalence results and role of the future horizon. IEEE Trans Automat Control, 2010, 55: 634–649
Tóth R, Laurain V, Gilson M, et al. Instrumental variable scheme for closed-loop LPV model identification. Automatica, 2012, 48: 2314–2320
Pintelon R, Schoukens J. System Identification: a Frequency Domain Approach. New York: John Wiley & Sons, 2004
van Overschee P, de Moor B. Continuous-time frequency domain subspace system identification. Signal Process, 1996, 52: 179–194
Ding F, Liu P X, Liu G. Multi-innovation least squares identification for system modelling. IEEE Trans Syst Man Cybern Part B-Cybern, 2010, 40: 767–778
Ding F, Liu P X, Liu G. Gradient based and least-squares based iterative identification methods for OE and OEMA systems. Digit Signal Process, 2010, 20: 664–677
Chiuso A. The role of vector autoregressive modeling in predictor-based subspace identification. Automatica, 2007, 43: 1034–1048
van Der Veen G, van Wingerden J W, Verhaegen M. Closed-loop MOESP subspace model identification with parametrisable disturbances. In: Proceedings of the 49th IEEE Conference on Decision and Control, Atlanta, 2014. 2813–1818
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, J., Miller, D., Wang, H. et al. Closed-loop subspace identification algorithm based on correlation function estimates. Sci. China Inf. Sci. 58, 1–10 (2015). https://doi.org/10.1007/s11432-014-5242-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11432-014-5242-1
Keywords
- subspace identification method
- correlation function estimates
- closed-loop system
- asymptotic properties
- the system dynamics