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

다국어 초록 (Multilingual 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 thenoise effect on consistent estimation. The extended observability matrix and the triangular block-Toeplitz matrixare 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 proposedmethod 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 generallyenhances the estimated model efficiency/accuracy thanks to the use of future input data. Two examples arepresented to illustrate the effectiveness and merit of the proposed method.

참고문헌 (Reference)

1 A. Chiuso, "The asymptotic variance of subspace estimates" 118 (118): 257-291, 2004

2 W. E. Larimore, "System identification, reduced-order filtering and modeling via canonical variate analysis" 445-451, 1983

3 S. X. Ding, "Subspace method aided data-driven design of fault detection and isolation systems" 19 (19): 1496-1510, 2009

4 W. Li, "Subspace identification of continuous time models for process fault detection and isolation" 13 (13): 407-421, 2003

5 T. Katayama, "Subspace Methods for System Identification" Springer 2006

6 P. V. Overschee, "Subspace Identification for Linear Systems: Theory-implementation-applications" Springer 2012

7 Zeng Liao, "Subspace Identification for Fractional Order Hammerstein Systems Based on Instrumental Variables" 제어·로봇·시스템학회 10 (10): 947-953, 2012

8 J. Hou, "Subspace Hammerstein model identification under periodic disturbance" 51 (51): 335-340, 2018

9 V. Filipovic, "Robust identification of pneumatic servo actuators in the real situations" 75 (75): 183-196, 2011

10 V. Stojanovic, "Robust identification of OE model with constrained output using optimal input design" 353 (353): 576-593, 2016

11 J. Hou, "Recursive subspace identification subject to relatively slow time-varying load disturbance" 91 (91): 648-664, 2018

12 J. Hou, "Orthogonal projection based subspace identification against colored noise" 15 (15): 69-77, 2017

13 H. Yang, "Order estimation of multivariable ill-conditioned processes based on PCA method" 22 (22): 1397-1403, 2012

14 M. Jansson, "On consistency of subspace methods for system identification" 34 (34): 1507-1519, 1998

15 P. V. Overschee, "N4SID : subspace algorithms for the identification of combined deterministicstochastic systems" 30 (30): 75-93, 1994

16 D. S. Bernstein, "Matrix Mathematics" Princeton University Press 2009

17 V. Stojanovic, "Joint state and parameter robust estimation of stochastic nonlinear systems" 26 (26): 3058-3074, 2016

18 M. Verhaegen, "Identification of the deterministic part of MIMO state-space models given in innovations form from input-output data" 30 (30): 61-74, 1994

19 D. Maurya, "Identification of Errors-in-Variables models using dynamic iterative principal component analysis" 57 (57): 11939-11954, 2018

20 K. Peng, "Event-triggered fault detection framework based on subspace identification method for the networked control systems" 239 (239): 257-267, 2017

21 D. Bauer, "Estimating ARMAX systems for multivariate time series using the state approach to subspace algorithms" 100 (100): 397-421, 2009

22 S. Yin, "Datadriven monitoring for stochastic systems and its application on batch process" 44 (44): 1366-1376, 2013

23 J. S. Wang, "Data-driven output-feedback fault-tolerant compensation control for digital PID control systems with unknown dynamics" 63 (63): 7029-7039, 2016

24 G. Wang, "Data-driven fault-tolerant control design for wind turbines with robust residual generator" 9 (9): 1173-1179, 2015

25 S. Yin, "Data-driven design of robust fault detection system for wind turbines" 24 (24): 298-306, 2014

26 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" 24 (24): 431-449, 2014

27 J. S. Wang, "Data-driven compensation method for sensor drift faults in digital PID systems with unknown dynamics" 65 : 15-33, 2018

28 Y. Wang, "Control performance assessment for ILC-controlled batch processes in a 2-D system framework" 48 (48): 1493-1504, 2017

29 W. Li, "Consistent dynamic PCA based on errors-in-variables subspace identification" 11 (11): 661-678, 2001

30 A. Micchi, "Comparison of input signals in subspace identification of multivariable illconditioned systems" 18 (18): 582-593, 2008

31 J. Wang, "Closed-loop subspace identification using the parity space" 42 (42): 315-320, 2006

32 T. Liu, "Bias-eliminated subspace model identification under time-varying deterministic type load disturbance" 25 : 41-49, 2015

33 S. J. Qin, "An overview of subspace identification" 30 (30): 1502-1513, 2006

34 P. V. Overschee, "A unifying theorem for three subspace system identification algorithms" 31 (31): 1853-1864, 1995

35 S. Yin, "A review on basic data-driven approaches for industrial process monitoring" 61 (61): 6418-6428, 2014

36 H. Oku, "A recursive 4SID from the inputoutput point of view" 1 (1): 258-269, 1999

37 P. Wu, "A new subspace identification approach based on principal component analysis and noise estimation" 54 (54): 5106-5114, 2015

38 J. Wang, "A new subspace identification approach based on principal component analysis" 12 (12): 841-855, 2002