Bias-eliminated subspace model identification under time-varying deterministic type load disturbance

Tao LIU*, Biao HUANG, S. Joe QIN

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

20 Citations (Scopus)


Unexpected or time-varying deterministic type load disturbances are often encountered when performing identification tests in practical applications. A bias-eliminated subspace identification method is proposed in this paper by developing an orthogonal projection approach to guarantee consistent estimation on the deterministic part of the plant, in combination with a Maclaurin time series approximation on the output response arising from deterministic type load disturbance. The rank condition for such an orthogonal projection is disclosed in terms of the state-space model structure adopted for identification. Using principal component analysis (PCA), the extended observability matrix and the lower triangular Toeplitz matrix of the state-space model are explicitly derived. Accordingly, the plant state-space matrices can be retrieved from the above matrices through a shift-invariant algorithm. A benchmark example from the literature and an illustrative example of industrial injection molding are used to demonstrate the effectiveness and merit of the proposed identification method.
Original languageEnglish
Pages (from-to)41-49
Number of pages9
JournalJournal of Process Control
Early online date26 Nov 2014
Publication statusPublished - Jan 2015
Externally publishedYes

Bibliographical note

This work is supported in part by the National Thousand Talents Program of China, NSF China Grants 61473054 and 61020106003, the Fundamental Research Funds for the Central Universities of China, SAPI State Key Lab Fundamental Research Funds (2013ZCX02-01), and the Oversea Changjiang Scholar Program of China.


  • Extended observability matrix
  • Orthogonal projection
  • Rank condition
  • Singular value decomposition
  • Subspace identification


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