Multidimensional Systems and Signal Processing

, Volume 28, Issue 4, pp 1499–1521 | Cite as

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

  • Jinxu Cheng
  • Mengqi Fang
  • Youqing Wang


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.


Subspace algorithms Closed-loop 2-D CRSD model identification The white noise external excitation case Consistency and efficiency 



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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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.College of Information Science and TechnologyBeijing University of Chemical TechnologyBeijingChina

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