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

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.

[1]  Leonard M. Silverman,et al.  Approximation of 2-D separable in denominator filters , 1983 .

[2]  R. Roesser.  A discrete state-space model for linear image processing , 1975 .

[3]  Tohru Katayama,et al.  An approach to closed-loop subspace identification by orthogonal decomposition , 2007, Autom..

[4]  T. Kaczorek.  Two-Dimensional Linear Systems , 1985 .

[5]  V. Sreeram,et al.  Balanced identification and model reduction of a separable denominator 2-D system , 2004, 2004 5th Asian Control Conference (IEEE Cat. No.04EX904).

[6]  Victor Sreeram,et al.  Identification and model reduction of 2-D systems via the extended impulse response Gramians , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[7]  Michel Verhaegen,et al.  Closed-loop subspace identification methods: an overview , 2013 .

[8]  Harish K. Pillai,et al.  On restrictions of n-d systems to 1-d subspaces , 2014, Multidimens. Syst. Signal Process..

[9]  Christian Cachard,et al.  Comparison of the existing tool localisation methods on two-dimensional ultrasound images and their tracking results , 2015 .

[10]  Bart De Moor,et al.  A unifying theorem for three subspace system identification algorithms , 1995, Autom..

[11]  S. Ding,et al.  Closed-loop subspace identification: an orthogonal projection approach , 2004 .

[12]  U. Kruger,et al.  Dynamic Principal Component Analysis Using Subspace Model Identification , 2005, ICIC.

[13]  Ying Bai,et al.  An Algorithm for Balanced Approximation and Model Reduction of 2-D Separable-in-Denominator Filters , 2005, Multidimens. Syst. Signal Process..

[14]  Tony Gustafsson.  Subspace-based system identification: weighting and pre-filtering of instruments , 2002, Autom..

[15]  Masayuki Kawamata,et al.  Ga-Based Design of 2D State-Space Digital Filters with Linear Phase Characteristics , 2007, J. Circuits Syst. Comput..

[16]  Magnus Jansson,et al.  Subspace Identification and ARX Modeling , 2003 .

[17]  Salah Laghrouche,et al.  Adaptive-Gain Second Order Sliding Mode Observer Design for Switching Power Converters , 2013, ArXiv.

[18]  J. Ramos,et al.  A subspace algorithm for identifying 2-D separable in denominator filters , 1994 .

[19]  David Di Ruscio,et al.  Closed and Open Loop Subspace System Identification of the Kalman Filter , 2009 .

[20]  B. Moor,et al.  Subspace state space system identification for industrial processes , 1998 .

[21]  Donghua Zhou,et al.  H∞ design of 2D controller for batch processes with uncertainties and interval time-varying delays , 2013 .

[22]  T. Hinamoto,et al.  Realizations of a state-space model from two-dimensional input-output map , 1980 .

[23]  Alessandro Chiuso,et al.  Consistency analysis of some closed-loop subspace identification methods , 2005, Autom..

[24]  L. Ljung,et al.  On consistency of closed-loop subspace identification with innovation estimation , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[25]  Tohru Katayama,et al.  Subspace Methods for System Identification , 2005 .

[26]  Huijun Gao,et al.  I filtering for 2D Markovian jump systems , 2008, Autom..

[27]  Lennart Ljung,et al.  Subspace identification from closed loop data , 1996, Signal Process..

[28]  Ahmed Alenany,et al.  Subspace algorithms for identifying separable-in-denominator two-dimensional systems with deterministic inputs , 2011 .

[29]  Tao Liu.  A Bias-Eliminated Subspace Identification Method for Errors-in-Variables Systems , 2012 .

[30]  Lennart Ljung,et al.  Closed-Loop Subspace Identification with Innovation Estimation , 2003 .

[31]  Biao Huang,et al.  Dynamic Modeling, Predictive Control and Performance Monitoring: A Data-driven Subspace Approach , 2008 .

[32]  Furong Gao,et al.  Robust design of integrated feedback and iterative learning control of a batch process based on a 2D Roesser system , 2005 .

[33]  Si-Zhao Joe Qin,et al.  An overview of subspace identification , 2006, Comput. Chem. Eng..

[34]  Dietmar Bauer,et al.  Asymptotic properties of subspace estimators , 2005, Autom..

[35]  Soo-Chang Pei,et al.  A new structure and design method for variable fractional-delay 2-D FIR digital filters , 2014, Multidimens. Syst. Signal Process..

[36]  Torsten Söderström,et al.  Errors-in-variables methods in system identification , 2018, Autom..

[37]  Alessandro Chiuso,et al.  The role of vector autoregressive modeling in predictor-based subspace identification , 2007, Autom..

[38]  Salah Laghrouche,et al.  Observer-based higher order sliding mode control of power factor in three-phase AC/DC converter for hybrid electric vehicle applications , 2013, Int. J. Control.

[39]  Tao Liu,et al.  Consistency analysis of orthogonal projection based closed-loop subspace identification methods , 2013, 2013 European Control Conference (ECC).

[40]  Jin Wang,et al.  Closed-loop subspace identification using the parity space , 2006, Autom..

[41]  Cishen Zhang,et al.  H2 and mixed H2/Hinfinity control of two-dimensional systems in Roesser model , 2006, Autom..

[42]  Ruijie Zhao,et al.  A fast design algorithm for elliptic-error and phase-error constrained LS 2-D FIR filters , 2016, Multidimens. Syst. Signal Process..