Order estimation of multivariable ill-conditioned processes based on PCA method

Abstract Ill-conditioned multivariable processes exhibit significantly strong interactions among system variables and large gain directions from the system inputs to the outputs, which makes the identification and control a challenging task. The objective of this paper is to develop an order estimation algorithm for model identification of ill-conditioned processes using subspace methods. In this paper, the order is determined from noise-corrupted samples with high accuracy based on the principal component analysis (PCA) method. To excite each direction in the ill-conditioned process, test signals are designed carefully based on the system characteristics. Using the PCA modeling, the model prediction error is first reconstructed, and the Akaike Information Criterion (AIC) is then used to examine the modeling error bound and thus to determine the process order. A new weighted direction variable is proposed to strengthen the interactions along the small gain directions, thus improving the identifiability and accuracy of the ill-conditioned model. The effectiveness of the proposed method is confirmed by an application study on a high purity distillation column process under noise conditions.

[1]  Michel Gevers,et al.  Identification of multi-input systems: variance analysis and input design issues , 2006, Autom..

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

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

[4]  Yucai Zhu,et al.  Multivariable System Identification For Process Control , 2001 .

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

[6]  Jeremy S. Conner,et al.  An Evaluation of MIMO Input Designs for Process Identification , 2004 .

[7]  S. Joe Qin,et al.  Consistent dynamic PCA based on errors-in-variables subspace identification , 2001 .

[8]  Barry Lennox,et al.  Use of dynamic modelling and plant historian data for improved control design , 2010 .

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

[10]  Sheng Chen,et al.  Model selection approaches for non-linear system identification: a review , 2008, Int. J. Syst. Sci..

[11]  George W. Irwin,et al.  Improved Nonlinear PCA for Process Monitoring Using Support Vector Data Description , 2011 .

[12]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .

[13]  M. Morari,et al.  LV-Control of a high-purity distillation column , 1987 .

[14]  J. Macgregor,et al.  Design of identification experiments for robust control. A geometric approach for bivariate processes , 1993 .

[15]  Yucai Zhu,et al.  Simple control-relevant identification test methods for a class of ill-conditioned processes , 2006 .

[16]  Rachelle Howard,et al.  A novel pattern-based approach for diagnostic controller performance monitoring , 2010 .

[17]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[18]  H. Akaike A new look at the statistical model identification , 1974 .

[19]  E. Bristol On a new measure of interaction for multivariable process control , 1966 .

[20]  G. Pannocchia,et al.  Comparison of input signals in subspace identification of multivariable ill-conditioned systems , 2008 .