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

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.

► Multivariable system's order is determined based on PCA method for ill-conditioned processes with strong interactions and directions in the outputs.
► Based on this PCA modeling, model predictive error can be reconstructed and adapted to reveal the number of linear relationships.
► AIC criteria with a new weighted direction variable is then construct to test modeling error bound and thus to determine the process order.