Prior-knowledge-based subspace identification for batch processes

Abstract In this paper, a prior-knowledge-based subspace identification method (SIM) is proposed for batch processes subject to repeatable disturbances. The proposed method is a two-step procedure for state-space model identification: in the first step, the extended observability and triangular Toeplitz matrices are estimated simultaneously from a parity space of the experimental data and, based on which, the corresponding system matrices are retrieved in the second step. More specifically, A and C are retrieved from the estimated extended observability matrix, while B and D are retrieved from the estimated triangular Toeplitz matrix. The proposed method shows several superiorities in the following aspects. Firstly, it is able to provide unbiased parameter estimation in the presence of repeatable disturbances, thanks to the proposed difference operator which eliminates the disturbance effect. Secondly, it shows better robustness to measurement noise compared with the existing SIMs using parity space, due to the inherent instrumental variable mechanism and the new technique to build the instrument, which greatly enhance the estimated model efficiency/accuracy. Lastly, by taking the auxiliary static-gain information into account in the identification procedure, the variance properties of the parameters can be improved, especially for the system matrices B and D. All the above-mentioned developments are analyzed with strict mathematical proofs, along with two illustrative examples to confirm the effectiveness and merits.