A predictor form PARSIMonious algorithm for closed-loop subspace identification

In this paper, we present a novel subspace identification algorithm in which all non-causal terms are removed, and the specific Toeplitz structure of the Markov parameter’s matrices is fully exploited in the spirit of the so-called PARSIMonious algorithms. We use the state-space formulation in predictor form, and we show that consistent estimates of the Markov parameters are granted both for open-loop and closed-loop data. Furthermore, we propose to evaluate the system matrices (BK=B-KD,D,K)(BK=B-KD,D,K) and the initial condition by a single Least Squares problem, which is well conditioned even for unstable systems. We present identification results for two multi-variable systems to show the main features of the proposed method, and to assess its performance against that achieved by other subspace methods. Furthermore, we compare the performance of Model Predictive Controllers, based on models identified from closed-loop data using the different subspace algorithms, in the control of the Wood–Berry distillation column. Results indicate that the proposed method is suitable for MPC design purposes, and compares favorably with the other subspace algorithms.