VARMAX-based closed-loop subspace model identification

In this paper a predictor-based subspace model identification method is presented that relaxes the requirement that the past window has to be large for asymptotical consistent estimates. By utilizing a VARMAX model, a finite description of the input-output relation is formulated. An extended least squares recursion is used to estimate the Markov parameters in the VARMAX model set. Using the Markov parameters the state sequence can be estimated and consequently the system matrices can be recovered. The effectiveness of the proposed method in comparison with an existing method is emphasized with a simulation study on a wind turbine model operating in closed loop.