Closed-loop identification of multivariable equation error model with unknown disturbances

Closed-loop identification for industrial processes has been widely studied in the past decades. Multivariable equation error models (ARX) are frequently used for closed-loop modeling with input and output measurements. When unmeasured disturbances (errors) exist in the equation error models, the traditional prediction error methods are used to identify the models by treating the disturbances as filtered white noises, which is not the case for many disturbances and thus seriously deteriorating the estimation results. In this paper, a recursive least squares estimation with unknown disturbances (RLSE-UD) approach is introduced to estimate the parameters of multivariable equation error models, as well as the unmeasured disturbances. No prior information of the unknown disturbances is required for RLSE-UD and the estimator is proven unbiased and consistent. Simulation results demonstrate that the RLSE-UD approach is capable of identifying the parameters of multivariable equation error models and unmeasured disturbances in closed-loop cases well.