Subspace Identification for Closed-Loop Systems With Unknown Deterministic Disturbances

This paper presents a subspace identification method for closed-loop systems with unknown deterministic disturbances. To deal with the unknown deterministic disturbances, two strategies are implemented to construct the row space that can be used to approximately represent the unknown deterministic disturbances using the trigonometric functions or Bernstein polynomials depending on whether the disturbance frequencies are known. For closed-loop identification, CCF-N4SID is extended to the case with unknown deterministic disturbances using the oblique projection. In addition, a proper Bernstein polynomial order can be determined using the Akaike information criterion (AIC) or the Bayesian information criterion (BIC). Numerical simulation results demonstrate the effectiveness of the proposed identification method for both periodic and aperiodic deterministic disturbances.