A new excitation scheme for closed-loop subspace identification using additional sampling outputs and its extension to instrumental variable method

Abstract

It is known that feedback from outputs to inputs causes non-identifiability in many subspace identification algorithms. In this paper, a new excitation method is proposed for closed-loop subspace identification. By adding an output sampling point within two adjacent control times, a difficult closed loop identification issue is recast into an open loop identification. Uncorrelation between the process inputs and the noises in closed loop is obtained, and the persistently exciting condition is proven to be satisfied based on spectral analysis and innovation state space models so that the consistent estimates with no demand for external exciting signals can be guaranteed. Simultaneously, the additional sampling scheme offers different selections of instrumental variables for the non-error-in-variable case and the error-in-variable case in some instrumental variables-based identification algorithms. A simulation is performed to test the identification efficiency of the new scheme.