Consistency of noise covariance estimation in joint input–output closed-loop subspace identification with application in LQG benchmarking

The LQG trade-off curve has been used as a benchmark for control loop performance assessment. The subspace approach to estimating the LQG benchmark has been proposed in the literature which requires certain intermediate matrices in subspace identification as well as the covariance matrix of the noise. It is shown in this paper that many existing closed-loop identification methods do not give a consistent estimate of the noise covariance matrix. As a result, we propose an alternative subspace formulation for the joint input–output closed-loop identification for which the consistency of the required subspace matrices and noise covariance is guaranteed. Simulation studies and experimental results are provided to demonstrate the utility of the proposed method.