Closed-loop MOESP subspace model identification with parametrisable disturbances

A new subspace identification method for systems operating either in open-loop or in closed-loop is presented. The method obtains an estimate of the innovation sequence by performing an RQ-factorization of the measurement data, thereby avoiding explicitly solving a least-squares problem. In a second step, the estimated innovation sequence is used to perform ordinary MOESP to find the system matrices up to a similarity transformation. The closed-loop identification algorithm also applies to cases where certain disturbance inputs are present that can be parametrised in terms of suitable basis functions. All computations are performed using orthogonal factorisations of the data. The method is illustrated by applying it to a system operating in closed-loop and to measurements from a real system with periodic disturbances.