Parametric identification of closed-loop linear systems using cyclic-spectral analysis

The problem of closed-loop system identification given noisy time-domain input-output measurements is considered. It is assumed that the various disturbances affecting the system are zero-mean stationary whereas the closed-loop system operates under an external cyclostationary input which is not measured. Noisy measurements of the (direct) input and output of the plant are assumed to be available. The closed-loop system must be stable but it is allowed to be unstable in open-loop. Two new identification algorithms are proposed using cyclic-spectral analysis of noisy input-output data. For both approaches, the open-loop transfer function is first estimated using the cyclic-spectrum and cyclic cross-spectrum of the input-output data. These transfer function estimates are then used as "data" for the proposed algorithms. Both classes of parameter estimators are shown to be weakly consistent in any stationary and a class of cyclostationary noise (both at input as well as output). Computer simulation examples are presented in support of the proposed approaches.