Direct closed-loop identification of mechanical resonances above the nyquist frequency without any external persistently exciting signals

In this paper, a general multirate approach is proposed for direct closed-loop identification of mechanical resonances above the Nyquist frequency without injecting any external persistently exciting (PE) signals. Based on the polynomial transformation technique, an extended least-squares (ELS) algorithm is designed to estimate parameters of the mixed-rate model, from which parameters of the fast-rate model is extracted. Convergence properties of the ELS algorithm are analyzed, and the parameter identifiability is ensured if the plant output sampling rate is non-integer multiples of the controller sampling rate. The performance of the proposed approach is evaluated by simulation results on the head-positioning servo control system of a hard disk drive (HDD) during track-following mode, where no external PE signal is added on.