A general multirate approach for direct closed-loop identification to the Nyquist frequency and beyond

Without injecting any external persistently exciting signals, a general multirate approach is proposed for direct closed-loop identification. First, an extended least-squares algorithm is designed to identify the mixed-rate model after polynomial transformation. Next, the identified mixed-rate model is used to compute the fast-rate model, from which system dynamics to the Nyquist frequency and beyond can be obtained. Identifiability is mathematically proven if the plant output sampling rate is non-integer multiples of the controller sampling rate. The effectiveness of the proposed approach is evaluated by both the simulation and experimental results in a hard disk drive.