Multirate Identification of Mechanical Resonances Beyond the Nyquist Frequency in High-Performance Mechatronic Systems

Due to the aliasing effect produced by the sampling operation, mechanical resonant modes beyond the Nyquist frequency are difficult to be identified using conventional system identification techniques. In this paper, a parametric approach is proposed to identify these resonances. Identification is performed in a closed-loop multirate sampled-data system, where the input is sampled integer times faster than the output. First, the polynomial transformation technique-based recursive least-squares algorithm with a dead-zone is designed to identify the mixed-rate model. Next, the identified mixed-rate model is used to compute the fast-rate model, from which the resonant modes beyond the Nyquist frequency can be extracted. The proposed approach is evaluated on the head-positioning servo control system of a hard disk drive during the track-seeking mode and the effectiveness is verified by both simulation and experimental results. As compared to analog sensors, the proposed approach can potentially be implemented to identify mechanical resonances to arbitrarily high frequencies by increasing the sampling rate of the digital-to-analog converter.