Tracking of signals beyond the Nyquist frequency

This paper studies the problem of tracking or disturbance rejection for sampled-data control systems, where the tracking signal can have frequency components higher than the Nyquist frequency. In view of the well-known sampling theorem, one recognizes that any high-frequency components may be detected only as an alias in the low base band, and hence it is impossible to recover or detect such frequency components. This paper examines the basic underlying assumption, and shows that this assumption depends crucially on the underlying analog model. We show that it is indeed possible to recover such high-frequency signals, and also that, by introducing multirate signal processing techniques, it is possible to track or reject such frequency components. Detailed analysis of multirate closed-loop systems and zeros and poles are given. It is shown via examples that tracking of high-frequency signals beyond the Nyquist frequency can be achieved with satisfactory accuracy.