We study the problem of tracking or disturbance rejection for signals beyond the Nyquist frequency in the sampled-data context. Given the well-established sampling theorem, one is inclined to infer that it is possible to track or reject only those signals below the Nyquist frequency. However, such a high-frequency signal may be detected as an aliased signal, and this opens a new possibility in tracking and regulation. This article shows that a multirate processing with a suitable choice of a weighting function enables tracking or rejection of high-frequency signals beyond the Nyquist frequency. An example is given to illustrate the result.
|Title of host publication||Emerging Applications of Control and Systems Theory|
|Subtitle of host publication||Lecture Notes in Control and Information Sciences - Proceedings|
|Editors||Roberto Tempo, Stephen Yurkovich, Pradeep Misra|
|Number of pages||379|
|Publication status||Published - Feb 25 2018|
Yamamoto, K., Yamamoto, Y., & Nagahara, M. (2018). Hypertracking Beyond the Nyquist Frequency. In R. Tempo, S. Yurkovich, & P. Misra (Eds.), Emerging Applications of Control and Systems Theory: Lecture Notes in Control and Information Sciences - Proceedings (pp. 369). Springer. https://doi.org/10.1007/978-3-319-67068-3_27