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DOI: 10.1109/TAC.2022.3230599

Hypertracking and Hyperrejection: Control of Signals beyond the Nyquist Frequency

Kaoru YamamotoYutaka YamamotoMasaaki Nagahara
Dec 2022
摘要
This paper studies the problem of signal tracking and disturbance rejectionfor sampled-data control systems, where the pertinent signals can reside beyondthe so-called Nyquist frequency. In light of the sampling theorem, it isgenerally understood that manipulating signals beyond the Nyquist frequency iseither impossible or at least very difficult. On the other hand, such controlobjectives often arise in practice, and control of such signals is muchdesired. This paper examines the basic underlying assumptions in the samplingtheorem and pertinent sampled-data control schemes, and shows that thelimitation above can be removed by assuming a suitable analog signal generatormodel. Detailed analysis of multirate closed-loop systems, zeros and poles aregiven, which gives rise to tracking or rejection conditions. Robustness of thenew scheme is fully characterized; it is shown that there is a closerelationship between tracking/rejection frequencies and the delay lengthintroduced for allowing better performance. Examples are discussed toillustrate the effectiveness of the proposed method here.
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