Hypertracking and Hyperrejection: Control of Signals beyond the Nyquist Frequency

TL;DR

This paper introduces a novel control approach that enables tracking and disturbance rejection of signals beyond the Nyquist frequency by leveraging a specific analog signal generator model, challenging traditional sampling limitations.

Contribution

It proposes a new control scheme that removes Nyquist frequency limitations by assuming a suitable analog signal generator, supported by detailed analysis of multirate systems and robustness.

Findings

Effective control of signals beyond Nyquist frequency demonstrated

Robustness characterized with relation to delay length

Examples confirm the method's practical effectiveness

Abstract

This paper studies the problem of signal tracking and disturbance rejection for sampled-data control systems, where the pertinent signals can reside beyond the so-called Nyquist frequency. In light of the sampling theorem, it is generally understood that manipulating signals beyond the Nyquist frequency is either impossible or at least very difficult. On the other hand, such control objectives often arise in practice, and control of such signals is much desired. This paper examines the basic underlying assumptions in the sampling theorem and pertinent sampled-data control schemes, and shows that the limitation above can be removed by assuming a suitable analog signal generator model. Detailed analysis of multirate closed-loop systems, zeros and poles are given, which gives rise to tracking or rejection conditions. Robustness of the new scheme is fully characterized; it is shown that there is a close relationship between tracking/rejection frequencies and the delay length introduced for allowing better performance. Examples are discussed to illustrate the effectiveness of the proposed method here.