Spectral distribution and implications of feedback regulation beyond Nyquist frequency

A fundamental challenge in digital and sampled-data control arises when the continuous-time plant is subject to fast disturbances that possess significant frequency components beyond Nyquist frequency. Such intrinsic difficulties are more and more encountered in modern manufacturing applications, where the measurement speed of the sensor is physically limited compared to the plant dynamics. The paper analyzes the spectral properties of the closed-loop signals under such scenarios, and uncovers several fundamental limitations in the process.