What is the significance of the 'Nyquist frequency' in a digital control system?

The Nyquist frequency in a digital control system is half the sampling frequency of the system. Its significance lies in determining the maximum frequency component of a signal that can be accurately represented and processed by the digital system without introducing aliasing. Aliasing occurs when a continuous-time signal is sampled at a rate lower than twice its highest frequency component. This results in the higher frequency components being misinterpreted as lower frequency components, distorting the signal. According to the Nyquist-Shannon sampling theorem, to accurately reconstruct a signal from its samples, the sampling frequency must be at least twice the highest frequency component of the signal. This minimum sampling frequency is called the Nyquist rate, and half of the sampling frequency is the Nyquist frequency. In a digital control system, the Nyquist frequency determines the upper limit of the frequencies that the system can effectively control. If a signal contains frequency components higher than the Nyquist frequency, these components will be aliased and can cause instability or poor performance in the control system. Therefore, it is crucial to ensure that the sampling frequency is high enough to satisfy the Nyquist criterion and to filter out any frequency components above the Nyquist frequency before sampling, using an anti-aliasing filter.