The Nyquist criteria provide a quantitative measure for determining the stability of feedback control systems. They state that a feedback control system is st...
The Nyquist criteria provide a quantitative measure for determining the stability of feedback control systems. They state that a feedback control system is stable when the Nyquist rate of the system, which represents the maximum rate at which the system can be controlled, is less than the bandwidth of the system.
Nyquist Rate:
The Nyquist rate is the maximum angular frequency at which the system can be controlled with perfect feedback.
It is measured in radians per second (rad/s).
Bandwidth:
The bandwidth is the range of frequencies over which the feedback control system has significant influence on the closed-loop system.
It is measured in Hz.
Nyquist Criteria:
A feedback control system is stable if the Nyquist rate is less than the bandwidth.
If the Nyquist rate is greater than the bandwidth, the system is unstable.
Examples:
Stable system: A feedback control system with a bandwidth of 10 Hz and a Nyquist rate of 20 Hz is stable.
Unstable system: A feedback control system with a bandwidth of 10 Hz and a Nyquist rate of 40 Hz is unstable.
The Nyquist criteria provide a valuable tool for assessing the stability of feedback control systems. By understanding the Nyquist rate and bandwidth, designers can select controllers that will ensure stable and optimal system performance