Nyquistelemzések

Nyquistelemzések, also known as Nyquist analysis or Nyquist stability criterion, is a graphical method used in control theory to determine the stability of a feedback system. It was developed by Harry Nyquist in 1932. The analysis involves plotting the frequency response of the open-loop transfer function of the system.

The frequency response is represented on a polar plot, where the real part of the transfer function is plotted against the imaginary part for various frequencies. The plot traces a curve as the frequency varies from zero to infinity. The Nyquist criterion states that a closed-loop system is stable if and only if the open-loop Nyquist plot does not encircle the critical point (-1, 0) in the complex plane, in a counter-clockwise direction, a number of times equal to the number of unstable poles of the open-loop transfer function.

If the system is open-loop stable, then the number of encirclements of (-1, 0) must be zero for the closed-loop system to be stable. If the open-loop system has unstable poles, these must be accounted for by adding additional counter-clockwise encirclements of the critical point for the closed-loop system to be stable. The Nyquist criterion provides a robust way to assess stability, especially for systems with complex dynamics or potential instability. It is a fundamental tool for control system engineers in designing and analyzing systems.