Nyquistmenetelmä

Nyquistmenetelmä, often referred to as the Nyquist criterion or Nyquist stability criterion, is a graphical method used in control theory to determine the stability of a closed-loop system. It was developed by Harry Nyquist in 1932. The method analyzes the open-loop transfer function of a system, typically denoted as G(s)H(s), in the complex frequency domain.

The core of the Nyquist method involves plotting the frequency response of the open-loop transfer function, which maps the magnitude and phase of the output as a function of input frequency. This plot is known as the Nyquist plot. The stability of the closed-loop system is then determined by examining the encirclements of the critical point (-1, 0) on the complex plane by the Nyquist plot.

Specifically, the Nyquist stability criterion states that the closed-loop system is stable if and only if the number of counterclockwise encirclements of the point (-1, 0) by the Nyquist plot is equal to N, where N is the difference between the number of poles of the open-loop transfer function in the right-half of the complex plane and the number of zeros of the open-loop transfer function in the right-half of the complex plane. This criterion provides a robust way to assess stability, even in the presence of time delays or other complex system dynamics, without needing to explicitly find the roots of the characteristic equation.