Nyquistkritériumot

Nyquistkritériumot, often translated as the Nyquist criterion, is a fundamental concept in control theory and signal processing. It provides a way to determine the stability of a closed-loop system by analyzing the open-loop frequency response of the system. Specifically, it relates the stability of a feedback system to the number of times the open-loop transfer function's Nyquist plot encircles the critical point (-1, 0) in the complex plane.

The Nyquist criterion states that for a stable closed-loop system, the number of clockwise encirclements of the -1 point in the Nyquist plot of the open-loop transfer function must equal the number of open-loop poles in the right-half of the complex plane. If the open-loop system has no poles in the right-half plane, then for closed-loop stability, the Nyquist plot must not encircle the -1 point at all.

This graphical method is powerful because it can assess stability even when the open-loop system is unstable. It is particularly useful for systems with time delays, which can be challenging to analyze with other methods. The Nyquist plot maps the imaginary part of the open-loop transfer function against its real part as the frequency varies from zero to infinity. The encirclements of the -1 point directly indicate the presence of unstable closed-loop poles.