Nyquistdiagrammi

Nyquistdiagrammi is a graphical tool used in control system engineering to analyze the stability of a system. It plots the frequency response of a system, specifically the open-loop transfer function, in the complex plane. The horizontal axis represents the real part of the transfer function's output, and the vertical axis represents the imaginary part. As frequency varies from zero to infinity, the plot traces a curve.

The Nyquist stability criterion relates the number of encirclements of the critical point (-1, 0) by the Nyquist plot to the number of unstable poles of the closed-loop system. If the open-loop transfer function has $P$ poles in the right-half of the complex plane, and the Nyquist plot encircles the point (-1, 0) $N$ times in the counter-clockwise direction, then the closed-loop system will have $Z = P - N$ poles in the right-half plane. For stability, $Z$ must be zero, meaning $N = P$.

The diagram provides insights into system robustness, indicating how much the system's gain and phase can change before instability occurs. It is particularly useful for analyzing systems with time delays or unstable open-loop configurations. The Nyquist plot is generated by evaluating the open-loop transfer function at different frequencies and plotting the resulting complex numbers.