Nyquistkuvaaja

Nyquistkuvaaja, also known as the Nyquist plot or Nyquist diagram, is a graphical representation used in control theory and signal processing to analyze the stability of a feedback system. It plots the frequency response of an open-loop system. Specifically, it shows the locus of the transfer function $G(j\omega)H(j\omega)$ as the angular frequency $\omega$ varies from zero to infinity. The horizontal axis represents the real part of the transfer function, and the vertical axis represents the imaginary part.

The Nyquist plot is a powerful tool for determining the stability of a closed-loop system based on the behavior of its open-loop counterpart. The Nyquist stability criterion, which is directly related to the Nyquist plot, states that the number of unstable poles in the closed-loop system is equal to the number of net clockwise encirclements of the critical point (-1, 0) by the Nyquist plot, plus the number of unstable poles of the open-loop system. A stable closed-loop system is achieved if there are no encirclements of the critical point and the open-loop system is itself stable.

The plot can reveal important information about the system's performance, such as gain margin and phase margin, which are indicators of how close the system is to instability. These margins are measured from the Nyquist curve to the critical point (-1, 0). The gain margin is the amount of gain that can be added to the system before it becomes unstable, while the phase margin is the amount of phase lag that can be added before instability occurs. Analyzing the Nyquist plot helps engineers design robust control systems that can maintain stability under various operating conditions and disturbances.