Nyquistkuvaukseen

Nyquistkuvaukseen, often translated as Nyquist plot or Nyquist diagram, is a graphical method used in control theory and signal processing to analyze the stability of a dynamical system. It was developed by Harry Nyquist in the 1930s. The plot visualizes the frequency response of a system.

The Nyquist plot is generated by plotting the imaginary part of the system's open-loop transfer function against its real part for all frequencies from zero to infinity. The frequency is typically represented by the parameter omega. As the frequency varies, a curve is traced in the complex plane.

A key aspect of the Nyquist plot is its relationship to the Nyquist stability criterion. This criterion relates the number of encirclements of the critical point (-1, 0) in the Nyquist plot to the number of unstable poles of the closed-loop system. Specifically, if N is the number of counter-clockwise encirclements of the point (-1, 0) by the Nyquist curve, and P is the number of open-loop poles in the right-half complex plane, then the number of closed-loop poles in the right-half plane, Z, is given by Z = N + P. For a system to be stable, Z must be zero.

The Nyquist plot provides valuable insights into a system's stability margins, such as gain margin and phase margin, which indicate how much the gain or phase can be altered before the system becomes unstable. It is a fundamental tool for designing and analyzing feedback control systems, particularly in determining if a system will oscillate or remain stable under various operating conditions.