NicholsDiagramme

NicholsDiagramme, commonly known as the Nichols diagram, is a graphical tool used in control theory to analyze the frequency response of linear time-invariant systems. It represents the open-loop transfer function L(jω) by plotting each frequency point as a coordinate that encodes phase and magnitude.

Construction and interpretation: The horizontal axis shows the phase of L(jω) in degrees, typically spanning a range such as -360 to 0, while the vertical axis shows the magnitude in decibels, 20 log10|L(jω)|. As frequency increases, the locus of points traces the NicholsDiagramme curve. Lines of constant magnitude (gain) and constant phase are often drawn to facilitate reading of margins and stability information. The diagram is especially useful for assessing how gain and phase changes affect closed-loop behavior.

Relation to other plots: The NicholsDiagramme is closely related to Bode and Nyquist plots. It can be derived from a Bode magnitude and phase plot or from a Nyquist plot by a mapping that preserves gain and phase information. The diagram provides a single-view representation that can simplify certain compensator design tasks and stability analyses.

Applications and limitations: It is widely used for designing compensators, evaluating robustness, and reading gain and phase margins in unity-feedback configurations. While powerful for intuition and quick assessment, the NicholsDiagramme can become less intuitive for very high-order systems or highly nonlinear responses, and proper interpretation often requires familiarity with its specific stability boundaries.

See also: Bode plot, Nyquist plot, gain margin, phase margin, stability criterion.