Phase Margin and Gain Margin (Nyquist Stability Criterion)

Опубликовано: 06 Март 2025
на канале: Essential Electrical

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Nyquist plots are the continuation of polar plots for finding the stability of the closed-loop control systems by varying ω from −∞ to ∞. That means Nyquist plots are used to draw the complete frequency response of the open-loop transfer function.

The Nyquist stability criterion works on the principle of argument. It states that if there are P poles and Z zeros are enclosed by the ‘s’ plane closed path, then the corresponding G(s)H(s) plane must encircle the origin P−Z times. So, we can write the number of encirclements N as,
N=P−Z
If the enclosed ‘s’ plane closed path contains only poles, then the direction of the encirclement in the G(s)H(s) plane will be opposite to the direction of the enclosed closed path in the ‘s’ plane.

If the enclosed ‘s’ plane closed path contains only zeros, then the direction of the encirclement in the G(s)H(s) plane will be in the same direction as that of the enclosed closed path in the ‘s’ plane.