Important Terminologies of Nyquist Plot
Important terminologies of Nyquist Plot are mentioned below:
- Nyquist Path or Contour
- Nyquist Encirclement
- Nyquist Mapping
- Gain Crossover Frequency
- Phase cross over frequency
- Phase Margin
- Gain Margin
1. Nyquist Path or Contour
The Nyquist Path or Contour is a closed contour on the right side of the s-plane. To enclose the entire RHS of the plane, a large semicircle lane is drawn with a diameter along the ‘j’ axis and center at the source. The semicircle radius is simply treated as Nyquist Encirclement. The Nyquist Contour is shown in the figure below:
Nyquist Contour
In the above plot, marked points are denoting:
Point 1 is denoting s = jω
Point 2 is denoting s = where, θ = +90o to -90o
Point 3 is denoting s = -jω
Point 2 is denoting s = where, θ = -90o to +90o
2. Nyquist Encirclement
It is a point, if it is found in the curve, is known to be encircled by a line.
3. Nyquist Mapping
Mapping is the process of transforming a point in the s-plane into a point in the F(s) plane, and F(s) is the result of mapping.
4. Gain Crossover Frequency
It is the frequency at which the Nyquist plot has unity magnitude. It is denoted by ‘ωgc‘.
5. Phase cross over frequency
It is the frequency at which point the Nyquist plot crosses the negative real axis is called the phase cross-over frequency and it is denoted with ‘ωpc‘.
6. Phase Margin
The phase margin indicates how much more phase shift we may put in the open loop transfer function before our system becomes unstable. It can be calculated from the phase at the gain cross-over frequency.
7. Gain Margin
The gain margin is the amount of open loop gain that can be increased before our system becomes unstable. It can be calculated from the gain at the phase cross-over frequency.
Nyquist Plot
A Nyquist plot is a graphical representation used in control engineering. It is used to analyze the stability and frequency response of a system. The plot represents the complex transfer function of a system in a complex plane. The x-axis represents the real part of the complex numbers and the y-axis represents the imaginary part. Each point on the Nyquist plot reflects the complex value of the transfer function at that frequency.
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