Plotting the Nyquist Diagram - Stuck

In summary, drawing a Nyquist plot involves considering the gain and phase at different frequencies and plotting them on a complex plane. It is important to determine the phase as it helps understand the behavior of the plot. The j-axis should take values from -1 to 1 and the plot should not loop around the real axis.
  • #1
thomas49th
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Homework Statement


http://gyazo.com/8187e80897fe361d555dbb9e5399366d

Okay, quite stuck here. Spent a few hours with the notes and tried some websites, but I'm still not confident in plotting Nyquist Diagrams

Homework Equations


N = Z-P

The Attempt at a Solution


Well, at w=0, gain is -2 and at w= ∞ gain = 0.

We also have a pole at s=0.5 in the right half plane... so P=1, correct? As we have an unstable pole?

As for the phase it goes from 0 to -90°. WHY is calculating the phase important, where is this show on the Nyquist plot!?Do I now have enough information to draw it?
How would you go about drawing it?

How do I know what values to the j-axis should take? How do I know if it's meant to loop around under the real axis and back up to (0,0)

Many Thanks
ThomasAnswers:
http://gyazo.com/da99d7751508263c497af7270010228f
 
Last edited:
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  • #2
Yes, you have enough information to draw the Nyquist plot. The phase is important because it helps you determine how the plot behaves at different frequencies. For the j-axis, it should take values from -1 to 1. The plot should not loop around the real axis and back up to (0,0). This is because the pole at s=0.5 is in the right half plane and the gain is decreasing from -2 at w=0 to 0 at w=∞.
 

1. What is a Nyquist diagram?

A Nyquist diagram is a graphical representation of the frequency response of a system. It shows the relationship between the magnitude and phase of a system's response to different frequencies.

2. How do you plot a Nyquist diagram?

To plot a Nyquist diagram, you need to first determine the transfer function of the system. Then, you can use this transfer function to calculate the gain and phase at various frequencies. Finally, you can plot the gain and phase on a complex plane to create the Nyquist diagram.

3. What does it mean when a Nyquist diagram is "stuck"?

When a Nyquist diagram is "stuck", it means that there is a point on the diagram where the phase is not changing as the frequency increases. This is often seen as a horizontal line on the diagram, indicating a phase margin of 180 degrees.

4. How do you interpret a "stuck" Nyquist diagram?

A "stuck" Nyquist diagram can indicate that the system is unstable. This means that there is a possibility of the system oscillating or diverging as time goes on. However, it is important to consider other factors such as the gain margin and stability criteria before determining the stability of a system based on a Nyquist diagram.

5. How can a "stuck" Nyquist diagram be corrected?

If a Nyquist diagram is "stuck", it may be possible to adjust the parameters of the system to improve stability. This could include changing the gain or phase margin, adjusting the feedback loop, or using different components in the system. It is important to carefully analyze the system and make strategic changes to ensure stability.

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