Root Locus: Identifying Asymptotes for Negative Feedback System

In summary, when sketching a root locus for a closed loop negative feedback system with positive gain K, if there are more poles than zeros, the poles will tend towards infinity along asymptotes. However, it is not possible to determine which pole will travel along which asymptote. This can be seen in the example of a simple unity gain feedback loop with G(s) = (s-3)/[s^2(s+10)], where the MATLAB plot shows the general shape of the root locus but not the specific location of each pole along the asymptotes.
  • #1
Shaybay92
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When sketching a root locus of a simple closed loop negative feedback system (with positive gain K)... if you have more poles than zeros, we know that they will tend towards infinity along some asymptotes. How do you know which pole will travel along which asymptote?

For example in the system where we have a simple unity gain feedback loop, and G(s) = (s-3)/[s^2(s+10)]

I have attached the MATLAB plot for the system. I was able to draw basically the whole thing, except for which pole goes along which asymptote.

Thanks!
 

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  • #2
You can't say that. It is the system that has two asymptotes, not each pole.
 

1. What is a root locus?

A root locus is a graphical representation of the locations of the closed-loop poles of a negative feedback system as a function of a parameter, usually the gain. It can help determine the stability and performance of a system.

2. How is a root locus plot constructed?

To construct a root locus plot, the open-loop transfer function of the system is first determined. Then, the poles and zeros of the transfer function are plotted on the complex plane. The root locus is then drawn by varying the gain parameter and tracing the path of the closed-loop poles.

3. What do the asymptotes on a root locus plot represent?

The asymptotes on a root locus plot represent the behavior of the closed-loop poles as the gain parameter approaches infinity. They can provide information on the stability of the system and its response to a step input.

4. How can asymptotes be identified on a root locus plot?

Asymptotes can be identified on a root locus plot by counting the number of poles and zeros of the open-loop transfer function. The number of asymptotes will be equal to the difference between the number of poles and zeros.

5. What is the significance of identifying asymptotes on a root locus plot?

Identifying asymptotes on a root locus plot can help determine the stability and performance of a system. The direction and angle of the asymptotes can also provide insight into the system's behavior and response to different inputs. Additionally, knowing the location of the asymptotes can aid in selecting an appropriate gain value to achieve desired system characteristics.

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