Root Locus Sketching: Learn How to Draw and Analyze

In summary, root locus sketching is a graphical method used to analyze the behavior of a closed-loop control system by plotting the roots of the characteristic equation on a complex plane. It is important because it provides a visual representation of the system, helping in understanding and designing control systems. To sketch a root locus, you need to determine the open-loop transfer function, plot poles and zeros, and add asymptotes, break points, and angles. The root locus plot tells us about the stability and performance of the system. However, it has limitations such as only applying to LTI systems with a single input and output, and accuracy depends on the open-loop transfer function.
  • #1
Natalie89
29
0
Hello,

I do not understand very well how to sketch a root locus plot. I am able to find poles/zeros, where the root locus exist on the real axis, the break away/in points, intersection of asymptotes, crossing of the imaginary axis, etc., but I do not understand how to actually draw the root locus at the end.

If anyone can give me some clarification that would be very much appreciated.
 
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  • #2
Please refer to the content of followig link.
lpsa.swarthmore.edu/Root_Locus/RLocusExamples.html
I think you will be able to understand.
 
  • #3
Thanks!
 

Related to Root Locus Sketching: Learn How to Draw and Analyze

1. What is root locus sketching?

Root locus sketching is a graphical method used to analyze the behavior of a closed-loop control system. It involves plotting the roots (or locations) of the characteristic equation of the system on a complex plane, which can help determine the stability and performance of the system.

2. Why is root locus sketching important?

Root locus sketching is important because it provides a visual representation of the behavior of a closed-loop control system. This can help engineers and scientists in understanding and designing control systems for various applications.

3. How do you sketch a root locus?

To sketch a root locus, you first need to determine the open-loop transfer function of the system. Then, you can plot the poles and zeros of the transfer function on a complex plane. Next, you can draw asymptotes, breakaway and break-in points, and angles of departure and arrival to complete the root locus plot.

4. What does the root locus plot tell us?

The root locus plot provides information about the stability and performance of a closed-loop control system. By analyzing the plot, we can determine the locations of the closed-loop poles, which can indicate the stability of the system. We can also calculate the damping ratio and natural frequency of the system, which can help assess the performance of the system.

5. Are there any limitations to root locus sketching?

One limitation of root locus sketching is that it only applies to linear time-invariant (LTI) systems. It also assumes that the system has a single input and single output. Additionally, the accuracy of the root locus plot depends on the accuracy of the open-loop transfer function, which can be challenging to obtain in some cases.

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