# Matlab help (Root Locus using Z Domain)

• MATLAB
• Ethers0n
In summary, the speaker is seeking guidance on producing a plot of a root locus for an open loop transfer function in the z-domain with a gain K. They have already solved for the characteristic equation by hand but are unsure of how to use Matlab to plot the root locus in the z-domain. They are wondering if the process is the same as in the Laplace domain and if they need to specify the sampling time in Matlab. The suggested solution is to inform Matlab of the sampling time and use the command rlocus to draw the root locus for the z variable.
Ethers0n
I'm trying to prooduce a plot of a root locus for an open loop transfer function.
The transfer function is in the z-domain, with a gain K. I've already solved for the charectoristic equation of the system by hand.

But, how do I use Matlab to plot the root locus of a transfer function in the Z - Domain? I've seen examples in the Laplace (s) Domain...do these work the same way? (as in...i won't need to do anything differently?)

thank you.

When describing your system in Matlab you must inform the sampling time. Matlab will automatically know that you are using a discrete variable. The command rlocus will draw your root locus for your z variable.

Hi there,

Thank you for reaching out for help with plotting a root locus in the z-domain using Matlab. The process for creating a root locus plot in the z-domain is similar to that in the Laplace (s) domain, but there are a few differences to keep in mind.

First, let's briefly review the steps for generating a root locus plot in Matlab:

1. Define the transfer function in either the s-domain or z-domain.
2. Use the 'rlocus' function to generate the root locus data.
3. Plot the root locus using the 'plot' function.

Now, for the z-domain specifically, there are a few things to consider:

1. The 'rlocus' function in Matlab only accepts transfer functions in the s-domain. Therefore, you will need to convert your z-domain transfer function to the s-domain before using the 'rlocus' function. This can be done using the 'c2d' function in Matlab, which converts a continuous-time transfer function to a discrete-time transfer function.
2. Once you have converted your transfer function to the s-domain, you can proceed with generating the root locus data and plotting it using the 'rlocus' and 'plot' functions as usual.

I hope this helps you get started with plotting your root locus in the z-domain using Matlab. If you need further assistance, I recommend consulting the Matlab documentation or reaching out to their support team for more specific guidance.

Best of luck with your project!

## 1. What is the purpose of using the Z-domain in Root Locus analysis?

The Z-domain is used in Root Locus analysis to represent the behavior of a discrete-time system. It allows for the analysis of stability and performance of a system in the frequency domain.

## 2. How is the Root Locus plot generated using the Z-domain?

The Root Locus plot is generated by plotting the roots of the closed-loop transfer function in the Z-domain. The plot shows the locations of the roots as the gain or a parameter is varied, providing insight into the system's stability and performance.

## 3. What is the significance of the location of the poles and zeros in the Z-domain Root Locus plot?

The location of the poles and zeros in the Z-domain Root Locus plot determines the stability and performance of the system. The poles represent the closed-loop poles and their location determines the system's stability. The zeros represent the open-loop poles and their location affects the system's performance.

## 4. How can the Z-domain Root Locus plot be used to design a controller?

The Z-domain Root Locus plot can be used to design a controller by adjusting the gain or parameters to achieve desired stability and performance. The plot can also be used to determine the optimal location of a compensator to improve the system's response.

## 5. Are there any limitations to using Root Locus analysis in the Z-domain?

One limitation of using Root Locus analysis in the Z-domain is that it assumes the system is linear and time-invariant. If the system is highly nonlinear, the Root Locus plot may not accurately represent its behavior. Additionally, Root Locus analysis may not be suitable for systems with large delays or unstable open-loop poles.

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