create a script that uses rlocus to plot the root locus of a given system characteristic equation in matlab

To plot the root locus of a given system characteristic equation using rlocus function in MATLAB, you can follow these steps:

1. Define the system characteristic equation: You need to know the transfer function or the closed-loop characteristic equation of the system you want to plot the root locus for. You can represent it in MATLAB using the symbolic toolbox or define it directly as a transfer function.

2. Use the rlocus function: The rlocus function in MATLAB is used to plot the root locus of a given system characteristic equation. It takes the characteristic equation as input and returns the root locus plot.

Here is an example of how to create a script to plot the root locus:

main.m
% Step 1: Define the system characteristic equation
s = tf('s');
G = 1 / (s^2 + 2*s + 1); % Example transfer function

% Step 2: Use the rlocus function
rlocus(G)
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In this example, we define a transfer function G using the tf function. The transfer function represents a second-order system with a characteristic equation of s^2 + 2*s + 1.

We then pass the transfer function G to the rlocus function, which plots the root locus.

You can customize the root locus plot by adjusting the axis limits, adding grid lines, or labeling the plot using MATLAB's plotting functions.

Note: The rlocus function is part of the Control Systems Toolbox in MATLAB. Make sure you have the toolbox installed to use this function.