Find exact point on root locus?

Hi so I made a root locus and I'd like to find the point (real and imainary point) and gain at damping=0.456 but when i plot it (rlocus) and use the data tips button it skips between 0.453 and 0.479. how can I get the data tip to go on that exact point, damping=0.456? Thank You

Answer 1

[Ameer Hamza]

You can get the output of rlocus function in the numeric form too

s = tf(1, [1 2 3]);
[r, k] = rlocus(s);

r is the location of roots, and k is the corresponding gain. You can then interpolate the outputs to find the gain at a specific root location.

Answer 2

[Helin Qais]

When using the data tip button in MATLAB or Octave to obtain the coordinates of a specific point on a root locus plot, it is sometimes difficult to select the exact point of interest due to the automatic snap-to-grid feature of the data tip. However, there are several ways to obtain the precise coordinates and gain value at a damping ratio of 0.456.

One way is to use the `rlocus` function in combination with the `sgrid` function to draw a grid that intersects with the desired point on the root locus. Here's an example code snippet that shows how to do this:

```matlab % Define the transfer function G(s) G = tf([1 5], [1 0 0]);

% Plot the root locus of G(s) rlocus(G);

% Draw a damping ratio grid that intersects with the point of interest sgrid(0.456, [], 'r');

% Use the data cursor to obtain the precise coordinates and gain value % of the intersection point ```

In this example, we first define the transfer function `G(s)` as `s + 5 / s^2`. Then we plot the root locus of `G(s)` using the `rlocus` function. Next, we draw a damping ratio grid using the `sgrid` function, specifying the desired damping ratio of 0.456 and leaving the natural frequency blank. The `sgrid` function will draw a red line on the root locus plot that intersects with the desired point. Finally, we can use the data cursor to obtain the precise coordinates and gain value of the intersection point.

Another way to obtain the precise coordinates and gain value is to use the `rltool` function. The `rltool` function provides a graphical user interface that allows you to interactively adjust the gain value and damping ratio while observing the resulting closed-loop system response. The gain and damping ratio values are displayed on the interface, so you can easily read off the values at the desired point. To use `rltool`, you can simply type `rltool(G)` in the MATLAB or Octave command window, where `G` is your transfer function.

I hope this helps!