A Tool for Learning to Sketch Root Locus Plots
RLocusGui is a graphical user interface written in the Matlab® programming language. It takes a transfer function and applies the standard rules for sketching a root locus plot by hand. Of course, Matlab can do this more accurately, but it is important to know how pole and zero locations affect the final plot. It is hoped that the RLocusGui program will be a versatile program for teaching and learning the construction of root locus diagrams.
Files for the program are found on github.
I have largely stopped updating RLocusGUI and have instead implemented the functionality in a web page at https://lpsa.swarthmore.edu/Root_Locus/RLDraw.html.
Consider the transfer function:
This function consists of a zero at s=-3, and poles at s=0, -1, and -2±2j. We can define the system, and invoke the GUI.
>> mySys=tf([1 3],poly([0 -2+2j -2-2j -1])) %define Xfer function
Transfer function:
s + 3
----------------------------------------
s^4 + 5 s^3 + 12 s^2 + 8 s
>> RLocusGui(mySys) %Invoke GUI
The GUI generates a window as shown below.
Starting in the upper right and going counterclockwise, the window shows:
- The transfer function.
- The completed Root Locus plot. You could get the same root locus plot from Matlab directly:
>>rlocus(mySys)- A set of radio buttons listing all of the root locus rules (see below).
- A text box that describes the application of the radio button selected in (3): "Description of Rule."
- A button, "Rule Detail (web)," that will open a web page describing the selected rule in detail.
- A button, "Make Web Page," that will generate a web page that describes the application of the root locus rules to the chosen transfer function (see below).
- A button, "Web Resources," that links to my files describing the root locus.
- A button, "Exit," that closes the GUI.
By selecting each of the radio buttons, you can change what is displayed. For example if you select the "Locus on Real Axis" radio button, the display changes as shown below.
There are two notable differences in the figure. First, the box in the lower right hand corner describes the application of the selected rule. Even more noticeable is the second graph (at the right). This graph shows the original root locus, and illustrates (graphically) the application of the selected rule.
Any of the other rules may be chosen in turn. The calculation of the "Angle of Departure" from the complex poles is illustrated below
If the rule doesn't apply (e.g., "Angle of Arrival"), the "Description of Rule" box states this, and there is no graphic (below)
The last two choices "Choose point of locus and determine gain" and "Choose gain and find point on locus" are not really rules of the locus, but are instead application (the former is more or less equivalent to the Matlab command "rlocfind", but describes how it would be done by hand). Both of them allow further interaction and exploration (through a check box that appears above "Description of Rule."
The program will also automatically generate a web page that displays all of the rules and the graphics illustrating the rule. For example, if you hit the "Make Web Page" button, each rule is invoked and a web page is created and opened. Note the web page and its associated files are created in the current Matlab directory (i.e., the directory you see when you use Matlab's "ls" command).
Please let me know (links are below) if you find any problems with this software, or have any suggestions.