I have recently (summer 2020) developed this page to help student learn how to sketch the root locus by hand. You can enter a numerator and denominator for G(s)H(s) (i.e., the loop gain) and the program will guide you through the steps to develop a sketch of the root locus by hand.
It is not the intention of this page to be used as a generic design tool, it is simply a teaching tool. As such, it is only designed to work with poles and zeros that are relatively small numbers (say between 0 and 20).
Please let me know if you find any problems with this page (contact links are at the bottom). Here is link to known problems with page.
We start with the loop gain transfer function:
The characteristic equation (i.e., the denominator of the closed loop transfer function) is 1+K⋅G(s)⋅H(s)=0, or 1+K⋅N(s)D(s)=0, which we can rewrite as: \[D(s) + K \cdot N(s) = s^{2}-s-2 + K \left( s+3 \right)= 0\].
If we plot the roots of this equation as K varies, we
obtain the root locus. A program (like MATLAB) can do this easily, but to make a sketch, by hand, of
the location
of the roots as K varies we need some information:
(The explanation of the rule applied to this loop gain is below the graph.)
As you can see the locus is symmetric about the real (horizontal) axis. You can select one of the root locus rules (above) to see how it is applied for the given loop gain.
As I find problems with the code, I will list them here.
© Copyright 2005 to 2022 Erik Cheever This page may be freely used for educational purposes, but the url must be referenced.
Comments? Questions? Suggestions? Corrections?