The root locus provides an incredibly elegant and insightful way to investigate feedback control systems. It provides a graphical depiction of how a system responds to a whole family of feedback laws. It allows one to see what is possible with different types of feedback.
Table of Links
- Root Locus Rules
- Example Problem A
- Example Problem B
- Root Locus for PD & PID controllers, and rltool
I do not have Rules 0 through 3 yet, but here are the two parts of Rule 4. This rule deals with the branches as the gain K approaches positive inifinity. Part A of the rule is provided in the following video.
Part B of Rule 4 is provided in the video below.
Here’s a simple insightful example problem to get you started. You should try it out before watching the video.
Here’s another one. Again, try sketching the plot before watching the video.
In this video, I consider P, PD, and PID controllers for a single system. We sketch root locus plots for these cases by hand. Then we discuss how to use Matlab’s rltool and root locus to determine controller gains. [Note. In the video, I use something in Matlab called sisotool. Since then, I have discovered that you can use the Matlab command ‘rltool’ to activate only the part of sisotool that we care about here.]