# Root Locus

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

#### Root Locus Rules

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.

#### Example Problem A

Here’s a simple insightful example problem to get you started. You should try it out before watching the video.

#### Example Problem B

Here’s another one. Again, try sketching the plot before watching the video.

#### Root Locus for PD & PID Controller, and rltool

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.]