MATLAB Root Locus
From ControlTheoryPro.com

Contents
1 Introduction to Root Locus using the rlocus MATLAB command
MATLAB's rlocus command plots the root locus via the Evan's method. It requires the Control System Toolbox.
MATLAB's rlocus command must be passed SISO open loop systems. It will return the closed loop pole trajectories as a function of feedback gain. Where
and the closed loop poles are
where
 is the open loop transfer function and
 is the feedback gain.
2 Basic Usage of rlocus for plotting the Root Locus
The rlocus command plots the root locus of the open system sys with the following command:
>> rlocus(sys)
where
 sys is the open loop transfer function.
The root locus can also be plotted at a particular feedback gain k with the following:
>> rlocus(sys, k)
Like plot the rlocus command can take multiple systems like this
>> rlocus(sys1, 'b',sys2, 'r.:',sys3, 'g').
3 Required Toolboxes for rlocus
Control System Toolbox