Matlab code for example 6.6 from the book "Regeltechniek voor het HBO"
Break away points and entry points on the real axis of a root locus
Date : 02/03/2022
Revision : 1.0
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clear all variables from Workspace and close all figures.
clear variables;
close all;
% Define 's' variable
s=tf('s');
Given system and rootlocus equation
Suppose in the system of figure 6.4 is:
.
The root locus equation of the closed system is:
→.
We can say right now that (for positive ) the parts of the real axis between and and to the left of belong to the root locus.
Determine break away or entry points
The place of break away points or entry points on the real axis we can determine by formula 6.23:
. →→
The numerator must be zero:
.
Or: → (abc formula) and .
Is is clear that must be a break away point and an entry point. As will be proved later (example 6.9), in this case where the poles are complex conjugated the complex part of the root locus is a circle with radius and center in ; see figure 6.8.
For the angles at which the branches of the root locus depart or arrive on the real axis the same rule applies as stated for the asymptotes in section 6.3.3: they divide into equal parts. In the most common cases of two departing or arriving branches of the root locus this means that the angles are and .
Matlab code for this example
% clear all variables from Workspace and close all figures.