Matlab code for example 6.2 from the book "Regeltechniek voor het HBO"
Start and end points of a root locus
Date : 02/03/2022
Revision : 1.0
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In the block diagram of figure 6.4 the transfer function equals:
and the transfer function of the total system then equals:
So the root locus equation becomes:
.
We often prefer to wtite this in so called "normaal vorm" (see formula 6.5):
.
Solutions for various values of K'
The solutions of this equation for (starting points) are of course: and .
The solutions of this equation for are: but also .
We will prove this last formally, but first of all we have to realize that two starting points always mean two end points too. That's why beside the solution there must be a second one: when , then and for we get . So here really is a solution of the root locus equation for .
From the two starting points in and one branche of the root locus will leave and end in , and the other one will leave and end somewhere infinitely far away from the origin. Later we will see where exactly.
Matlab code for this example
% clear all variables from Workspace and close all figures.