Example H8.2
MATLAB code for example 8.2 from the book "Regeltechniek voor het HBO"
Effect of a P-Controller on a second order process
- Date : 02/03/2022
- Revision : 1.0
Copyright (c) 2022, Studieboeken Specialist Permission is granted to copy, modify and redistribute this file, provided that this header message is retained.
Table of Contents
In figure 8.6 a second order process is controlled by a P-controller with gain 
.
.The root locus of this system for 
is shown in figure 8.7. In figure 6.13d we can see that the break away point on the real axis in this case is just in the middle of the two starting points, so 
. Substituting this value 
in the root locus equation
is shown in figure 8.7. In figure 6.13d we can see that the break away point on the real axis in this case is just in the middle of the two starting points, so . Substituting this value in the root locus equation
yields 
. For 
the poles become complex conjugated and an oscillation will occur in the transient of a step response.
the poles become complex conjugated and an oscillation will occur in the transient of a step response. For the absolute damping λ is constant and equal to .
the absolute damping λ is constant and equal to .
(this follows from 
) and 
(this follows from ). The overshoot is also increasing when .
. If we demand that the overshoot remains limited to 4%, then 
can increase until the two poles 
equal 
, because here 
, and 
.
can increase until the two poles equal , because here , and . Then the value of turns out to be 
(by substituting 
or 
in the root locus equation you can determine this). This value of means an area of proportionality of 
.
turns out to be (by substituting or in the root locus equation you can determine this). This value of means an area of proportionality of . The static behaviour of the system we can determine by substituting 
(see example 6.10) in the overall transfer function:
(see example 6.10) in the overall transfer function:
→ for 
→ 
.So the accuracy is 68% and the error 
.
.