Example H3.1

Matlab code for example 3.1 from the book "Regeltechniek voor het HBO"

Determine the pz-map of a third order system given by differential equation

Date : 28/07/2021
Revision : 1.0

Table of Contents

Determine the pz-map of a third order system given by differential equation PZ map of the system Generate Matlab figure(s) for usage in the book Init create Enhanced Figures Enhance the figures

PZ map of the system

The system is defined by the following differential equation:

Transforming to the s-domain goes as follows:

Calculate and show the poles of

to check the calculations above:

% clear all variables from Workspace and close all figures
clear variables;
close all;
 
% Define 's' variable
s=tf('s');
 
% Define the transfer function of the system
H=(4*s+24)/(s^3+8*s^2+25*s);

Using the function zpk will give you the locations of the zeros, poles and gain

zpk(H)
ans =
 
       4 (s+6)
  -----------------
  s (s^2 + 8s + 25)
 
Continuous-time zero/pole/gain model.

Notice that the gain is given by the single number in the numerator. For this example it is 4. Using the function pzmap will show you the locations of the zeros, poles graphically

figure(101);

pzmap(H);

Generate Matlab figure(s) for usage in the book

Init create Enhanced Figures

Close all the earlier enhanced figures with a certain tag

EnhancedFig = findobj(0, 'Tag', 'EnhancedImage');
close(EnhancedFig);

Enhance the figures

figure1=figure(1001);

% Give it a tag

set(gcf, 'Tag','EnhancedImage');

% create the pzmap plot again but now with a figure handle

h=pzplot(H);

grid on;

% get the handle to the plot options

p=getoptions(h);

% Adjust Title

p.Title.String='PN beeld van \itH(s)';

p.XLim=[-7 1];

p.YLim=[-4 4];

% write the options to the figure

setoptions(h,p);