Example H5.4

MATLAB code for example 5.4 from the book "Regeltechniek voor het HBO"

Investigation of the stability of a system

Date : 02/03/2022
Revision : 1.0

Table of Contents

Investigation of the stability of a system Assignment Solution MATLAB code for this example

Assignment

An electrical circuit with input

and output

is described by the following differential equation:

The question is: is this system stable or unstable?

Solution

Transforming the differential equation to the laplace domain gives:

The pole and zero plot is shown in figure 5.8. The sytem is stable because all poles are to the left of the imaginary axis. From a stability point of view, the zero to the right of the imaginary axis is no problem at all. Stability is solely and solely determined by thre position of the poles.

MATLAB code for this example

% clear all variables from Workspace and close all figures.

clear variables;

close all;

% Define 's' variable

s=tf('s');

% Make the transferfunction H

H=(4*s-12)/(s^3+5*s^2+12*s+8);

% Find the poles and zeros

zpk(H)

ans =

        4 (s-3)
  --------------------
  (s+1) (s^2 + 4s + 8)

Continuous-time zero/pole/gain model.

% plot the pz map

figure(101);

pzmap(H);