Example H3.2

Determine the stepresponse in s-domain from a given pz-map

• Date : 28/07/2021
• Revision : 1.0

a) Determine response in s-domain

Determine the response in the s-domain from pz-map given in figure below:

This could be the result of where the system H1 and the input X1 are equal to:

Visualize the steps above: response of proces H1 to input:

Calculate and show the poles of

% clear all variables from Workspace and close all figures

clear variables;

close all;

% Define 's' variable

s=tf('s');

 

H1=5*(s+2)/((s+3)*(s+5));

X1=2/s^2;

Y1=X1*H1;

zpk(Y1)

ans = 10 (s+2) --------------- s^2 (s+5) (s+3) Continuous-time zero/pole/gain model.

figure(101);

pzmap(Y1);

Tsim1=1; % Simulation time in seconds

figure(102);

t1 = 0:Tsim1/100:Tsim1;

x1 = 2*t1;

% Simulate the response of system H1 to the input x1

lsimplot(H1,x1,t1);

grid on;

title('Response to an input 2*t');

b) Determine response in s-domain

Determine the response in the s-domain from pz-map given in figure below:

This could be the result of where the system H2 and the input X2 are equal to:

Visualize the steps above: response of proces H2 to input:

Calculate and show the poles of

H2=3*(s+6)/((s+1)*(s+4));

X2=5*s/(s^2+9);

Y2=X2*H2;

zpk(Y2)

ans = 15 s (s+6) --------------------- (s+4) (s+1) (s^2 + 9) Continuous-time zero/pole/gain model.

figure(103);

pzmap(Y2);

Tsim2=7; % Simulation time in seconds

figure(104);

t2 = 0:Tsim2/100:Tsim2;

x2 = 5*cos(3*t2);

% Simulate the response of system H2 to the input x2

lsimplot(H2,x2,t2);

grid on;

title('Response to an input 5*cos(3*t)');

Generate MATLAB figure(s) for usage in the book

Init create Enhanced Figures

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(X1*H1);

grid on;

% get the handle to the plot options

p=getoptions(h);

% Adjust Title

p.Title.String='PN beeld van \itY_1(s)';

p.XLim=[-6 1];

p.YLim=[-2 2];

% write the options to the figure

setoptions(h,p);

 

figure(1002);

% Give it a tag

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

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

h=lsimplot(H1,x1,t1);

grid on;

% get the handle to the plot options

p=getoptions(h);

% Adjust Title

p.Title.String='Slope response \ity_1(t)';

% Make input invisible. If this does not work

% create the figure again with this code in an m-

% script and toggle with a right mouse click in

% the figure the input signal

p.InputVisible={'off'};

p.XLim=[0 Tsim1];

p.YLim=[0 2];

% write the options to the figure

setoptions(h,p);

 

figure(1003);

% Give it a tag

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

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

h=pzplot(X2*H2);

grid on;

% get the handle to the plot options

p=getoptions(h);

% Adjust Title

p.Title.String='PN beeld van \itY_2(s)';

p.XLim=[-6 1];

p.YLim=[-2 2];

% write the options to the figure

setoptions(h,p);

 

figure(1004);

% Give it a tag

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

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

h=lsimplot(H2,x2,t2);

grid on;

% get the handle to the plot options

p=getoptions(h);

% Adjust Title

p.Title.String='Sine response \ity_2(t)';

% Make input invisible. If this does not work

% create the figure again with this code in an m-

% script and toggle with a right mouse click in

% the figure the input signal

p.InputVisible={'off'};

p.XLim=[0 Tsim2];

p.YLim=[-7 7];

% write the options to the figure

setoptions(h,p);