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Schéma4.m
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Schéma4.m
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pkg load control ;
pkg load specfun ;
clear all ;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% some functions :
function Y = dirac_function(X)
%DIRAC Delta function.
% DIRAC(X) is zero for all X, except X == 0 where it is infinite.
% more comments
Y = zeros(size(X));
Y(X == 0) = 1;
endfunction;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure('Name','Schéma N° 04','NumberTitle','off');% the window title
sys = tf([0 1],[1 70]); % Transfer function of an RC circuit with L/R = 1 ms
t = -2:0.001:10;
ht = exp(-t).*(t>=0); % System impulse response
%ht = impulse(sys, t); % System impulse response
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1: le signal indicielle (échelon unité)
subplot(5,2,1);
unitstep = t>=0; % the Step function // échelon unité
plot(t,unitstep);
title('La représentation graphique du signal indicielle');
%sgtitle('Subplot Grid Title')
ylabel('x(t)');
box off;
xlim([min(t) max(t)]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2: La réponse indicielle (échelon unité)
subplot(5,2,2);
y = lsim(sys,unitstep,t); % Simulate the output of the system
plot(t,ht,'g',t,y,'r');
legend('h(t) : La réponse impulsionnelle','y(t): La sortie du système');
title('La réponse indicielle');
ylabel('y(t)');
box off;
xlim([min(t) max(t)]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3: Le Dirac
subplot(5,2,3);
plot(t,dirac_function(t));
title('La représentation graphique du Dirac');
ylabel('x(t)');
box off;
xlim([min(t) max(t)]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4: La réponse au Dirac
subplot(5,2,4);
z = (t>0 & t<0.1)/0.1;
y = lsim(sys,z,t); % Simulate the output of the system
plot(t,ht,'g',t,y,'r');
legend('h(t) : La réponse impulsionnelle','y(t): La sortie du système');
title('La réponse au Dirac');
ylabel('y(t)');
box off;
xlim([min(t) max(t)]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 5: le signal rampe
subplot(5,2,5);
ramp = t.*unitstep; % the Ramp function
plot(t,ramp)
title('La représentation graphique du signal rampe');
ylabel('x(t)');
box off;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 6: La réponse à une rampe
subplot(5,2,6);
y = lsim(sys,ramp,t); % Simulate the output of the system
plot(t,ht,'g',t,y,'r');
legend('h(t) : La réponse impulsionnelle','y(t): La sortie du système');
title('La réponse à une rampe');
ylabel('y(t)');
box off;
xlim([min(t) max(t)]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 7: le signal parabole
subplot(5,2,7);
quad = t.^2.*unitstep;% the Quad function (le signal parabole)
plot(t,quad);
title('La représentation graphique du parabole');
ylabel('x(t)');
box off;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 8: La réponse à une parabole
subplot(5,2,8);
y = lsim(sys,quad,t); % Simulate the output of the system
plot(t,ht,'g',t,y,'r');
legend('h(t) : La réponse impulsionnelle','y(t): La sortie du système');
title('La réponse à une parabole');
ylabel('y(t)');
box off;
xlim([min(t) max(t)]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 9: le signal sinusoidal
subplot(5,2,9);
sinus = sin(t).*(t>=0);% la fonction sin(x)
plot(t,sinus);
title('La représentation graphique du signal sinusoidal');
ylabel('x(t)');
box off;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 10: La réponse à une sinusoide
subplot(5,2,10);
y = lsim(sys,sinus,t); % Simulate the output of the system
plot(t,ht,'g',t,y,'r');
legend('h(t) : La réponse impulsionnelle','y(t): La sortie du système');
title('La réponse à une sinusoide');
ylabel('y(t)');
box off;
xlim([min(t) max(t)]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%