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Questions 9-10

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Nolan Reynier Nomer 2026-05-05 14:14:15 +02:00
parent f721f824b2
commit e08a04f14d
3 changed files with 47 additions and 14 deletions
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BE_Beam.m
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@ -60,8 +60,8 @@ plot(eig_cont, 'x');
axis square; axis square;
grid on; grid on;
xline(0, 'r--'); xline(0, 'r--');
xlabel('Axe Réel'); xlabel('Réel');
ylabel('Axe Imaginaire'); ylabel('Imaginaire');
title({'Valeurs propres en temps continu'}); title({'Valeurs propres en temps continu'});
subplot(1,3,2); subplot(1,3,2);
@ -88,7 +88,7 @@ plot(eig_zoh2,'x', 'LineWidth',1);
plot(eig_zoh3,'x', 'LineWidth',1); plot(eig_zoh3,'x', 'LineWidth',1);
axis square; axis square;
legend("Ts1", "Ts2", "Ts3"); legend("Ts1", "Ts2", "Ts3");
theta = linspace(0, 2*pi, 100); % theta = linspace(0, 2*pi, 100);
plot(cos(theta), sin(theta), 'k--', 'HandleVisibility','off','LineWidth',0.25); plot(cos(theta), sin(theta), 'k--', 'HandleVisibility','off','LineWidth',0.25);
xlim([-1.1, 1.1]); xlim([-1.1, 1.1]);
ylim([-1.1, 1.1]); ylim([-1.1, 1.1]);
@ -155,27 +155,60 @@ end
%% Question 9 %% Question 9
sys_CL = feedback(sys,k); sys_CL = feedback(sys,k);
[y, tOut] = lsim(sys_CL, -3.*cmd, t); % [y, tOut] = lsim(sys_CL, H.*cmd, t);
% plot(t, Cw(L)*y, t, u) % plot(t, Cw(L)*y, t, u)
eig_cont_CL = eig(sys_CL); eig_cont_CL = eig(sys_CL);
figure; Question9 = figure;
subplot(1,2,1) ; subplot(1,2,1) ;
plot(eig_cont_CL, 'x'); plot(eig_cont_CL, 'x');
hold off; axis square;
grid on;
xline(0, 'r--');
title({'Valeurs propres en temps continu'});
xlabel('Réel');
ylabel('Imaginaire');
subplot(1,2,2); subplot(1,2,2);
eig_zoh1 = eig(c2d(sys_CL, Ts1, 'zoh')) ; eig_zoh1 = eig(feedback(c2d(sys, Ts1, 'zoh'), k)) ;
eig_zoh2 = eig(c2d(sys_CL, Ts2, 'zoh')) ; eig_zoh2 = eig(feedback(c2d(sys, Ts2, 'zoh'), k)) ;
eig_zoh3 = eig(c2d(sys_CL, Ts3, 'zoh')) ; eig_zoh3 = eig(feedback(c2d(sys, Ts3, 'zoh'), k)) ;
plot(eig_zoh1,'x'); plot(eig_zoh1,'x', 'LineWidth',1);
hold on; hold on;
plot(eig_zoh3,'x'); plot(eig_zoh2,'x','LineWidth',1);
plot(eig_zoh3,'x', 'LineWidth',1);
axis square;
plot(cos(theta), sin(theta), 'k--', 'HandleVisibility','off','LineWidth',0.25);
xlim([-1.5, 1.5]);
ylim([-1.5, 1.5]);
grid on;
legend("Ts1", "Ts2", "Ts3");
title({'Valeurs propres en temps discret',' avec un bloqueur d''ordre 0'});
xlabel('Réel');
ylabel('Imaginaire');
hold off; hold off;
if SAVE
exportgraphics(Question9, './latex/Illustrations/Question9.pdf')
end
%% %%
sys_CL_Ts = c2d(sys_CL, 1, 'zoh'); sys_CL_Ts = feedback(c2d(sys, 0.037, 'zoh'),k);
figure t_d = 0:0.037:10 ;
step(sys_CL_Ts) cmd = double (t_d >= 1) ;
[y, t_d, x] = lsim(sys_CL_Ts, H*cmd, t_d) ;
u_d = H*cmd'-k*y ;
Question10 = figure ;
plot(t_d, u_d, t_d, y, t_d, cmd, t_d, (Cw_L*x')');
xlabel("Temps (s)");
ylabel("Amplitude");
legend("$u(t)$", "$y(t)$", "$w_c(L,t)$", "$w(L,t)$", 'Interpreter', 'latex');
title({'Simulation du retour de sortie avec pré-gain'},{'avec un bloqueur d''ordre 0'}) ;
if SAVE
exportgraphics(Question10, './latex/Illustrations/Question10.pdf')
end
%% Question 11 %% Question 11

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