Ajout des figures 1eres questions
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7 changed files with 29 additions and 21 deletions
43
BE_Beam.m
43
BE_Beam.m
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@ -51,28 +51,30 @@ eig_tustin3 = eig(c2d(sys, Ts3, 'tustin')) ;
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eig_zoh1 = eig(c2d(sys, Ts1, 'zoh')) ;
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eig_zoh1 = eig(c2d(sys, Ts1, 'zoh')) ;
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eig_zoh2 = eig(c2d(sys, Ts2, 'zoh')) ;
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eig_zoh2 = eig(c2d(sys, Ts2, 'zoh')) ;
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eig_zoh3 = eig(c2d(sys, Ts3, 'zoh')) ;
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eig_zoh3 = eig(c2d(sys, Ts3, 'zoh')) ;
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%%
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figure;
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Question4 = figure ;
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subplot(1,3,1) ;
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subplot(1,3,1) ;
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plot(eig_cont, 'x');
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plot(eig_cont, 'x');
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axis square;
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grid on;
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grid on;
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xline(0, 'r--');
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xline(0, 'r--');
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xlabel('Axe Réel');
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xlabel('Axe Réel');
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ylabel('Axe Imaginaire');
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ylabel('Axe Imaginaire');
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title('Pôles du système');
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title({'Valeurs propres en temps continu'});
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subplot(1,3,2);
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subplot(1,3,2);
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hold on;
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hold on;
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plot(eig_tustin1,'x', 'LineWidth',2);
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plot(eig_tustin1,'x', 'LineWidth',1);
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plot(eig_tustin2,'x', 'LineWidth',2);
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plot(eig_tustin2,'x', 'LineWidth',1);
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plot(eig_tustin3,'x', 'LineWidth',2);
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plot(eig_tustin3,'x', 'LineWidth',1);
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axis square;
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theta = linspace(0, 2*pi, 100);
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theta = linspace(0, 2*pi, 100);
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plot(cos(theta), sin(theta), 'k--', 'HandleVisibility','off');
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plot(cos(theta), sin(theta), 'k--', 'HandleVisibility','off','LineWidth',0.25);
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xlim([-1.1, 1.1]);
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xlim([-1.1, 1.1]);
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ylim([-1.1, 1.1]);
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ylim([-1.1, 1.1]);
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grid on;
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grid on;
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title('Pôles dans le plan en Z (Discret)');
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title({'Valeurs propres en temps discret',' avec la méthode de Tustin'});
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legend("Ts1", "Ts2", "Ts3");
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xlabel('Réel');
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xlabel('Réel');
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ylabel('Imaginaire');
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ylabel('Imaginaire');
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hold off;
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hold off;
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@ -82,20 +84,19 @@ hold on;
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plot(eig_zoh1,'x', 'LineWidth',1);
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plot(eig_zoh1,'x', 'LineWidth',1);
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plot(eig_zoh2,'x', 'LineWidth',1);
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plot(eig_zoh2,'x', 'LineWidth',1);
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plot(eig_zoh3,'x', 'LineWidth',1);
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plot(eig_zoh3,'x', 'LineWidth',1);
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axis square;
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legend("Eigen Values Ts1", "Eigen Values Ts2", "Eigen Values Ts3");
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legend("Ts1", "Ts2", "Ts3");
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theta = linspace(0, 2*pi, 100);
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theta = linspace(0, 2*pi, 100);
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plot(cos(theta), sin(theta), 'k--', 'HandleVisibility','off');
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plot(cos(theta), sin(theta), 'k--', 'HandleVisibility','off','LineWidth',0.25);
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xlim([-1.1, 1.1]);
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xlim([-1.1, 1.1]);
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ylim([-1.1, 1.1]);
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ylim([-1.1, 1.1]);
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grid on;
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grid on;
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title('Valeurs propres avec un bloqueur d''ordre 0 (ZOH)');
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title({'Valeurs propres en temps discret',' avec un bloqueur d''ordre 0'});
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xlabel('Réel');
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xlabel('Réel');
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ylabel('Imaginaire');
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ylabel('Imaginaire');
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hold off;
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hold off;
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% Conlsuion : On en conclut qqc.
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exportgraphics(gcf, './latex/Illustrations/Question4.pdf')
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%% Question 5
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%% Question 5
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@ -103,12 +104,14 @@ t = 0:0.01:10;
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cmd = double (t >= 1) ;
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cmd = double (t >= 1) ;
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[y, t] = lsim(sys,cmd,t) ;
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[y, t] = lsim(sys,cmd,t) ;
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figure ;
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Question5 = figure ;
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plot(t, cmd, t, y);
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plot(t, cmd, t, y);
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xlabel("Temps (s)");
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xlabel("Temps (s)");
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ylabel("Amplitude");
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ylabel("Amplitude");
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legend("u(t)", "y(t)");
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legend("u(t)", "y(t)");
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title("Simulation en boucle ouverte") ;
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title("Simulation en boucle ouverte") ;
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exportgraphics(Question5, './latex/Illustrations/Question5.pdf')
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%% Question 7
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%% Question 7
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@ -118,6 +121,7 @@ Cw = @(zeta) [zeta^2*(2*zeta^3-5*zeta^2+10)/20 ...
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zeta^4*(3*zeta-5)/60 ...
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zeta^4*(3*zeta-5)/60 ...
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0, 0, 0, 0];
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0, 0, 0, 0];
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Cw_L = Cw(L);
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Cw_L = Cw(L);
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%%
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TransientTime = [] ;
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TransientTime = [] ;
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for i = 0.01:0.01:10
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for i = 0.01:0.01:10
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@ -131,12 +135,15 @@ k = min_index * 0.01
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H = inv(Cw_L*inv(-A+B*C*k)*B)
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H = inv(Cw_L*inv(-A+B*C*k)*B)
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[y, t, x] = lsim(feedback(sys,k), H*cmd, t) ;
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[y, t, x] = lsim(feedback(sys,k), H*cmd, t) ;
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u = H*cmd'-k*y ;
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u = H*cmd'-k*y ;
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figure ;
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%%
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Question8 = figure ;
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plot(t, u, t, y, t, cmd, t, (Cw_L*x')');
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plot(t, u, t, y, t, cmd, t, (Cw_L*x')');
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xlabel("Temps (s)");
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xlabel("Temps (s)");
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ylabel("Amplitude");
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ylabel("Amplitude");
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legend("u(t)", "y(t)", "wc(t)", "w(t)");
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legend("$u(t)$", "$y(t)$", "$w_c(L,t)$", "$w(L,t)$", 'Interpreter', 'latex');
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title("Simulation du retour de sortie avec pré-gain") ;
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title("Simulation du retour de sortie avec pré-gain") ;
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exportgraphics(Question8, './latex/Illustrations/Question8.pdf')
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%% Question 9
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%% Question 9
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BIN
latex/Illustrations/Question4.pdf
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latex/Illustrations/Question4.pdf
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latex/Illustrations/Question5.pdf
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latex/Illustrations/Question5.pdf
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latex/Illustrations/Question8.pdf
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latex/Illustrations/Question8.pdf
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@ -115,10 +115,10 @@ Puis on a dans la deuxième ligne de l'équation 1 :
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\subsection{Exercice 4}
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\subsection{Exercice 4}
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\includegraphics[width=\textwidth]{Illustrations/Question4}
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\subsection{Exercice 5}
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\subsection{Exercice 5}
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\includegraphics[width=\textwidth]{Illustrations/Question5}
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\subsection{Exercice 6}
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\subsection{Exercice 6}
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@ -130,6 +130,7 @@ Puis on a dans la deuxième ligne de l'équation 1 :
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\subsection{Exercice 8}
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\subsection{Exercice 8}
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\includegraphics[width=\textwidth]{Illustrations/Question8}
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\subsection{Exercice 9}
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\subsection{Exercice 9}
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latex/main.pdf
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latex/main.pdf
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@ -8,7 +8,7 @@
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\newcommand{\firstcouverture}{
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\newcommand{\firstcouverture}{
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\parbox{\textwidth}{
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\parbox{\textwidth}{
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\sffamily % arial
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\sffamily % arial
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\textbf{Wissal GUARNI \\ Justin BOS \\ Nolan REYNIER-NOMER \\ Aleksander TABAN}\\
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\textbf{Wissal GUARNI \\ Justin BOS \\ Nolan REYNIER NOMER \\ Aleksander TABAN}\\
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Elèves Ingénieurs de l'INSA Toulouse\\
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Elèves Ingénieurs de l'INSA Toulouse\\
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Département GEI \\
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Département GEI \\
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Spécialité AE-SE \\
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Spécialité AE-SE \\
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