From d07ce259e3fb186257136360c5d2286424fc3f42 Mon Sep 17 00:00:00 2001 From: jubos Date: Tue, 14 Apr 2026 18:37:00 +0200 Subject: [PATCH] =?UTF-8?q?T=C3=A9l=C3=A9verser=20les=20fichiers=20vers=20?= =?UTF-8?q?"/"?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Animation.m | 54 +++++++++++++++++++++++ BE-Beam.pdf | Bin 0 -> 2525623 bytes BE_Beam.m | 116 ++++++++++++++++++++++++++++++++++++++++++++++++++ Simulink.slx | Bin 0 -> 83207 bytes Simulink.slxc | Bin 0 -> 5131 bytes 5 files changed, 170 insertions(+) create mode 100644 Animation.m create mode 100644 BE-Beam.pdf create mode 100644 BE_Beam.m create mode 100644 Simulink.slx create mode 100644 Simulink.slxc diff --git a/Animation.m b/Animation.m new file mode 100644 index 0000000..1a8ad1a --- /dev/null +++ b/Animation.m @@ -0,0 +1,54 @@ +function Animation(x,t) + +fs=20; lw=4; ms = 30; +fst = 0.8*fs; +x0screen=50;y0screen=200;WidthScreen=1300;HeightScreen=300; +Blue = [0 0.4470 0.7410]; +Orange = [0.8500 0.3250 0.0980]; +Yellow = [0.9290 0.6940 0.1250]; +Violet = [0.4940 0.1840 0.5560]; +Green = [0.4660 0.6740 0.1880]; +Cyan = [0.3010 0.7450 0.9330]; +quality = '-r210'; + + +a = 0; +b = 1; +Cw1 = @(zeta) (zeta^2*(2*zeta^3 - 5*zeta^2 + 10))/20; +Cw2 = @(zeta) -(zeta^4*(2*zeta - 5))/20; +Cw3 = @(zeta) (zeta^3*(3*zeta^2 - 10*zeta + 10))/60; +Cw4 = @(zeta) (zeta^4*(3*zeta - 5))/60; + + +zeta_d = linspace(a,b); +w = zeros(8,length(t)); +for i = 1:length(t) + for j = 1:length(zeta_d) + Cw = [Cw1(zeta_d(j)),Cw2(zeta_d(j)),Cw3(zeta_d(j)),Cw4(zeta_d(j)),0,0,0,0]; + w(j,i) = Cw*x(:,i); + end +end + +figure +set(gcf,'units','points','position',[x0screen,y0screen,WidthScreen,HeightScreen]) +hold on +% pu = plot(zeta_d,u(:,1),'LineWidth',lw); +% pv = plot(zeta_d,v(:,1),'LineWidth',lw); +pw = plot(zeta_d,w(:,1),'LineWidth',lw*4); +legend({'$w(\zeta,t)$'},'Interpreter','latex','FontSize',fs,'Location','Northwest') +xlabel({'space $\zeta$'},'Interpreter','latex','FontSize',fs) +set(gca,'FontSize',fst) +ylim([-0.7,0.7]) +xlim([a,b]) +% pause + +for i = 1:10:length(t) + + % set(pu,'YData',u(:,i)) + % set(pv,'YData',v(:,i)) + set(pw,'YData',w(:,i)) + pause(0.0001) +end + + +end \ No newline at end of file diff --git a/BE-Beam.pdf b/BE-Beam.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d881c63da610e2e308d3d55f9d85368715a95c92 GIT binary patch literal 2525623 zcmeFZ2UJztmMw}$k6;1}sDK0m2BLs~WWg+wgiQ`2AW3ot0S_Rk2pkm*L?dC7K_o~} zqJV%(&LBxQk|n3t7oNKR-l}?4_5T0u)%(BQ-P$=Q?zPrjGmOzk?|n`VrBi2k_<4mk za(t>UZQdxrew5w%iupzfiH&@!t~SQ(d>V>Z%#95lHu9-BUU69c%^7Pu%Z+@pvequ_ z+DGwy0U=@D2d>)js_%XD?Ah%nQLh*^-j#g0RQvI_gR!GeEaJNF*D}!f zQWfTGG23WtW%Sqe_!IG>M1%gb7d~%kU}C(HPuo&e+Vv)PY@C^cZ@= z%)wsC*zTmYrH!?fv6Tb+@r`^Zt*=?zsn{48q6beIJDC|8Upg!Mx3?5PcM1H<3;x6V z;mgE(DjC>W+Dl0Mx()h>_=BURmHq0||D6Z&DcKntnHf4*+p+T>MIZfLH%0vDFuP7_ z$d_Jb*;Yh<%v|Zjj>G5n`E1|V*iEV;U1?KicxGxDuJzh2)O%6yj>^l!`&z|9%{Ms~ zJvX&Ha&yz~KlL^W9M(%bxkE|T*L&yo_xskJqxoZz?T1%wHAmffstnP*uHXWb(afef 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+Cw_L = Cw(L); + +TransientTime = [] ; +for i = 0.01:0.01:10 + TransientTime(end+1) = stepinfo(feedback(sys, i)).TransientTime ; +end +[minimum, min_index] = min(TransientTime) +k = min_index * 0.01; +lsim(feedback(sys,k), u, t) ; +H = -3 +%% +sys_CL = feedback(sys,k); +[y, tOut] = lsim(sys_CL, -3.*u, t); +% plot(t, Cw(L)*y, t, u) +eig_cont_CL = eig(sys_CL); +figure; +subplot(1,2,1) ; +plot(eig_cont_CL, 'x'); +hold off; + +subplot(1,2,2); +eig_zoh1 = eig(c2d(sys_CL, Ts1, 'zoh')) ; +eig_zoh2 = eig(c2d(sys_CL, Ts2, 'zoh')) ; +eig_zoh3 = eig(c2d(sys_CL, Ts3, 'zoh')) ; +plot(eig_zoh1,'x'); +hold on; +plot(eig_zoh3,'x'); +hold off; +%% +sys_CL_Ts = c2d(sys_CL, 10, 'zoh'); +figure +step(sys_CL_Ts) +%% +K = lqr(sys, eye(size(A)), 1) +sys_CL_lqr = ss(A-B*K, B*H, C, 0); +lsim(sys_CL_lqr, u, t); \ No newline at end of file diff --git a/Simulink.slx b/Simulink.slx new file mode 100644 index 0000000000000000000000000000000000000000..86546133e14733ffc263f854cb8020ab2371aefc GIT binary patch literal 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