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z|LLv#9`@c2`7hY7zk~g6bL98%_Xfs)!SihYEz){~h*c>GFHl`}&8!SUyGno%Lrm#Cz8JS-ihkU=9DB_0KuI n_q6wy?|;#>n*WXV?qXh11{`o+0|Fuj{NMtHgF?SYEkOSd|Ab(i literal 0 HcmV?d00001 diff --git a/index.org b/index.org new file mode 100644 index 0000000..d0e88ce --- /dev/null +++ b/index.org @@ -0,0 +1,370 @@ +#+TITLE: SVD Control +:DRAWER: +#+STARTUP: overview + +#+LANGUAGE: en +#+EMAIL: dehaeze.thomas@gmail.com +#+AUTHOR: Dehaeze Thomas + +#+HTML_LINK_HOME: ../index.html +#+HTML_LINK_UP: ../index.html + +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: + +#+HTML_MATHJAX: align: center tagside: right font: TeX + +#+PROPERTY: header-args:matlab :session *MATLAB* +#+PROPERTY: header-args:matlab+ :comments org +#+PROPERTY: header-args:matlab+ :results none +#+PROPERTY: header-args:matlab+ :exports both +#+PROPERTY: header-args:matlab+ :eval no-export +#+PROPERTY: header-args:matlab+ :output-dir figs +#+PROPERTY: header-args:matlab+ :tangle no +#+PROPERTY: header-args:matlab+ :mkdirp yes + +#+PROPERTY: header-args:shell :eval no-export + +#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/tikz/org/}{config.tex}") +#+PROPERTY: header-args:latex+ :imagemagick t :fit yes +#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150 +#+PROPERTY: header-args:latex+ :imoutoptions -quality 100 +#+PROPERTY: header-args:latex+ :results raw replace :buffer no +#+PROPERTY: header-args:latex+ :eval no-export +#+PROPERTY: header-args:latex+ :exports both +#+PROPERTY: header-args:latex+ :mkdirp yes +#+PROPERTY: header-args:latex+ :output-dir figs +:END: + +* Simscape Model +** Matlab Init :noexport:ignore: +#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) + <> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes + <> +#+end_src + +** Simulink +#+begin_src matlab + open('gravimeter.slx') +#+end_src + +#+begin_src matlab + %% Name of the Simulink File + mdl = 'gravimeter'; + + %% Input/Output definition + clear io; io_i = 1; + io(io_i) = linio([mdl, '/F1'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/F2'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/F3'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Acc_side'], 1, 'openoutput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Acc_side'], 2, 'openoutput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Acc_top'], 1, 'openoutput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Acc_top'], 2, 'openoutput'); io_i = io_i + 1; + + G = linearize(mdl, io); +#+end_src + +#+begin_src matlab + freqs = logspace(-1, 2, 1000); + + figure; + for in_i = 1:3 + for out_i = 1:4 + subplot(4, 3, 3*(out_i-1)+in_i); + plot(freqs, abs(squeeze(freqresp(G(out_i,in_i)/s^2, freqs, 'Hz'))), '-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + end + end +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace + exportFig('figs/open_loop_tf.pdf', 'width', 'full', 'height', 'full'); +#+end_src + +#+name: fig:open_loop_tf +#+caption: Open Loop Transfer Function from 3 Actuators to 4 Accelerometers +#+RESULTS: +[[file:figs/open_loop_tf.png]] + +** Matlab Code +#+begin_src matlab + clc; + % close all + + g = 100000; + + w0 = 2*pi*.5; % MinusK BM1 tablle + l = 0.5; %[m] + la = 1; %[m] + h = 1.7; %[m] + ha = 1.7;% %[m] + m = 400; %[kg] + k = 15e3;%[N/m] + kv = k; + kh = 15e3; + I = 115;%[kg m^2] + % c = 0.06; + % l = 0.4719; %[m] + % la = .477; %[m] + % h = 1.8973; %[m] + % ha = 1.9060;% %[m] + % m = 98.1421; %[kg] + % k = 14512;%[N/m] + % I = 28.5372;%[kg m^2] + cv = 0.03; + ch = 0.03; + + %% System definition + [Fr, x1, z1, x2, z2, wx, wz, x12, z12, PHIwx, PHIwz,xsum,zsum,xdelta,zdelta,rot]... + = modelGeneration(m,I,k,h,ha,l,la,cv,ch,kv,kh); + + %% Bode options + P = bodeoptions; + P.FreqUnits = 'Hz'; + P.MagUnits = 'abs'; + P.MagScale = 'log'; + P.Grid = 'on'; + P.PhaseWrapping = 'on'; + P.Xlim = [1e-1,1e2]; + %P.PhaseVisible = 'off'; + w = 2*pi*logspace(-1,2,1000); + + %% curves points + % slide 4 + F_sl4 = [2e-1 4e-1 7e-1 1 2 3 5]; + Amp_sl4 = [ 1 2 4 2.5 1 7e-1 7e-1]; + F_sl4_phase = [2e-1 4e-1 7e-1 1 ]; + Phase_sl4 = (180/pi).*[0 0 -0.5 -1.7]; + + %slide 6 + F_sl6 = [2e-1 4e-1 1 2 3 5]; + Amp_sl6 = [1 1 6e-1 2e-1 3e-1 3e-1]; + F_sl6_phase = [2e-1 4e-1 1 ]; + Phase_sl6 = (180/pi).*[0 0 0 ]; + + %slide 9 + F_sl9 = [2.5e-1 4e-1 6e-1 1 1.7 2.2 3 5 10]; + Amp_sl9 = [3 6 1 5e-1 1 2 7e-1 2.5e-1 7e-2]; + Phase_sl9 = (180/pi)*[0 -1 -pi 0 -1 -1.5 -pi -pi -pi]; + + % slide 14 + F_sl14 = [ 2e-1 4e-1 6e-1 8e-1 1 2 3 5 10]; + Amp_sl14 = [9e-1 1.5 1.2 0.35 .3 1.2 .3 .1 5e-2]; + F_sl14_phase = [ 2e-1 4e-1 6e-1 8e-1 ]; + Phase_sl14 = (180/pi).*[0 0 -1.7 -2]; + + %rotation + F_rot = [1e-1 2e-1 4e-1 5e-1 7e-1 1 2 3 6.5 10 20]; + Amp_rot = [7e-8 2.2e-7 3e-7 1e-7 2e-8 9e-9 3e-8 9e-9 1e-9 4e-10 8e-11]; + + %% Plots + % %slide 3 + % figure + % loglog(Fr,abs(x2).^.5,Fr,abs(x1).^.5,Fr,abs(xsum).^.5,Fr,abs(xdelta).^.5) + % xlabel('Frequency [Hz]');ylabel('Acceleration [m/s^2/rtHz]') + % legend('Top sensor','Bottom sensor','Half sum','Half difference'); + % title('Horizontal') + % xlim([7e-2 1e1]); + + %slide 4 + figure + subplot 211 + loglog(Fr, abs(x12)./abs(x1));hold on; + loglog(F_sl4,Amp_sl4,'*'); + xlabel('Frequency [Hz]');ylabel('Amplitude [-]'); + title('X direction Top/bottom sensor'); + xlim([7e-2 1e1]); + subplot 212 + semilogx(Fr, (180/pi).*angle(x12./abs(x1)));hold on; + loglog(F_sl4_phase,Phase_sl4,'*'); + xlabel('Frequency [Hz]');ylabel('Phase [deg]'); + xlim([7e-2 1e1]); + + %slide 6 + figure + subplot 211 + loglog(Fr, abs(z12)./abs(z1));hold on; + loglog(F_sl6,Amp_sl6,'*'); + xlabel('Frequency [Hz]');ylabel('Amplitude [-]'); + title('Z direction Top/bottom sensor'); + xlim([7e-2 1e1]); + subplot 212 + semilogx(Fr, (180/pi).*angle(z12./abs(z1)));hold on; + loglog(F_sl6_phase,Phase_sl6,'*'); + xlabel('Frequency [Hz]');ylabel('Phase [deg]'); + xlim([7e-2 1e1]);ylim([-180 180]); + + % %slide 6 + % figure + % loglog(Fr,abs(z2).^.5,Fr,abs(z1).^.5,Fr,abs(zsum).^.5,Fr,abs(zdelta).^.5) + % xlabel('Frequency [Hz]');ylabel('Acceleration [m/s^2/rtHz]') + % legend('Top sensor','Bottom sensor','Half sum','Half difference'); + % title('Vertical') + % xlim([7e-2 1e1]); + + %slide 9 + figure + subplot 211 + loglog(Fr, abs(PHIwx)./abs(wx));hold on; + loglog(F_sl9,Amp_sl9,'*'); + xlabel('Frequency [Hz]');ylabel('Amplitude [-]'); + title('X direction bottom/ground sensor'); + xlim([7e-2 1e1]); + ylim([0.01 10]); + subplot 212 + semilogx(Fr, (180/pi).*angle(PHIwx./abs(wx)));hold on; + loglog(F_sl9,Phase_sl9,'*'); + xlabel('Frequency [Hz]');ylabel('Phase [deg]'); + xlim([7e-2 1e1]); + + % %slide 8 + % figure + % loglog(Fr,abs(wx).^.5,Fr,abs(x1).^.5,'-.',Fr,abs(x2).^.5,'.'); + % grid on;xlabel('Frequency [Hz]'); + % ylabel('ASD [m/s^2/rtHz]'); + % xlim([7e-2 1e1]); + % legend('Ground','Bottom sensor','Top sensor'); + % title('Horizontal'); + % + % %slide 13 + % figure + % loglog(Fr,abs(wz).^.5,Fr,abs(z1).^.5,'-.',Fr,abs(z2).^.5,'.'); + % grid on;xlabel('Frequency [Hz]'); + % ylabel('ASD [m/s^2/rtHz]'); + % xlim([7e-2 1e1]); + % legend('Ground','Bottom sensor','Top sensor'); + % title('Vertical'); + + %slide 14 + figure + subplot 211 + loglog(Fr, abs(PHIwz)./abs(wz));hold on; + loglog(F_sl14,Amp_sl14,'*'); + xlabel('Frequency [Hz]');ylabel('Amplitude [-]'); + title('Z direction bottom/ground sensor'); + xlim([7e-2 1e1]); + ylim([0.01 10]); + subplot 212 + semilogx(Fr, (180/pi).*angle(PHIwz./abs(wz)));hold on; + loglog(F_sl14_phase,Phase_sl14,'*'); + xlabel('Frequency [Hz]');ylabel('Phase [deg]'); + xlim([7e-2 1e1]); + + %rotation + figure + loglog(Fr,abs(rot).^.5./((2*pi*Fr').^2),F_rot,Amp_rot,'*'); + xlabel('Frequency [Hz]');ylabel('Rotation [rad/rtHz]') + xlim([7e-2 1e1]); +#+end_src + +** Model Generation +#+begin_src matlab + function [Fr, x1, z1, x2, z2, wx, wz, x12, z12, PHIwx, PHIwz,xsum,zsum,xdelta,zdelta,rot] = modelGeneration(m,I,k,h,ha,l,la,dampv,damph,kv,kh) + %% generation of the state space model + M = [m 0 0 + 0 m 0 + 0 0 I]; + + %Jacobian of the bottom sensor + Js1 = [1 0 h/2 + 0 1 -l/2]; + %Jacobian of the top sensor + Js2 = [1 0 -h/2 + 0 1 0]; + + %Jacobian of the actuators + Ja = [1 0 ha/2 %Left horizontal actuator + %1 0 h/2 %Right horizontal actuator + 0 1 -la/2 %Left vertical actuator + 0 1 la/2]; %Right vertical actuator + Jah = [1 0 ha/2]; + Jav = [0 1 -la/2 %Left vertical actuator + 0 1 la/2]; %Right vertical actuator + Jta = Ja'; + Jtah = Jah'; + Jtav = Jav'; + K = kv*Jtav*Jav + kh*Jtah*Jah; + C = dampv*kv*Jtav*Jav+damph*kh*Jtah*Jah; + + E = [1 0 0 + 0 1 0 + 0 0 1]; %projecting ground motion in the directions of the legs + + AA = [zeros(3) eye(3) + -M\K -M\C]; + + BB = [zeros(3,6) + M\Jta M\(k*Jta*E)]; + + CC = [[Js1;Js2] zeros(4,3); + zeros(2,6) + (Js1+Js2)./2 zeros(2,3) + (Js1-Js2)./2 zeros(2,3) + (Js1-Js2)./(2*h) zeros(2,3)]; + + DD = [zeros(4,6) + zeros(2,3) eye(2,3) + zeros(6,6)]; + + system_dec = ss(AA,BB,CC,DD); + %input = three actuators and three ground motions + %output = the bottom sensor; the top sensor; the ground motion; the half + %sum; the half difference; the rotation + + %% Injecting ground motion in the system to have the output + Fr = logspace(-2,3,1e3); + w=2*pi*Fr*1i; + %fit of the ground motion data in m/s^2/rtHz + Fr_ground_x = [0.07 0.1 0.15 0.3 0.7 0.8 0.9 1.2 5 10]; + n_ground_x1 = [4e-7 4e-7 2e-6 1e-6 5e-7 5e-7 5e-7 1e-6 1e-5 3.5e-5]; + Fr_ground_v = [0.07 0.08 0.1 0.11 0.12 0.15 0.25 0.6 0.8 1 1.2 1.6 2 6 10]; + n_ground_v1 = [7e-7 7e-7 7e-7 1e-6 1.2e-6 1.5e-6 1e-6 9e-7 7e-7 7e-7 7e-7 1e-6 2e-6 1e-5 3e-5]; + + n_ground_x = interp1(Fr_ground_x,n_ground_x1,Fr,'linear'); + n_ground_v = interp1(Fr_ground_v,n_ground_v1,Fr,'linear'); + % figure + % loglog(Fr,abs(n_ground_v),Fr_ground_v,n_ground_v1,'*'); + % xlabel('Frequency [Hz]');ylabel('ASD [m/s^2 /rtHz]'); + % return + + %converting into PSD + n_ground_x = (n_ground_x).^2; + n_ground_v = (n_ground_v).^2; + + %Injecting ground motion in the system and getting the outputs + system_dec_f = (freqresp(system_dec,abs(w))); + PHI = zeros(size(Fr,2),12,12); + for p = 1:size(Fr,2) + Sw=zeros(6,6); + Iact = zeros(3,3); + Sw(4,4) = n_ground_x(p); + Sw(5,5) = n_ground_v(p); + Sw(6,6) = n_ground_v(p); + Sw(1:3,1:3) = Iact; + PHI(p,:,:) = (system_dec_f(:,:,p))*Sw(:,:)*(system_dec_f(:,:,p))'; + end + x1 = PHI(:,1,1); + z1 = PHI(:,2,2); + x2 = PHI(:,3,3); + z2 = PHI(:,4,4); + wx = PHI(:,5,5); + wz = PHI(:,6,6); + x12 = PHI(:,1,3); + z12 = PHI(:,2,4); + PHIwx = PHI(:,1,5); + PHIwz = PHI(:,2,6); + xsum = PHI(:,7,7); + zsum = PHI(:,8,8); + xdelta = PHI(:,9,9); + zdelta = PHI(:,10,10); + rot = PHI(:,11,11); +#+end_src