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