576 lines
19 KiB
Org Mode
576 lines
19 KiB
Org Mode
#+TITLE: Tomography Experiment
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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 matlab/tomo_exp.m
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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/thesis/latex/}{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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* Introduction :ignore:
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The goal here is to simulate some scientific experiments with the tuned Simscape model when no control is applied to the nano-hexapod.
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This has several goals:
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- Validate the model
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- Estimate the expected error motion for the experiments
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- Estimate the stroke that we may need for the nano-hexapod
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The document in organized as follow:
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- In section [[sec:simscape_model]] the Simscape model is initialized
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- In section [[sec:tomo_no_dist]] a tomography experiment is performed where the sample is aligned with the rotation axis. No disturbance is included
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- In section [[sec:tomo_dist]], the same is done but with disturbance included
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- In section [[sec:tomo_hexa_trans]] the micro-hexapod translate the sample such that its center of mass is no longer aligned with the rotation axis. No disturbance is included
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- In section [[sec:ty_scans]], scans with the translation stage are simulated with no perturbation included
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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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#+begin_src matlab :tangle no
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simulinkproject('../');
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#+end_src
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* Simscape Model
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<<sec:simscape_model>>
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#+begin_src matlab
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open('nass_model.slx');
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#+end_src
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We load the shared simulink configuration and we set the =StopTime=.
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#+begin_src matlab
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load('mat/conf_simulink.mat');
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set_param(conf_simulink, 'StopTime', '5');
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#+end_src
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We first initialize all the stages.
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#+begin_src matlab
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initializeGround();
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initializeGranite();
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initializeTy();
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initializeRy();
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initializeRz();
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initializeMicroHexapod();
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initializeAxisc();
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initializeMirror();
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initializeNanoHexapod('actuator', 'piezo');
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initializeSample('mass', 1);
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#+end_src
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We initialize the reference path for all the stages.
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All stage is set to its zero position except the Spindle which is rotating at 60rpm.
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#+begin_src matlab
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initializeReferences('Rz_type', 'rotating', 'Rz_period', 1);
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#+end_src
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* Tomography Experiment with no disturbances
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<<sec:tomo_no_dist>>
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** Introduction :ignore:
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** Simulation Setup
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And we initialize the disturbances to be equal to zero.
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#+begin_src matlab
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initializeDisturbances(...
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'Dwx', false, ... % Ground Motion - X direction
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'Dwy', false, ... % Ground Motion - Y direction
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'Dwz', false, ... % Ground Motion - Z direction
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'Fty_x', false, ... % Translation Stage - X direction
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'Fty_z', false, ... % Translation Stage - Z direction
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'Frz_z', false ... % Spindle - Z direction
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);
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#+end_src
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We simulate the model.
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#+begin_src matlab
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sim('nass_model');
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#+end_src
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And we save the obtained data.
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#+begin_src matlab
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tomo_align_no_dist = struct('t', t, 'MTr', MTr);
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save('experiment_tomography/mat/experiment.mat', 'tomo_align_no_dist', '-append');
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#+end_src
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** Analysis
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#+begin_src matlab
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load('experiment_tomography/mat/experiment.mat', 'tomo_align_no_dist');
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t = tomo_align_no_dist.t;
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MTr = tomo_align_no_dist.MTr;
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#+end_src
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#+begin_src matlab
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Edx = squeeze(MTr(1, 4, :));
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Edy = squeeze(MTr(2, 4, :));
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Edz = squeeze(MTr(3, 4, :));
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% The angles obtained are u-v-w Euler angles (rotations in the moving frame)
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Ery = atan2( squeeze(MTr(1, 3, :)), squeeze(sqrt(MTr(1, 1, :).^2 + MTr(1, 2, :).^2)));
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Erx = atan2(-squeeze(MTr(2, 3, :))./cos(Ery), squeeze(MTr(3, 3, :))./cos(Ery));
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Erz = atan2(-squeeze(MTr(1, 2, :))./cos(Ery), squeeze(MTr(1, 1, :))./cos(Ery));
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#+end_src
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#+begin_src matlab :exports none
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figure;
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ax1 = subplot(1, 3, 1);
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plot(t, Edx, 'DisplayName', '$\epsilon_{x}$')
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ylabel('Displacement [m]');
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legend('location', 'northeast');
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ax2 = subplot(1, 3, 2);
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plot(t, Edy, 'DisplayName', '$\epsilon_{y}$')
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xlabel('Time [s]');
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legend('location', 'northeast');
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ax3 = subplot(1, 3, 3);
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plot(t, Edz, 'DisplayName', '$\epsilon_{z}$')
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legend('location', 'northeast');
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linkaxes([ax1,ax2,ax3],'x');
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xlim([2, inf]);
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#+end_src
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#+HEADER: :tangle no :exports results :results none :noweb yes
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#+begin_src matlab :var filepath="figs/exp_tomo_without_dist_trans.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:exp_tomo_without_dist_trans
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#+CAPTION: X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances ([[./figs/exp_tomo_without_dist_trans.png][png]], [[./figs/exp_tomo_without_dist_trans.pdf][pdf]])
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[[file:figs/exp_tomo_without_dist_trans.png]]
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#+begin_src matlab :exports none
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figure;
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ax1 = subplot(1, 3, 1);
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plot(t, Erx, 'DisplayName', '$\epsilon_{\theta x}$')
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ylabel('Rotation [rad]');
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legend('location', 'northeast');
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ax2 = subplot(1, 3, 2);
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plot(t, Ery, 'DisplayName', '$\epsilon_{\theta y}$')
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xlabel('Time [s]');
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legend('location', 'northeast');
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ax3 = subplot(1, 3, 3);
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plot(t, Erz, 'DisplayName', '$\epsilon_{\theta z}$')
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legend('location', 'northeast');
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linkaxes([ax1,ax2,ax3],'x');
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xlim([2, inf]);
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#+end_src
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#+HEADER: :tangle no :exports results :results none :noweb yes
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#+begin_src matlab :var filepath="figs/exp_tomo_without_dist_rot.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:exp_tomo_without_dist_rot
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#+CAPTION: X-Y-Z rotations of the sample w.r.t. granite when performing tomography experiment with no disturbances ([[./figs/exp_tomo_without_dist_rot.png][png]], [[./figs/exp_tomo_without_dist_rot.pdf][pdf]])
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[[file:figs/exp_tomo_without_dist_rot.png]]
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** Conclusion
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#+begin_important
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When everything is aligned, the resulting error motion is very small (nm range) and is quite negligible with respect to the error when disturbances are included.
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This residual error motion probably comes from a small misalignment somewhere.
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#+end_important
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* Tomography Experiment with included perturbations
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<<sec:tomo_dist>>
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** Introduction :ignore:
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** Simulation Setup
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We now activate the disturbances.
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#+begin_src matlab
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initializeDisturbances(...
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'Dwx', true, ... % Ground Motion - X direction
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'Dwy', true, ... % Ground Motion - Y direction
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'Dwz', true, ... % Ground Motion - Z direction
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'Fty_x', true, ... % Translation Stage - X direction
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'Fty_z', true, ... % Translation Stage - Z direction
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'Frz_z', true ... % Spindle - Z direction
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);
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#+end_src
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We simulate the model.
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#+begin_src matlab
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sim('nass_model');
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#+end_src
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And we save the obtained data.
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#+begin_src matlab
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tomo_align_dist = struct('t', t, 'MTr', MTr);
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save('experiment_tomography/mat/experiment.mat', 'tomo_align_dist', '-append');
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#+end_src
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** Analysis
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#+begin_src matlab
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load('experiment_tomography/mat/experiment.mat', 'tomo_align_dist');
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t = tomo_align_dist.t;
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MTr = tomo_align_dist.MTr;
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#+end_src
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#+begin_src matlab
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Edx = squeeze(MTr(1, 4, :));
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Edy = squeeze(MTr(2, 4, :));
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Edz = squeeze(MTr(3, 4, :));
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% The angles obtained are u-v-w Euler angles (rotations in the moving frame)
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Ery = atan2( squeeze(MTr(1, 3, :)), squeeze(sqrt(MTr(1, 1, :).^2 + MTr(1, 2, :).^2)));
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Erx = atan2(-squeeze(MTr(2, 3, :))./cos(Ery), squeeze(MTr(3, 3, :))./cos(Ery));
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Erz = atan2(-squeeze(MTr(1, 2, :))./cos(Ery), squeeze(MTr(1, 1, :))./cos(Ery));
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#+end_src
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#+begin_src matlab :exports none
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figure;
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ax1 = subplot(1, 3, 1);
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plot(t, Edx, 'DisplayName', '$\epsilon_{x}$')
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ylabel('Displacement [m]');
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legend('location', 'northeast');
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ax2 = subplot(1, 3, 2);
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plot(t, Edy, 'DisplayName', '$\epsilon_{y}$')
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xlabel('Time [s]');
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legend('location', 'northeast');
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ax3 = subplot(1, 3, 3);
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plot(t, Edz, 'DisplayName', '$\epsilon_{z}$')
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legend('location', 'northeast');
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linkaxes([ax1,ax2,ax3],'x');
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xlim([2, inf]);
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#+end_src
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#+HEADER: :tangle no :exports results :results none :noweb yes
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#+begin_src matlab :var filepath="figs/exp_tomo_dist_trans.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:exp_tomo_dist_trans
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#+CAPTION: X-Y-Z translation of the sample w.r.t. the granite when performing tomography experiment with disturbances ([[./figs/exp_tomo_dist_trans.png][png]], [[./figs/exp_tomo_dist_trans.pdf][pdf]])
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[[file:figs/exp_tomo_dist_trans.png]]
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#+begin_src matlab :exports none
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figure;
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ax1 = subplot(1, 3, 1);
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plot(t, Erx, 'DisplayName', '$\epsilon_{\theta x}$')
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ylabel('Rotation [rad]');
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legend('location', 'northeast');
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ax2 = subplot(1, 3, 2);
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plot(t, Ery, 'DisplayName', '$\epsilon_{\theta y}$')
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xlabel('Time [s]');
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legend('location', 'northeast');
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ax3 = subplot(1, 3, 3);
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plot(t, Erz, 'DisplayName', '$\epsilon_{\theta z}$')
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legend('location', 'northeast');
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linkaxes([ax1,ax2,ax3],'x');
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xlim([2, inf]);
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#+end_src
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#+HEADER: :tangle no :exports results :results none :noweb yes
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#+begin_src matlab :var filepath="figs/exp_tomo_dist_rot.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:exp_tomo_dist_rot
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#+CAPTION: X-Y-Z rotations of the sample w.r.t. the granite when performing tomography experiment with disturbances ([[./figs/exp_tomo_dist_rot.png][png]], [[./figs/exp_tomo_dist_rot.pdf][pdf]])
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[[file:figs/exp_tomo_dist_rot.png]]
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** Conclusion
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#+begin_important
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Error motion is what expected from the disturbance measurements.
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#+end_important
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* Tomography when the micro-hexapod is not centered
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<<sec:tomo_hexa_trans>>
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** Introduction :ignore:
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** Simulation Setup
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We first set the wanted translation of the Micro Hexapod.
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#+begin_src matlab
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P_micro_hexapod = [0.01; 0; 0]; % [m]
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#+end_src
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We initialize the reference path.
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#+begin_src matlab
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initializeReferences('Dh_pos', [P_micro_hexapod; 0; 0; 0], 'Rz_type', 'rotating', 'Rz_period', 1);
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#+end_src
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We initialize the stages.
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#+begin_src matlab
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initializeMicroHexapod('AP', P_micro_hexapod);
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#+end_src
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And we initialize the disturbances to zero.
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#+begin_src matlab
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initializeDisturbances(...
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'Dwx', false, ... % Ground Motion - X direction
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'Dwy', false, ... % Ground Motion - Y direction
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'Dwz', false, ... % Ground Motion - Z direction
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'Fty_x', false, ... % Translation Stage - X direction
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'Fty_z', false, ... % Translation Stage - Z direction
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'Frz_z', false ... % Spindle - Z direction
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);
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#+end_src
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We simulate the model.
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#+begin_src matlab
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sim('nass_model');
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#+end_src
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And we save the obtained data.
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#+begin_src matlab
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tomo_not_align = struct('t', t, 'MTr', MTr);
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save('experiment_tomography/mat/experiment.mat', 'tomo_not_align', '-append');
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#+end_src
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** Analysis
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#+begin_src matlab
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load('experiment_tomography/mat/experiment.mat', 'tomo_not_align');
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t = tomo_not_align.t;
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MTr = tomo_not_align.MTr;
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#+end_src
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#+begin_src matlab
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Edx = squeeze(MTr(1, 4, :));
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Edy = squeeze(MTr(2, 4, :));
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Edz = squeeze(MTr(3, 4, :));
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% The angles obtained are u-v-w Euler angles (rotations in the moving frame)
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Ery = atan2( squeeze(MTr(1, 3, :)), squeeze(sqrt(MTr(1, 1, :).^2 + MTr(1, 2, :).^2)));
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Erx = atan2(-squeeze(MTr(2, 3, :))./cos(Ery), squeeze(MTr(3, 3, :))./cos(Ery));
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Erz = atan2(-squeeze(MTr(1, 2, :))./cos(Ery), squeeze(MTr(1, 1, :))./cos(Ery));
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#+end_src
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#+begin_src matlab :exports none
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figure;
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ax1 = subplot(1, 3, 1);
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plot(t, Edx, 'DisplayName', '$\epsilon_{x}$')
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ylabel('Displacement [m]');
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legend('location', 'northeast');
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ax2 = subplot(1, 3, 2);
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plot(t, Edy, 'DisplayName', '$\epsilon_{y}$')
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xlabel('Time [s]');
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legend('location', 'northeast');
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ax3 = subplot(1, 3, 3);
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plot(t, Edz, 'DisplayName', '$\epsilon_{z}$')
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legend('location', 'northeast');
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linkaxes([ax1,ax2,ax3],'x');
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xlim([2, inf]);
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#+end_src
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#+HEADER: :tangle no :exports results :results none :noweb yes
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#+begin_src matlab :var filepath="figs/exp_tomo_offset_trans.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:exp_tomo_offset_trans
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#+CAPTION: X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances ([[./figs/exp_tomo_offset_trans.png][png]], [[./figs/exp_tomo_offset_trans.pdf][pdf]])
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[[file:figs/exp_tomo_offset_trans.png]]
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#+begin_src matlab :exports none
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figure;
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ax1 = subplot(1, 3, 1);
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plot(t, Erx, 'DisplayName', '$\epsilon_{\theta x}$')
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ylabel('Rotation [rad]');
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legend('location', 'northeast');
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ax2 = subplot(1, 3, 2);
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plot(t, Ery, 'DisplayName', '$\epsilon_{\theta y}$')
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xlabel('Time [s]');
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legend('location', 'northeast');
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ax3 = subplot(1, 3, 3);
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plot(t, Erz, 'DisplayName', '$\epsilon_{\theta z}$')
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legend('location', 'northeast');
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linkaxes([ax1,ax2,ax3],'x');
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xlim([2, inf]);
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#+end_src
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#+HEADER: :tangle no :exports results :results none :noweb yes
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#+begin_src matlab :var filepath="figs/exp_tomo_offset_rot.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
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|
<<plt-matlab>>
|
|
#+end_src
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|
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#+NAME: fig:exp_tomo_offset_rot
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|
#+CAPTION: X-Y-Z rotations of the sample w.r.t. granite when performing tomography experiment with no disturbances ([[./figs/exp_tomo_offset_rot.png][png]], [[./figs/exp_tomo_offset_rot.pdf][pdf]])
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[[file:figs/exp_tomo_offset_rot.png]]
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|
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** Conclusion
|
|
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#+begin_important
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|
The main motions are translations in the X direction of the mobile platform (corresponds to the eccentricity of the micro-hexapod) and rotations along the rotating Y axis.
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|
#+end_important
|
|
|
|
* Raster Scans with the translation stage
|
|
<<sec:ty_scans>>
|
|
** Introduction :ignore:
|
|
|
|
** Simulation Setup
|
|
We set the reference path.
|
|
#+begin_src matlab
|
|
initializeReferences('Dy_type', 'triangular', 'Dy_amplitude', 10e-3, 'Dy_period', 1);
|
|
#+end_src
|
|
|
|
We initialize the stages.
|
|
#+begin_src matlab
|
|
initializeGround();
|
|
initializeGranite();
|
|
initializeTy();
|
|
initializeRy();
|
|
initializeRz();
|
|
initializeMicroHexapod();
|
|
initializeAxisc();
|
|
initializeMirror();
|
|
initializeNanoHexapod('actuator', 'piezo');
|
|
initializeSample('mass', 1);
|
|
#+end_src
|
|
|
|
And we initialize the disturbances to zero.
|
|
#+begin_src matlab
|
|
initializeDisturbances(...
|
|
'Dwx', false, ... % Ground Motion - X direction
|
|
'Dwy', false, ... % Ground Motion - Y direction
|
|
'Dwz', false, ... % Ground Motion - Z direction
|
|
'Fty_x', false, ... % Translation Stage - X direction
|
|
'Fty_z', false, ... % Translation Stage - Z direction
|
|
'Frz_z', false ... % Spindle - Z direction
|
|
);
|
|
#+end_src
|
|
|
|
We simulate the model.
|
|
#+begin_src matlab
|
|
sim('nass_model');
|
|
#+end_src
|
|
|
|
And we save the obtained data.
|
|
#+begin_src matlab
|
|
ty_scan = struct('t', t, 'MTr', MTr);
|
|
save('experiment_tomography/mat/experiment.mat', 'ty_scan', '-append');
|
|
#+end_src
|
|
|
|
** Analysis
|
|
#+begin_src matlab
|
|
load('experiment_tomography/mat/experiment.mat', 'ty_scan');
|
|
t = ty_scan.t;
|
|
MTr = ty_scan.MTr;
|
|
#+end_src
|
|
|
|
#+begin_src matlab
|
|
Edx = squeeze(MTr(1, 4, :));
|
|
Edy = squeeze(MTr(2, 4, :));
|
|
Edz = squeeze(MTr(3, 4, :));
|
|
% The angles obtained are u-v-w Euler angles (rotations in the moving frame)
|
|
Ery = atan2( squeeze(MTr(1, 3, :)), squeeze(sqrt(MTr(1, 1, :).^2 + MTr(1, 2, :).^2)));
|
|
Erx = atan2(-squeeze(MTr(2, 3, :))./cos(Ery), squeeze(MTr(3, 3, :))./cos(Ery));
|
|
Erz = atan2(-squeeze(MTr(1, 2, :))./cos(Ery), squeeze(MTr(1, 1, :))./cos(Ery));
|
|
#+end_src
|
|
|
|
#+begin_src matlab :exports none
|
|
figure;
|
|
ax1 = subplot(1, 3, 1);
|
|
plot(t, Edx, 'DisplayName', '$\epsilon_{x}$')
|
|
ylabel('Displacement [m]');
|
|
legend('location', 'northeast');
|
|
|
|
ax2 = subplot(1, 3, 2);
|
|
plot(t, Edy, 'DisplayName', '$\epsilon_{y}$')
|
|
xlabel('Time [s]');
|
|
legend('location', 'northeast');
|
|
|
|
ax3 = subplot(1, 3, 3);
|
|
plot(t, Edz, 'DisplayName', '$\epsilon_{z}$')
|
|
legend('location', 'northeast');
|
|
|
|
linkaxes([ax1,ax2,ax3],'x');
|
|
xlim([2, inf]);
|
|
#+end_src
|
|
|
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
|
#+begin_src matlab :var filepath="figs/exp_ty_scan_trans.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
|
|
<<plt-matlab>>
|
|
#+end_src
|
|
|
|
#+NAME: fig:exp_ty_scan_trans
|
|
#+CAPTION: X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances ([[./figs/exp_ty_scan_trans.png][png]], [[./figs/exp_ty_scan_trans.pdf][pdf]])
|
|
[[file:figs/exp_ty_scan_trans.png]]
|
|
|
|
#+begin_src matlab :exports none
|
|
figure;
|
|
ax1 = subplot(1, 3, 1);
|
|
plot(t, Erx, 'DisplayName', '$\epsilon_{\theta x}$')
|
|
ylabel('Rotation [rad]');
|
|
legend('location', 'northeast');
|
|
|
|
ax2 = subplot(1, 3, 2);
|
|
plot(t, Ery, 'DisplayName', '$\epsilon_{\theta y}$')
|
|
xlabel('Time [s]');
|
|
legend('location', 'northeast');
|
|
|
|
ax3 = subplot(1, 3, 3);
|
|
plot(t, Erz, 'DisplayName', '$\epsilon_{\theta z}$')
|
|
legend('location', 'northeast');
|
|
|
|
linkaxes([ax1,ax2,ax3],'x');
|
|
xlim([2, inf]);
|
|
#+end_src
|
|
|
|
#+HEADER: :tangle no :exports results :results none :noweb yes
|
|
#+begin_src matlab :var filepath="figs/exp_ty_scan_rot.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
|
|
<<plt-matlab>>
|
|
#+end_src
|
|
|
|
#+NAME: fig:exp_ty_scan_rot
|
|
#+CAPTION: X-Y-Z rotations of the sample w.r.t. granite when performing tomography experiment with no disturbances ([[./figs/exp_ty_scan_rot.png][png]], [[./figs/exp_ty_scan_rot.pdf][pdf]])
|
|
[[file:figs/exp_ty_scan_rot.png]]
|
|
|
|
** Conclusion
|
|
|
|
#+begin_important
|
|
This is logic that the main error moving is translation along the Y axis and rotation along the X axis.
|
|
In order to reduce the errors, we can make a smoother reference path for the translation stage.
|
|
#+end_important
|