Reworked the compensation of gravity forces
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@ -34,41 +34,33 @@ In order to start the simulation at steady state in presence of gravity:
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- section [[sec:compensation]]: Then, the equilibrium position of each joint is modified in such a way that at t=0, the forces in each joints exactly compensate the forces due to gravity forces
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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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#+BEGIN_SRC matlab
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simulinkproject('../');
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#+end_src
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#+END_SRC
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#+begin_src matlab
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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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#+END_SRC
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* Initialization of the Experimental Conditions
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We don't inject any perturbations and no reference tracking.
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#+begin_src matlab
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#+BEGIN_SRC matlab
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initializeReferences();
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initializeDisturbances('enable', false);
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initializeController();
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#+end_src
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#+END_SRC
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We include the gravity and log all the signals to display.
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#+begin_src matlab
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#+BEGIN_SRC matlab
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initializeSimscapeConfiguration('gravity', true);
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initializeLoggingConfiguration('log', 'all');
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#+end_src
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#+END_SRC
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* Without compensation
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<<sec:no_compensation>>
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Let's simulate the system without any compensation of gravity forces.
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#+begin_src matlab
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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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@ -79,69 +71,19 @@ Let's simulate the system without any compensation of gravity forces.
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initializeMirror();
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initializeNanoHexapod();
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initializeSample();
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#+end_src
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#+END_SRC
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#+begin_src matlab
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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', '0.5');
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#+end_src
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#+END_SRC
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#+begin_src matlab
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#+BEGIN_SRC matlab
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sim('nass_model');
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sim_no_compensation = simout;
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#+end_src
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#+END_SRC
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And we can observe on Figure [[fig:transient_phase_gravity_no_compensation]] that there are some motion in the system.
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#+begin_src matlab :exports none
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figure;
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ax1 = subplot(2, 3, 1);
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hold on;
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plot(sim_no_compensation.Em.En.Time, sim_no_compensation.Em.En.Data(:, 1))
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hold off;
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xlabel('Time [s]');
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ylabel('Dx [m]');
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ax2 = subplot(2, 3, 2);
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hold on;
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plot(sim_no_compensation.Em.En.Time, sim_no_compensation.Em.En.Data(:, 2))
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hold off;
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xlabel('Time [s]');
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ylabel('Dy [m]');
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ax3 = subplot(2, 3, 3);
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hold on;
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plot(sim_no_compensation.Em.En.Time, sim_no_compensation.Em.En.Data(:, 3))
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hold off;
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xlabel('Time [s]');
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ylabel('Dz [m]');
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ax4 = subplot(2, 3, 4);
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hold on;
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plot(sim_no_compensation.Em.En.Time, sim_no_compensation.Em.En.Data(:, 4))
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hold off;
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xlabel('Time [s]');
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ylabel('Rx [rad]');
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ax5 = subplot(2, 3, 5);
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hold on;
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plot(sim_no_compensation.Em.En.Time, sim_no_compensation.Em.En.Data(:, 5))
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hold off;
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xlabel('Time [s]');
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ylabel('Ry [rad]');
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ax6 = subplot(2, 3, 6);
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hold on;
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plot(sim_no_compensation.Em.En.Time, sim_no_compensation.Em.En.Data(:, 6))
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hold off;
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xlabel('Time [s]');
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ylabel('Rz [rad]');
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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/transient_phase_gravity_no_compensation.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:transient_phase_gravity_no_compensation
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#+caption: Motion of the sample at the start of the simulation in presence of gravity ([[./figs/transient_phase_gravity_no_compensation.png][png]], [[./figs/transient_phase_gravity_no_compensation.pdf][pdf]])
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[[file:figs/transient_phase_gravity_no_compensation.png]]
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@ -150,7 +92,7 @@ And we can observe on Figure [[fig:transient_phase_gravity_no_compensation]] tha
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<<sec:compute_forces>>
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We here wish to simulate the system in order to compute the required force in each joint to compensate the gravity forces.
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#+begin_src matlab
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#+BEGIN_SRC matlab
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initializeGround();
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initializeGranite('type', 'init');
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initializeTy('type', 'init');
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@ -161,30 +103,30 @@ We here wish to simulate the system in order to compute the required force in ea
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initializeMirror();
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initializeNanoHexapod('type', 'init');
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initializeSample('type', 'init');
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#+end_src
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#+END_SRC
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We simulate for a short time period (all the bodies are solid, so nothing should move).
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#+begin_src matlab
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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', '0.1');
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#+end_src
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#+END_SRC
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#+begin_src matlab
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#+BEGIN_SRC matlab
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sim('nass_model');
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#+end_src
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#+END_SRC
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Verification that nothing is moving by looking at the maximum displacement of the sample:
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#+begin_src matlab :results value replace
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#+BEGIN_SRC matlab
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max(max(simout.Em.En.Data))
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#+end_src
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#+END_SRC
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#+RESULTS:
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: 1.0681e-15
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We here show the measured total force/torque applied at the location of each joint.
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#+begin_src matlab :results value table replace :tangle no :post addhdr(*this*)
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#+BEGIN_SRC matlab
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data2orgtable([Fgm 0 0 0; Ftym; Fym; Fsm], {'Granite', 'Translation Stage', 'Tilt Stage', 'Sample'}, {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'}, ' %.1e ');
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#+end_src
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#+END_SRC
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#+RESULTS:
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| | Fx | Fy | Fz | Mx | My | Mz |
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@ -194,9 +136,9 @@ We here show the measured total force/torque applied at the location of each joi
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| Tilt Stage | -7.6e-12 | 1.2e-11 | -8800.0 | 33.0 | -0.52 | 6.6e-13 |
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| Sample | -5.7e-12 | 1.3e-11 | -490.0 | -2.5e-12 | -8.1e-13 | 2.7e-13 |
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#+begin_src matlab :results value table replace :tangle no :post addhdr(*this*)
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#+BEGIN_SRC matlab
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data2orgtable([Fhm; Fnm], {'Micro-Hexapod', 'Nano-Hexapod'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}, ' %.1e ');
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#+end_src
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#+END_SRC
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#+RESULTS:
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| | F1 | F2 | F3 | F4 | F5 | F6 |
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@ -205,14 +147,14 @@ We here show the measured total force/torque applied at the location of each joi
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| Nano-Hexapod | -160.0 | -160.0 | -160.0 | -160.0 | -160.0 | -160.0 |
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We save these forces in =Foffset.mat=.
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#+begin_src matlab
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#+BEGIN_SRC matlab
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save('mat/Foffset.mat', 'Fgm', 'Ftym', 'Fym', 'Fzm', 'Fhm', 'Fnm', 'Fsm');
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#+end_src
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#+END_SRC
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* New simulation with compensation of gravity forces
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<<sec:compensation>>
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We now initialize the stages with the option =Foffset=.
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#+begin_src matlab
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#+BEGIN_SRC matlab
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initializeGround();
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initializeGranite('Foffset', true);
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initializeTy('Foffset', true);
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@ -223,79 +165,20 @@ We now initialize the stages with the option =Foffset=.
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initializeMirror();
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initializeNanoHexapod('Foffset', true);
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initializeSample('Foffset', true);
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#+end_src
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#+END_SRC
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And we simulate the system for 0.5 seconds.
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#+begin_src matlab
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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', '0.5');
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#+end_src
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#+END_SRC
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#+begin_src matlab
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#+BEGIN_SRC matlab
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sim('nass_model');
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sim_compensation = simout;
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#+end_src
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#+END_SRC
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Verification that nothing is moving
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#+begin_src matlab :exports none
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figure;
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ax1 = subplot(2, 3, 1);
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hold on;
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plot(sim_compensation.Em.En.Time, sim_compensation.Em.En.Data(:, 1))
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plot(sim_no_compensation.Em.En.Time, sim_no_compensation.Em.En.Data(:, 1))
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hold off;
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xlabel('Time [s]');
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ylabel('Dx [m]');
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ax2 = subplot(2, 3, 2);
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hold on;
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plot(sim_compensation.Em.En.Time, sim_compensation.Em.En.Data(:, 2))
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plot(sim_no_compensation.Em.En.Time, sim_no_compensation.Em.En.Data(:, 2))
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hold off;
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xlabel('Time [s]');
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ylabel('Dy [m]');
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ax3 = subplot(2, 3, 3);
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hold on;
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plot(sim_compensation.Em.En.Time, sim_compensation.Em.En.Data(:, 3))
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plot(sim_no_compensation.Em.En.Time, sim_no_compensation.Em.En.Data(:, 3))
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hold off;
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xlabel('Time [s]');
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ylabel('Dz [m]');
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ax4 = subplot(2, 3, 4);
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hold on;
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plot(sim_compensation.Em.En.Time, sim_compensation.Em.En.Data(:, 4))
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plot(sim_no_compensation.Em.En.Time, sim_no_compensation.Em.En.Data(:, 4))
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hold off;
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xlabel('Time [s]');
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ylabel('Rx [rad]');
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ax5 = subplot(2, 3, 5);
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hold on;
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plot(sim_compensation.Em.En.Time, sim_compensation.Em.En.Data(:, 5))
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plot(sim_no_compensation.Em.En.Time, sim_no_compensation.Em.En.Data(:, 5))
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hold off;
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xlabel('Time [s]');
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ylabel('Ry [rad]');
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ax6 = subplot(2, 3, 6);
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hold on;
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plot(sim_compensation.Em.En.Time, sim_compensation.Em.En.Data(:, 6))
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plot(sim_no_compensation.Em.En.Time, sim_no_compensation.Em.En.Data(:, 6))
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hold off;
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xlabel('Time [s]');
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ylabel('Rz [rad]');
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linkaxes([ax1,ax2,ax3,ax4,ax5,ax6],'x');
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xlim([sim_compensation.Em.En.Time(1), sim_compensation.Em.En.Time(end)])
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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/transient_phase_gravity_compensation.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:transient_phase_gravity_compensation
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#+caption: Motion of the sample at the start of the simulation in presence of gravity when compensating the gravity forces ([[./figs/transient_phase_gravity_compensation.png][png]], [[./figs/transient_phase_gravity_compensation.pdf][pdf]])
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[[file:figs/transient_phase_gravity_compensation.png]]
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