#+end_export
#+latex: \clearpage
* Introduction
* Stepper Motors Calibration
:PROPERTIES:
:header-args:matlab+: :tangle matlab/dcm_stepper_lut.m
:END:
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** Introduction :ignore:
** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<>
#+end_src
#+begin_src matlab :tangle no :noweb yes
<>
#+end_src
#+begin_src matlab :eval no :noweb yes
<>
#+end_src
#+begin_src matlab :noweb yes
<>
#+end_src
** Schematic
** Simulation
In this section, we suppose that we are in the frame of one fast jack (all transformations are already done), and we wish to create a LUT for one fast jack.
Let's say with make a Bragg angle scan between 10deg and 60deg during 100s.
#+begin_src matlab
Fs = 10e3; % Sample Frequency [Hz]
t = 0:1/Fs:100; % Time vector [s]
theta = linspace(10, 60, length(t)); % Bragg Angle [deg]
#+end_src
The IcePAP steps are following the theoretical formula:
\begin{equation}
d_z = \frac{d_{\text{off}}}{2 \cos \theta}
\end{equation}
with $\theta$ the bragg angle and $d_{\text{off}} = 10\,mm$.
The motion to follow is then:
#+begin_src matlab
perfect_motion = 10e-3./(2*cos(theta*pi/180)); % Perfect motion [m]
#+end_src
And the IcePAP is generated those steps:
#+begin_src matlab
icepap_steps = perfect_motion; % IcePAP steps measured by Speedgoat [m]
#+end_src
#+begin_src matlab :exports none
%% Steps as a function of the bragg angle
figure;
plot(theta, icepap_steps);
xlabel('Bragg Angle [deg]'); ylabel('IcePAP Steps [m]');
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/bragg_angle_icepap_steps_idealized.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
#+name: fig:bragg_angle_icepap_steps_idealized
#+caption: IcePAP Steps as a function of the Bragg Angle
#+RESULTS:
[[file:figs/bragg_angle_icepap_steps_idealized.png]]
Then, we are measuring the motion of the Fast Jack using the Interferometer.
The motion error is larger than in reality to be angle to see it more easily.
#+begin_src matlab
motion_error = 100e-6*sin(2*pi*perfect_motion/1e-3); % Error motion [m]
measured_motion = perfect_motion + motion_error; % Measured motion of the Fast Jack [m]
#+end_src
#+begin_src matlab :exports none
%% Measured Motion and Idealized Motion
figure;
hold on;
plot(icepap_steps, measured_motion, ...
'DisplayName', 'Measured Motion');
plot(icepap_steps, perfect_motion, 'k--', ...
'DisplayName', 'Ideal Motion');
hold off;
xlabel('IcePAP Steps [m]'); ylabel('Measured Motion [m]');
legend('location', 'southeast');
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/measured_and_ideal_motion_fast_jacks.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
#+name: fig:measured_and_ideal_motion_fast_jacks
#+caption: Measured motion as a function of the IcePAP Steps
#+RESULTS:
[[file:figs/measured_and_ideal_motion_fast_jacks.png]]
Let's now compute the lookup table.
For each micrometer of the IcePAP step, another step is associated that correspond to a position closer to the wanted position.
#+begin_src matlab
%% Get range for the LUT
% We correct only in the range of tested/measured motion
lut_range = round(1e6*min(icepap_steps)):round(1e6*max(icepap_steps)); % IcePAP steps [um]
%% Initialize the LUT
lut = zeros(size(lut_range));
%% For each um in this range
for i = 1:length(lut_range)
% Get points indices where the measured motion is closed to the wanted one
close_points = measured_motion > 1e-6*lut_range(i) - 500e-9 & measured_motion < 1e-6*lut_range(i) + 500e-9;
% Get the corresponding closest IcePAP step
lut(i) = round(1e6*mean(icepap_steps(close_points))); % [um]
end
#+end_src
#+begin_src matlab :exports none
%% Generated Lookup Table
figure;
plot(lut_range, lut);
xlabel('IcePAP input step [um]'); ylabel('Lookup Table output [um]');
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/generated_lut_icepap.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
#+name: fig:generated_lut_icepap
#+caption: Generated Lookup Table
#+RESULTS:
[[file:figs/generated_lut_icepap.png]]
We can see that the LUT is *not* the motion error (Figure [[fig:lut_correct_and_motion_error]]).
#+begin_src matlab
motion_error_lut = zeros(size(lut_range));
for i = 1:length(lut_range)
% Get points indices where the icepap step is close to the wanted one
close_points = icepap_steps > 1e-6*lut_range(i) - 500e-9 & icepap_steps < 1e-6*lut_range(i) + 500e-9;
% Get the corresponding motion error
motion_error_lut(i) = lut_range(i) - 1e6*mean(measured_motion(close_points)); % [um]
end
#+end_src
#+begin_src matlab :exports none
%% Corrected motion and motion error at each step position
figure;
hold on;
plot(lut_range, lut-lut_range, ...
'DisplayName', 'Lookup Table Correction');
plot(lut_range, motion_error_lut, ...
'DisplayName', 'Motion Error');
hold off;
xlabel('IcePAP Steps [um]'); ylabel('Corrected motion [um]');
ylim([-110, 110])
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/lut_correct_and_motion_error.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
#+name: fig:lut_correct_and_motion_error
#+caption: LUT correction and motion error as a function of the IcePAP steps
#+RESULTS:
[[file:figs/lut_correct_and_motion_error.png]]
* Attocube Calibration :noexport:
* Helping Functions :noexport:
** Initialize Path
#+NAME: m-init-path
#+BEGIN_SRC matlab
%% Path for functions, data and scripts
addpath('./matlab/mat/'); % Path for data
addpath('./matlab/'); % Path for scripts
#+END_SRC
#+NAME: m-init-path-tangle
#+BEGIN_SRC matlab
%% Path for functions, data and scripts
addpath('./mat/'); % Path for data
#+END_SRC
** Initialize Simscape Model
#+NAME: m-init-simscape
#+begin_src matlab
#+end_src
** Initialize other elements
#+NAME: m-init-other
#+BEGIN_SRC matlab
%% Colors for the figures
colors = colororder;
%% Frequency Vector
freqs = logspace(1, 3, 1000);
#+END_SRC
* Bibliography :ignore:
#+latex: \printbibliography