Reworked analysis on the static measurements

static-to-dynamic/matlab/static_ty.m

@@ -0,0 +1,96 @@
+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+% Data - Plot
+
+% First, we plot the straightness error as a function of the position (figure [[fig:raw_data_tyz]]).
+
+
+figure;
+hold on;
+for i=1:data(end, 1)
+  plot(data(data(:, 1) == i, 3), data(data(:, 1) == i, 4), '-k');
+end
+hold off;
+xlabel('Target Value [mm]'); ylabel('Error Value [$\mu m$]');
+
+
+
+% #+NAME: fig:raw_data_tyz
+% #+CAPTION: Time domain Data
+% #+RESULTS: fig:raw_data_tyz
+% [[file:figs/raw_data_tyz.png]]
+
+% Then, we compute mean value of each position, and we remove this mean value from the data.
+% The results are shown on figure [[fig:processed_data_tyz]].
+
+mean_pos = zeros(sum(data(:, 1)==1), 1);
+for i=1:sum(data(:, 1)==1)
+  mean_pos(i) = mean(data(data(:, 2)==i, 4));
+end
+
+figure;
+hold on;
+for i=1:data(end, 1)
+  filt = data(:, 1) == i;
+  plot(data(filt, 3), data(filt, 4) - mean_pos, '-k');
+end
+hold off;
+xlabel('Target Value [mm]'); ylabel('Error Value [$\mu m$]');
+
+% Translate to time domain
+% We here make the assumptions that, during a scan with the translation stage, the Z motion of the translation stage will follow the guiding error measured.
+
+% We then create a time vector $t$ from 0 to 1 second that corresponds to a typical scan, and we plot the guiding error as a function of the time on figure [[fig:time_domain_tyz]].
+
+
+t = linspace(0, 1, length(data(data(:, 1)==1, 4)));
+
+figure;
+hold on;
+plot(t, data(data(:, 1) == 1, 4) - mean_pos, '-k');
+hold off;
+xlabel('Time [s]'); ylabel('Error Value [um]');
+
+% Compute the PSD
+
+% We first compute some parameters that will be used for the PSD computation.
+
+dt = t(2)-t(1);
+
+Fs = 1/dt; % [Hz]
+
+win = hanning(ceil(1*Fs));
+
+
+
+% We remove the mean position from the data.
+
+x = data(data(:, 1) == 1, 4) - mean_pos;
+
+
+
+% And finally, we compute the power spectral density of the displacement obtained in the time domain.
+
+% The result is shown on figure [[fig:psd_tyz]].
+
+[pxx, f] = pwelch(x, win, [], [], Fs);
+
+pxx_t = zeros(length(pxx), data(end, 1));
+
+for i=1:data(end, 1)
+  x = data(data(:, 1) == i, 4) - mean_pos;
+  [pxx, f] = pwelch(x, win, [], [], Fs);
+  pxx_t(:, i) = pxx;
+end
+
+figure;
+hold on;
+plot(f, sqrt(mean(pxx_t, 2)), 'k-');
+hold off;
+xlabel('Frequency (Hz)');
+ylabel('Amplitude Spectral Density $\left[\frac{m}{\sqrt{Hz}}\right]$');
+set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');