Analysis of the force sensor stiffness

test-bench-flexible-joints.org

@@ -1044,7 +1044,6 @@ addpath('./matlab/');
 addpath('./mat/');
 #+end_src
 
-
 *** Analysis                                                        :ignore:
 Let's load the measurement data.
 
@@ -1115,7 +1114,7 @@ exportFig('figs/force_noise_asd.pdf', 'width', 'wide', 'height', 'normal');
 [[file:figs/force_noise_asd.png]]
 
 
-** TODO Force Sensor Stiffness
+** Force Sensor Stiffness
 *** Introduction                                                    :ignore:
 
 The objective of this measurement is to estimate the stiffness of the force sensor [[file:doc/A700000007147087.pdf][FC2231-0000-0010-L]].
@@ -1157,25 +1156,56 @@ addpath('./mat/');
 Let's load the measured force as well as the measured displacement.
 #+begin_src matlab
 %% Load measurement data
-load('force_sensor_stiff_meas.mat', 't', 'F', 'd')
+load('force_sensor_stiffness_meas.mat', 't', 'F', 'd')
 #+end_src
 
+Some pre-processing is applied on the data.
 #+begin_src matlab
+%% Remove offset
+F  = F - mean(F(t > 0.5 & t < 1.0));
+
 %% Select important part of data
-F  = F( t > 1.55 & t < 4.65);
-d  = d( t > 1.55 & t < 4.65);
+F  = F( t > 4.55 & t < 7.24);
+d  = d( t > 4.55 & t < 7.24); d = d - d(1);
+t  = t( t > 4.55 & t < 7.24);
 #+end_src
 
+The linear fit is performed.
 #+begin_src matlab
 %% Linear fit
 fit_k = polyfit(F, d, 1);
 #+end_src
 
-#+begin_src matlab
-%% Force Sensor Stiffness
-fit_k(1)
+The displacement as a function of the force as well as the linear fit are shown in Figure [[fig:force_sensor_stiffness_fit]].
+#+begin_src matlab :exports none
+figure;
+hold on;
+plot(F, 1e6*d, '-', 'DisplayName', 'Raw Data');
+plot(F([1,end]), 1e6*(F([1,end])*fit_k(1) + fit_k(2)), '--', 'DisplayName', 'Line Fit');
+hold off;
+xlabel('Force [$N$]'); ylabel('Displacement [$\mu m$]');
+xlim([0,45]); ylim([0,60]);
+legend('location', 'southeast');
 #+end_src
 
+#+begin_src matlab :tangle no :exports results :results file replace
+exportFig('figs/force_sensor_stiffness_fit.pdf', 'width', 'wide', 'height', 'normal');
+#+end_src
+
+#+name: fig:force_sensor_stiffness_fit
+#+caption: Displacement as a function of the measured force
+#+RESULTS:
+[[file:figs/force_sensor_stiffness_fit.png]]
+
+And we obtain the following stiffness:
+#+begin_src matlab :results value replace :exports results
+%% Force Sensor Stiffness
+sprintf('k = %.2f [N/um]', 1e-6*1/fit_k(1));
+#+end_src
+
+#+RESULTS:
+: k = 0.76 [N/um]
+
 * Bending Stiffness Measurement
 :PROPERTIES:
 :header-args:matlab+: :tangle ./matlab/bending_stiff_meas.m