1 Measurement description
+1 Measurement description
Setup: @@ -310,7 +310,7 @@ The scans are done with the ELMO software.
-The North of the Geophones corresponds to the +Y direction and the East of the Geophones to the +X direction (see figure 1). +The North of the Geophones corresponds to the +Y direction and the East of the Geophones to the +X direction (see figure 1).
@@ -394,7 +394,7 @@ Each of the measurement mat file contains one data arr
-
Figure 1: Picture of the experimental setup
@@ -402,11 +402,11 @@ Each of the measurementmat file contains one data arr
2 Measurement Analysis
+2 Measurement Analysis
@@ -416,8 +416,8 @@ All the files (data and Matlab scripts) are accessible
-
We convert the measured voltage to velocity using the function
+We plot the measured velocity of the marble and sample in the vertical direction (figure 2) and in the X direction (figure 3).
+
+We also integrate the relative velocity to obtain the relative displacement (figure 4 in the X direction and figure 5 in the Z direction).
+ Figure 2: Z velocity of the sample and marble when scanning with the translation stage Figure 3: Z velocity of the sample and marble when scanning with the translation stage - Zoom Figure 4: Velocity of the sample and marble in the east direction when scanning with the translation stage Figure 3: Velocity of the sample and marble in the east direction when scanning with the translation stage Figure 5: Velocity of the sample and marble in the east direction when scanning with the translation stage - Zoom Figure 4: X relative displacement of the sample with respect to the marble Figure 5: Z relative disp of the sample with respect to the marble
We get the typical ground velocity to compare with the velocities measured.
@@ -547,19 +570,30 @@ First for the geophone located on the marble
And for the geophone located at the sample position.
+And finally for the relative velocity between the sample and the marble.
+
And we plot the ASD of the measured velocities:
Figure 6: Amplitude spectral density of the measured velocities corresponding to the geophone in the east direction located on the marble when the translation stage is OFF and when it is scanning at 1Hz Figure 7: Amplitude spectral density of the measured velocities corresponding to the geophone in the east direction located at the sample location when the translation stage is OFF and when it is scanning at 1Hz Figure 8: Amplitude spectral density of the measure velocity corresponding to the geophone in the vertical direction located on the granite and at the sample location when the translation stage is scanning at 1Hz Figure 9: Amplitude spectral density of the measured relative velocity in the X direction
Let's compute the transfer function for the marble velocity in the east direction to the sample velocity in the east direction.
-We first plot the time domain motions when every stage is off (figure 9).
+We first plot the time domain motions when every stage is off (figure 10).
Figure 9: Velocity in the east direction of the marble and sample when all the stages are OFF Figure 10: Velocity in the east direction of the marble and sample when all the stages are OFF Figure 10: Estimation of the transfer function from marble velocity in the east direction to sample velocity in the east direction Figure 11: Estimation of the transfer function from marble velocity in the east direction to sample velocity in the east direction
The position of the translation and current flowing in its actuator are measured using the elmo software and saved as an csv file.
Let's look at at the start of the csv file.
@@ -720,13 +776,13 @@ We then load this
We plot the position of the translation stage measured by the encoders.
There is 200000 encoder count for each mm, we then divide by 200000 to obtain mm.
-The result is shown on figure 11.
+The result is shown on figure 12.
Figure 11: Y position of the translation stage measured by the encoders Figure 12: Y position of the translation stage measured by the encoders Figure 12: Y position of the translation stage measured by the encoders - Zoom Figure 13: Y position of the translation stage measured by the encoders - Zoom
-We also plot the current as function of the time on figure 13.
+We also plot the current as function of the time on figure 14.
Figure 13: Current going through the actuator of the translation stage Figure 14: Current going through the actuator of the translation stage Figure 14: Current going through the actuator of the translation stage - Zoom Figure 15: Current going through the actuator of the translation stage - Zoom Created: 2019-05-15 mer. 14:37 Created: 2019-05-15 mer. 16:352.1 Load data
+2.1 Load data
z_ty = load('mat/data_040.mat', 'data'); z_ty = z_ty.data;
@@ -428,8 +428,8 @@ e_of = load(
-
2.2 Voltage to Velocity
+2.2 Voltage to Velocity
voltageToVelocityL22 (accessible here).
@@ -448,9 +448,17 @@ e_of(
2.3 Time domain plots
+2.3 Time domain plots
figure;
hold on;
@@ -458,26 +466,18 @@ plot(z_ty(z_ty(:, 3), z_ty(:, 2), 'DisplayName', 'Sample - Z');
hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
-xlim([0, 100]);
+xlim([0, 2]);
legend('Location', 'northeast');
-figure;
hold on;
@@ -485,29 +485,52 @@ plot(e_ty(e_ty(:, 3), e_ty(:, 2), 'DisplayName', 'Sample - X');
hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
-xlim([0, 100]);
+xlim([0, 2]);
legend('Location', 'northeast');
figure;
+plot(e_ty(:, 3), 1e6*lsim(1/s, e_ty(:, 2)-e_ty(:, 1), e_ty(:, 3)));
+xlabel('Time [s]'); ylabel('X Relative Displacement [$\mu m$]');
+xlim([0, 2]);
+
+
figure;
+plot(z_ty(:, 3), 1e6*lsim(1/s, z_ty(:, 2)-z_ty(:, 1), z_ty(:, 3)));
+xlabel('Time [s]'); ylabel('Z Relative Displacement [$\mu m$]');
+xlim([0, 2]);
+
+
+2.4 Frequency Domain analysis
+2.4 Frequency Domain analysis
[pxz_ty_s, f] = pwelch(z_ty(:, 2), win, [], [], Fs);
+
[pxz_ty_s, ~] = pwelch(z_ty(:, 2), win, [], [], Fs);
[pxe_ty_s, ~] = pwelch(e_ty(:, 2), win, [], [], Fs);
[pxe_of_s, ~] = pwelch(e_of(:, 2), win, [], [], Fs);
[pxz_ty_r, ~] = pwelch(z_ty(:, 2)-z_ty(:, 1), win, [], [], Fs);
+[pxe_ty_r, ~] = pwelch(e_ty(:, 2)-e_ty(:, 1), win, [], [], Fs);
+[pxe_of_r, ~] = pwelch(e_of(:, 2)-e_of(:, 1), win, [], [], Fs);
+
+
-
figure;
+hold on;
+plot(f, sqrt(pxe_of_r), 'DisplayName', 'Ty OFF - Relative - E');
+plot(f, sqrt(pxe_ty_r), 'DisplayName', 'Ty 1Hz - Relative - E');
+hold off;
+set(gca, 'xscale', 'log');
+set(gca, 'yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
+legend('Location', 'northwest');
+xlim([0.1, 500]);
+
+
+2.5 Transfer function from marble motion in the East direction to sample motion in the East direction
+2.5 Transfer function from marble motion in the East direction to sample motion in the East direction
2.6 Position of the translation stage and Current
+2.6 Position of the translation stage and Current
2.6.1 Data pre-processing
+2.6.1 Data pre-processing
cvs file starting at line 29.
2.6.2 Time domain data
+2.6.2 Time domain data
2.7 Conclusion
+2.7 Conclusion
@@ -800,7 +856,7 @@ xlabel(
-