diff --git a/disturbances/index.html b/disturbances/index.html index 8e63257..ffca036 100644 --- a/disturbances/index.html +++ b/disturbances/index.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Identification of the disturbances @@ -280,13 +280,13 @@ for the JavaScript code in this tag.

Table of Contents

@@ -296,7 +296,7 @@ The goal here is to extract the Power Spectral Density of the sources of perturb

-The sources of perturbations are (schematically shown in figure 1): +The sources of perturbations are (schematically shown in figure 1):

-Because we cannot measure directly the perturbation forces, we have the measure the effect of those perturbations on the system (in terms of velocity for instance using geophones, \(D\) on figure 1) and then, using a model, compute the forces that induced such velocity. +Because we cannot measure directly the perturbation forces, we have the measure the effect of those perturbations on the system (in terms of velocity for instance using geophones, \(D\) on figure 1) and then, using a model, compute the forces that induced such velocity.

-
+

uniaxial-model-micro-station.png

Figure 1: Schematic of the Micro Station and the sources of disturbance

@@ -321,18 +321,18 @@ Because we cannot measure directly the perturbation forces, we have the measure This file is divided in the following sections:

-
-

1 Identification

+
+

1 Identification

- +

@@ -373,15 +373,15 @@ G.OutputName = {

-
-

2 Sensitivity to Disturbances

+
+

2 Sensitivity to Disturbances

- +

-
+

sensitivity_dist_gm.png

Figure 2: Sensitivity to Ground Motion (png, pdf)

@@ -389,7 +389,7 @@ G.OutputName = { +

sensitivity_dist_fty.png

Figure 3: Sensitivity to vertical forces applied by the Ty stage (png, pdf)

@@ -397,7 +397,7 @@ G.OutputName = { +

sensitivity_dist_frz.png

Figure 4: Sensitivity to vertical forces applied by the Rz stage (png, pdf)

@@ -405,11 +405,11 @@ G.OutputName = {
-
-

3 Power Spectral Density of the effect of the disturbances

+
+

3 Power Spectral Density of the effect of the disturbances

- + The PSD of the relative velocity between the hexapod and the marble in \([(m/s)^2/Hz]\) are loaded for the following sources of disturbance:

    @@ -438,15 +438,15 @@ We now compute the relative velocity between the hexapod and the granite due to

-The Power Spectral Density of the relative motion/velocity of the hexapod with respect to the granite are shown in figures 5 and 6. +The Power Spectral Density of the relative motion/velocity of the hexapod with respect to the granite are shown in figures 5 and 6.

-The Cumulative Amplitude Spectrum of the relative motion is shown in figure 7. +The Cumulative Amplitude Spectrum of the relative motion is shown in figure 7.

-
+

dist_effect_relative_velocity.png

Figure 5: Amplitude Spectral Density of the relative velocity of the hexapod with respect to the granite due to different sources of perturbation (png, pdf)

@@ -454,14 +454,14 @@ The Cumulative Amplitude Spectrum of the relative motion is shown in figure + -
+

dist_effect_relative_motion_cas.png

Figure 7: Cumulative Amplitude Spectrum of the relative motion due to different sources of perturbation (png, pdf)

@@ -469,15 +469,15 @@ The Cumulative Amplitude Spectrum of the relative motion is shown in figure
-
-

4 Compute the Power Spectral Density of the disturbance force

+
+

4 Compute the Power Spectral Density of the disturbance force

- +

-Now, from the extracted transfer functions from the disturbance force to the relative motion of the hexapod with respect to the granite (section 2) and from the measured PSD of the relative motion (section 3), we can compute the PSD of the disturbance force. +Now, from the extracted transfer functions from the disturbance force to the relative motion of the hexapod with respect to the granite (section 2) and from the measured PSD of the relative motion (section 3), we can compute the PSD of the disturbance force.

@@ -487,7 +487,7 @@ tyz.psd_f = tyz.pxz_ty_r./abs +

dist_force_psd.png

Figure 8: Amplitude Spectral Density of the disturbance force (png, pdf)

@@ -495,11 +495,11 @@ tyz.psd_f = tyz.pxz_ty_r./abs -

5 Noise Budget

+
+

5 Noise Budget

- +

@@ -508,7 +508,7 @@ We should verify that this is coherent with the measurements.

-
+

psd_effect_dist_verif.png

Figure 9: Computed Effect of the disturbances on the relative displacement hexapod/granite (png, pdf)

@@ -516,7 +516,7 @@ We should verify that this is coherent with the measurements. -
+

cas_computed_relative_displacement.png

Figure 10: CAS of the total Relative Displacement due to all considered sources of perturbation (png, pdf)

@@ -524,8 +524,8 @@ We should verify that this is coherent with the measurements.
-
-

6 Approximation

+
+

6 Approximation

We approximate the PSD of the disturbance with the following transfer functions. @@ -541,14 +541,14 @@ G_gm = 0. +

estimate_spectral_density_disturbances.png

Figure 11: Estimated spectral density of the disturbances (png, pdf)

-
+

comp_estimation_cas_disturbances.png

Figure 12: Comparison of the CAS of the disturbances with the approximate ones (png, pdf)

@@ -556,8 +556,8 @@ We compute the effect of these approximate disturbances on \(D\).
-
-

7 Save

+
+

7 Save

The PSD of the disturbance force are now saved for further noise budgeting when control is applied (the mat file is accessible here). @@ -584,7 +584,7 @@ save(

Author: Dehaeze Thomas

-

Created: 2019-11-22 ven. 14:56

+

Created: 2019-11-22 ven. 15:42

Validate

diff --git a/disturbances/index.org b/disturbances/index.org index 7a565bd..ae82913 100644 --- a/disturbances/index.org +++ b/disturbances/index.org @@ -498,9 +498,9 @@ We approximate the PSD of the disturbance with the following transfer functions. We compute the effect of these approximate disturbances on $D$. #+begin_src matlab :exports none % Power Spectral Density of the relative Displacement - psd_gm_s = abs(squeeze(freqresp(G_gm*G('Vm', 'Dw')/s, dist_f.f, 'Hz'))).^2; - psd_ty_s = abs(squeeze(freqresp(G_ty*G('Vm', 'Fty')/s, dist_f.f, 'Hz'))).^2; - psd_rz_s = abs(squeeze(freqresp(G_rz*G('Vm', 'Frz')/s, dist_f.f, 'Hz'))).^2; + psd_gm_s = abs(squeeze(freqresp(G_gm*G('Vm', 'Dw')/s, gm.f, 'Hz'))).^2; + psd_ty_s = abs(squeeze(freqresp(G_ty*G('Vm', 'Fty')/s, gm.f, 'Hz'))).^2; + psd_rz_s = abs(squeeze(freqresp(G_rz*G('Vm', 'Frz')/s, gm.f, 'Hz'))).^2; #+end_src #+begin_src matlab :exports none @@ -508,11 +508,11 @@ We compute the effect of these approximate disturbances on $D$. ax1 = subplot(1, 2, 1); hold on; set(gca,'ColorOrderIndex',2); - plot(dist_f.f, sqrt(psd_ty_d), 'DisplayName', 'F - Ty'); - plot(dist_f.f, sqrt(psd_rz_d), 'DisplayName', 'F - Rz'); + plot(gm.f, sqrt(psd_ty_d), 'DisplayName', 'F - Ty'); + plot(gm.f, sqrt(psd_rz_d), 'DisplayName', 'F - Rz'); set(gca,'ColorOrderIndex',2); - plot(dist_f.f, sqrt(psd_ty_s), '--', 'HandleVisibility', 'off'); - plot(dist_f.f, sqrt(psd_rz_s), '--', 'HandleVisibility', 'off'); + plot(gm.f, sqrt(psd_ty_s), '--', 'HandleVisibility', 'off'); + plot(gm.f, sqrt(psd_rz_s), '--', 'HandleVisibility', 'off'); hold off; set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log'); xlabel('Frequency [Hz]'); ylabel('ASD of the disturbance force $\left[\frac{F}{\sqrt{Hz}}\right]$') @@ -521,9 +521,9 @@ We compute the effect of these approximate disturbances on $D$. ax2 = subplot(1, 2, 2); hold on; - plot(dist_f.f, sqrt(psd_gm_d), 'DisplayName', 'D - Gm'); + plot(gm.f, sqrt(psd_gm_d), 'DisplayName', 'D - Gm'); set(gca,'ColorOrderIndex',1); - plot(dist_f.f, sqrt(psd_gm_s), '--', 'HandleVisibility', 'off'); + plot(gm.f, sqrt(psd_gm_s), '--', 'HandleVisibility', 'off'); hold off; set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log'); xlabel('Frequency [Hz]'); ylabel('ASD of the ground displacement $\left[\frac{m}{\sqrt{Hz}}\right]$') @@ -543,15 +543,15 @@ We compute the effect of these approximate disturbances on $D$. #+begin_src matlab :exports none figure; hold on; - plot(dist_f.f, flip(sqrt(-cumtrapz(flip(dist_f.f), flip(psd_gm_d)))), 'DisplayName', 'Gm'); - plot(dist_f.f, flip(sqrt(-cumtrapz(flip(dist_f.f), flip(psd_ty_d)))), 'DisplayName', 'Ty'); - plot(dist_f.f, flip(sqrt(-cumtrapz(flip(dist_f.f), flip(psd_rz_d)))), 'DisplayName', 'Rz'); - plot(dist_f.f, flip(sqrt(-cumtrapz(flip(dist_f.f), flip(psd_gm_d + psd_ty_d + psd_rz_d)))), 'k-', 'DisplayName', 'tot'); + plot(gm.f, flip(sqrt(-cumtrapz(flip(gm.f), flip(psd_gm_d)))), 'DisplayName', 'Gm'); + plot(gm.f, flip(sqrt(-cumtrapz(flip(gm.f), flip(psd_ty_d)))), 'DisplayName', 'Ty'); + plot(gm.f, flip(sqrt(-cumtrapz(flip(gm.f), flip(psd_rz_d)))), 'DisplayName', 'Rz'); + plot(gm.f, flip(sqrt(-cumtrapz(flip(gm.f), flip(psd_gm_d + psd_ty_d + psd_rz_d)))), 'k-', 'DisplayName', 'tot'); set(gca,'ColorOrderIndex',1); - plot(dist_f.f, flip(sqrt(-cumtrapz(flip(dist_f.f), flip(psd_gm_s)))), '--', 'HandleVisibility', 'off'); - plot(dist_f.f, flip(sqrt(-cumtrapz(flip(dist_f.f), flip(psd_ty_s)))), '--', 'HandleVisibility', 'off'); - plot(dist_f.f, flip(sqrt(-cumtrapz(flip(dist_f.f), flip(psd_rz_s)))), '--', 'HandleVisibility', 'off'); - plot(dist_f.f, flip(sqrt(-cumtrapz(flip(dist_f.f), flip(psd_gm_s + psd_ty_s + psd_rz_s)))), 'k--', 'HandleVisibility', 'off'); + plot(gm.f, flip(sqrt(-cumtrapz(flip(gm.f), flip(psd_gm_s)))), '--', 'HandleVisibility', 'off'); + plot(gm.f, flip(sqrt(-cumtrapz(flip(gm.f), flip(psd_ty_s)))), '--', 'HandleVisibility', 'off'); + plot(gm.f, flip(sqrt(-cumtrapz(flip(gm.f), flip(psd_rz_s)))), '--', 'HandleVisibility', 'off'); + plot(gm.f, flip(sqrt(-cumtrapz(flip(gm.f), flip(psd_gm_s + psd_ty_s + psd_rz_s)))), 'k--', 'HandleVisibility', 'off'); hold off; set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log'); xlabel('Frequency [Hz]'); ylabel('Cumulative Amplitude Spectrum [m]') diff --git a/disturbances/mat/dist_psd.mat b/disturbances/mat/dist_psd.mat index 783d4a4..7296c39 100644 Binary files a/disturbances/mat/dist_psd.mat and b/disturbances/mat/dist_psd.mat differ diff --git a/figs/comp_estimation_cas_disturbances.png b/figs/comp_estimation_cas_disturbances.png index 9ccc198..79ba05c 100644 Binary files a/figs/comp_estimation_cas_disturbances.png and b/figs/comp_estimation_cas_disturbances.png differ diff --git a/figs/estimate_spectral_density_disturbances.png b/figs/estimate_spectral_density_disturbances.png index 32581f8..3650117 100644 Binary files a/figs/estimate_spectral_density_disturbances.png and b/figs/estimate_spectral_density_disturbances.png differ