diff --git a/docs/optimal_stiffness_disturbances.html b/docs/optimal_stiffness_disturbances.html index 3b5ce93..6ba74ed 100644 --- a/docs/optimal_stiffness_disturbances.html +++ b/docs/optimal_stiffness_disturbances.html @@ -4,7 +4,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Determination of the optimal nano-hexapod’s stiffness for reducing the effect of disturbances @@ -257,7 +257,7 @@
  • 2.3. Sensitivity to Stages vibration (Filtering)
  • 2.4. Effect of Ground motion (Transmissibility).
  • 2.5. Direct Forces (Compliance).
    • -
  • 2.6. Conclusion
    • +
  • 2.6. Conclusion
  • 3. Effect of granite stiffness @@ -270,7 +270,7 @@
  • 3.2. Soft Granite
  • 3.3. Effect of the Granite transfer function
    • -
  • 3.4. Conclusion
    • +
  • 3.4. Conclusion
  • 4. Open Loop Budget Error @@ -278,7 +278,7 @@
  • 4.1. Noise Budgeting - Theory
  • 4.2. Power Spectral Densities
  • 4.3. Cumulative Amplitude Spectrum
    • -
  • 4.4. Conclusion
    • +
  • 4.4. Conclusion
  • 5. Closed Loop Budget Error @@ -287,7 +287,7 @@
  • 5.2. Reduction thanks to feedback - Required bandwidth
    • -
  • 6. Conclusion
    • +
  • 6. Conclusion
    • @@ -497,8 +497,8 @@ The effect of direct forces/torques applied on the sample (cable forces for inst -
    -

    2.6 Conclusion

    +
    +

    2.6 Conclusion

    @@ -678,12 +678,14 @@ From Figures 11 and 12, we s

    -
    -

    3.4 Conclusion

    +
    +

    3.4 Conclusion

    -Having a soft granite suspension could greatly improve the sensitivity the ground motion and thus the level of sample vibration if it is found that ground motion is the limiting factor. +Having a soft granite suspension greatly decreases the sensitivity the ground motion. +Also, it does not affect much the sensitivity to stage vibration and direct forces. +Thus the level of sample vibration can be reduced by using a soft granite suspension if it is found that ground motion is the limiting factor.

    @@ -716,7 +718,7 @@ Let’s consider Figure 13 there \(G_d(s)\) is the

    psd_change_tf.png

    -

    Figure 13: Figure caption

    +

    Figure 13: Signal \(d\) going through and LTI transfer function \(G_d(s)\) to give a signal \(y\)

    @@ -742,7 +744,7 @@ Sometimes, we prefer to compute the Amplitude Spectral Density (ASD) whic

    psd_change_tf_multiple_pert.png

    -

    Figure 14: Figure caption

    +

    Figure 14: Block diagram showing and output \(y\) resulting from the addition of multiple perturbations \(d_i\)

    @@ -823,24 +825,6 @@ Similarly, the Cumulative Amplitude Spectrum of the sample vibrations are shown: The black dashed line corresponds to the performance objective of a sample vibration equal to \(10\ nm [rms]\).

    -
    -
    freqs = dist_f.f;
-
-figure;
-hold on;
-for i = 1:length(Ks)
-  plot(freqs, sqrt(flip(-cumtrapz(flip(freqs), flip(dist_f.psd_gm.*abs(squeeze(freqresp(Gd{i}('Ez', 'Dwz'), freqs, 'Hz'))).^2)))), '-', ...
-         'DisplayName', sprintf('$k = %.0g$ [N/m]', Ks(i)));
-end
-plot([freqs(1) freqs(end)], [10e-9 10e-9], 'k--', 'HandleVisibility', 'off');
-hold off;
-set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
-xlabel('Frequency [Hz]'); ylabel('CAS $E_y$ $[m]$')
-legend('Location', 'northeast');
-xlim([1, 500]); ylim([1e-10 1e-6]);
-
    -
    -

    opt_stiff_cas_dz_gm.png @@ -848,24 +832,6 @@ xlim([1, 500]); ylim([1e-10 1eFigure 18: Cumulative Amplitude Spectrum of the Sample vertical position error due to Ground motion for multiple nano-hexapod stiffnesses (png, pdf)

    -
    -
    freqs = dist_f.f;
-
-figure;
-hold on;
-for i = 1:length(Ks)
-  plot(freqs, sqrt(flip(-cumtrapz(flip(freqs), flip(dist_f.psd_rz.*abs(squeeze(freqresp(Gd{i}('Ez', 'Frz_z'), freqs, 'Hz'))).^2)))), '-', ...
-         'DisplayName', sprintf('$k = %.0g$ [N/m]', Ks(i)));
-end
-plot([freqs(1) freqs(end)], [10e-9 10e-9], 'k--', 'HandleVisibility', 'off');
-hold off;
-set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
-xlabel('Frequency [Hz]'); ylabel('CAS $[m]$')
-legend('Location', 'southwest');
-xlim([1, 500]); ylim([1e-10 1e-6]);
-
    -
    -

    opt_stiff_cas_dz_rz.png @@ -873,24 +839,6 @@ xlim([1, 500]); ylim([1e-10 1eFigure 19: Cumulative Amplitude Spectrum of the Sample vertical position error due to Vertical vibration of the Spindle for multiple nano-hexapod stiffnesses (png, pdf)

    -
    -
    freqs = dist_f.f;
-
-figure;
-hold on;
-for i = 1:length(Ks)
-  plot(freqs, sqrt(flip(-cumtrapz(flip(freqs), flip(psd_tot(:,i))))), '-', ...
-         'DisplayName', sprintf('$k = %.0g$ [N/m]', Ks(i)));
-end
-plot([freqs(1) freqs(end)], [10e-9 10e-9], 'k--', 'HandleVisibility', 'off');
-hold off;
-set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
-xlabel('Frequency [Hz]'); ylabel('CAS $E_z$ $[m]$')
-legend('Location', 'northeast');
-xlim([1, 500]); ylim([1e-10 1e-6]);
-
    -
    -

    opt_stiff_cas_dz_tot.png @@ -900,8 +848,8 @@ xlim([1, 500]); ylim([1e-10 1e -

    4.4 Conclusion

    +
    +

    4.4 Conclusion

    @@ -1064,8 +1012,8 @@ The obtained required bandwidth (approximate upper and lower bounds) to obtained

    -
    -

    6 Conclusion

    +
    +

    6 Conclusion

    @@ -1083,7 +1031,7 @@ From Figure 23 and Table 1,

    Author: Dehaeze Thomas

    -

    Created: 2020-04-08 mer. 12:12

    +

    Created: 2020-04-08 mer. 12:17

    diff --git a/org/optimal_stiffness_disturbances.org b/org/optimal_stiffness_disturbances.org index a505da8..2b6e0a5 100644 --- a/org/optimal_stiffness_disturbances.org +++ b/org/optimal_stiffness_disturbances.org @@ -693,7 +693,9 @@ From Figures [[fig:opt_stiff_soft_granite_Frz]] and [[fig:opt_stiff_soft_granite ** Conclusion #+begin_important - Having a soft granite suspension could greatly improve the sensitivity the ground motion and thus the level of sample vibration if it is found that ground motion is the limiting factor. + Having a soft granite suspension greatly decreases the sensitivity the ground motion. + Also, it does not affect much the sensitivity to stage vibration and direct forces. + Thus the level of sample vibration can be reduced by using a soft granite suspension if it is found that ground motion is the limiting factor. #+end_important * Open Loop Budget Error @@ -729,7 +731,7 @@ Let's consider Figure [[fig:psd_change_tf]] there $G_d(s)$ is the transfer funct #+end_src #+name: fig:psd_change_tf -#+caption: Figure caption +#+caption: Signal $d$ going through and LTI transfer function $G_d(s)$ to give a signal $y$ #+RESULTS: [[file:figs/psd_change_tf.png]] @@ -768,7 +770,7 @@ Sometimes, we prefer to compute the *Amplitude* Spectral Density (ASD) which is #+end_src #+name: fig:psd_change_tf_multiple_pert -#+caption: Figure caption +#+caption: Block diagram showing and output $y$ resulting from the addition of multiple perturbations $d_i$ #+RESULTS: [[file:figs/psd_change_tf_multiple_pert.png]] @@ -892,7 +894,7 @@ Similarly, the Cumulative Amplitude Spectrum of the sample vibrations are shown: The black dashed line corresponds to the performance objective of a sample vibration equal to $10\ nm [rms]$. -#+begin_src matlab +#+begin_src matlab :exports none freqs = dist_f.f; figure; @@ -918,7 +920,7 @@ The black dashed line corresponds to the performance objective of a sample vibra #+caption: Cumulative Amplitude Spectrum of the Sample vertical position error due to Ground motion for multiple nano-hexapod stiffnesses ([[./figs/opt_stiff_cas_dz_gm.png][png]], [[./figs/opt_stiff_cas_dz_gm.pdf][pdf]]) [[file:figs/opt_stiff_cas_dz_gm.png]] -#+begin_src matlab +#+begin_src matlab :exports none freqs = dist_f.f; figure; @@ -944,7 +946,7 @@ The black dashed line corresponds to the performance objective of a sample vibra #+caption: Cumulative Amplitude Spectrum of the Sample vertical position error due to Vertical vibration of the Spindle for multiple nano-hexapod stiffnesses ([[./figs/opt_stiff_cas_dz_rz.png][png]], [[./figs/opt_stiff_cas_dz_rz.pdf][pdf]]) [[file:figs/opt_stiff_cas_dz_rz.png]] -#+begin_src matlab +#+begin_src matlab :exports none freqs = dist_f.f; figure;