From c7207b96cbb1bc65f951163bfa0ea10e1c3a8279 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Tue, 17 Mar 2020 11:23:17 +0100 Subject: [PATCH] Rework the disturbance file --- docs/disturbances.html | 251 +++++++----------- .../cas_computed_relative_displacement.pdf | Bin 188092 -> 0 bytes .../cas_computed_relative_displacement.png | Bin 124163 -> 0 bytes docs/figs/dist_effect_relative_velocity.pdf | Bin 195865 -> 196733 bytes docs/figs/dist_effect_relative_velocity.png | Bin 177788 -> 165442 bytes docs/figs/nano_station_inputs_outputs.pdf | Bin 34552 -> 34552 bytes docs/figs/psd_effect_dist_verif.pdf | Bin 240453 -> 189459 bytes docs/figs/psd_effect_dist_verif.png | Bin 181346 -> 160263 bytes org/disturbances.org | 176 ++++-------- 9 files changed, 149 insertions(+), 278 deletions(-) delete mode 100644 docs/figs/cas_computed_relative_displacement.pdf delete mode 100644 docs/figs/cas_computed_relative_displacement.png diff --git a/docs/disturbances.html b/docs/disturbances.html index 45028c1..d160c15 100644 --- a/docs/disturbances.html +++ b/docs/disturbances.html @@ -4,7 +4,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Identification of the disturbances @@ -254,7 +254,6 @@
  • 5. Compute the Power Spectral Density of the disturbance force
  • 6. Noise Budget
  • 7. Save
  • -
  • 8. Error motion of the Sample without Control
  • @@ -277,7 +276,6 @@ Because we cannot measure directly the perturbation forces, we have the measure

    -

    uniaxial-model-micro-station.png

    @@ -324,7 +322,8 @@ We load the configuration and we set a small StopTime.

    -We initialize all the stages. +We initialize all the stages without the sample nor the nano-hexapod. +The obtained system corresponds to the status micro-station when the vibration measurements were conducted.

    initializeGround();
    @@ -339,6 +338,30 @@ initializeNanoHexapod('type', 'type', 'none');
     
    + +

    +Open Loop Control. +

    +
    +
    initializeController('type', 'open-loop');
    +
    +
    + +

    +We don’t need gravity here. +

    +
    +
    initializeSimscapeConfiguration('gravity', false);
    +
    +
    + +

    +We log the signals. +

    +
    +
    initializeLoggingConfiguration('log', 'all');
    +
    +
    @@ -351,41 +374,41 @@ The transfer functions from the disturbance forces to the relative velocity of t

    -
    %% Options for Linearized
    -options = linearizeOptions;
    -options.SampleTime = 0;
    -
    -%% Name of the Simulink File
    +
    %% Name of the Simulink File
     mdl = 'nass_model';
    -
    -
    -
    -
    %% Micro-Hexapod
    -  clear io; io_i = 1;
    -  io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Dwz'); io_i = io_i + 1; % Vertical Ground Motion
    -  io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Fty_z'); io_i = io_i + 1; % Parasitic force Ty
    -  io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Frz_z'); io_i = io_i + 1; % Parasitic force Rz
    -  io(io_i) = linio([mdl, '/Micro-Station/Granite/Modal Analysis/accelerometer'], 1, 'openoutput'); io_i = io_i + 1; % Absolute motion - Granite
    -  io(io_i) = linio([mdl, '/Micro-Station/Micro Hexapod/Modal Analysis/accelerometer'],  1, 'openoutput'); io_i = io_i + 1; % Absolute Motion - Hexapod
    -  % io(io_i) = linio([mdl, '/Vm'],   1, 'openoutput'); io_i = io_i + 1; % Relative Velocity hexapod/granite
    -
    -
    +%% Micro-Hexapod +clear io; io_i = 1; +io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Dwz'); io_i = io_i + 1; % Vertical Ground Motion +io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Fty_z'); io_i = io_i + 1; % Parasitic force Ty +io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Frz_z'); io_i = io_i + 1; % Parasitic force Rz -
    -
    % Run the linearization
    +io(io_i) = linio([mdl, '/Micro-Station/Granite/Modal Analysis/accelerometer'], 1, 'openoutput'); io_i = io_i + 1; % Absolute motion - Granite
    +io(io_i) = linio([mdl, '/Micro-Station/Micro Hexapod/Modal Analysis/accelerometer'],  1, 'openoutput'); io_i = io_i + 1; % Absolute Motion - Hexapod
    +% io(io_i) = linio([mdl, '/Vm'],   1, 'openoutput'); io_i = io_i + 1; % Relative Velocity hexapod/granite
    +
    +% Run the linearization
     G = linearize(mdl, io, 0);
    +
    +
    -% We Take only the outputs corresponding to the vertical acceleration -G = G([3,9], :); +

    +We Take only the outputs corresponding to the vertical acceleration. +

    +
    +
    G = G([3,9], :);
     
     % Input/Output names
     G.InputName  = {'Dw', 'Fty', 'Frz'};
     G.OutputName = {'Agm', 'Ahm'};
    +
    +
    -% We integrate 1 time the output to have the velocity and we -% substract the absolute velocities to have the relative velocity -G = (1/s)*tf([-1, 1])*G; +

    +We integrate 1 time the output to have the velocity and we substract the absolute velocities to have the relative velocity. +

    +
    +
    G = (1/s)*tf([-1, 1])*G;
     
     % Input/Output names
     G.InputName  = {'Dw', 'Fty', 'Frz'};
    @@ -402,6 +425,14 @@ G.OutputName = {'Vm'};
     
     

    +

    +The obtained sensitivity to disturbances are shown bellow: +

    +
      +
    • The transfer function from vertical ground motion \(D_w\) to the vertical relative displacement from the micro-hexapod to the granite \(D\) is shown in Figure 2
    • +
    • The sensitive from vertical forces applied in the Translation stage is shown in Figure 3
    • +
    +

    sensitivity_dist_gm.png @@ -432,10 +463,13 @@ G.OutputName = {'Vm'};

    -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: +

    + +

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

      -
    • Slip Ring Rotation
    • +
    • Slip Ring Rotation (\(F_{r_z}\))
    • Scan of the translation stage (effect in the vertical direction and in the horizontal direction)
    @@ -460,7 +494,7 @@ 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 and velocity of the hexapod with respect to the granite are shown in figures 5 and 6.

    @@ -487,6 +521,14 @@ 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)

    +
    + +
    +

    +From Figure 7, we can see that the translation stage and the rotation stage have almost the same effect on the position error. +Also, the ground motion has a relatively negligible effect on the position error. +

    +
    @@ -499,15 +541,22 @@ The Cumulative Amplitude Spectrum of the relative motion is shown in figure

    -Now, from the extracted transfer functions from the disturbance force to the relative motion of the hexapod with respect to the granite (section 3) and from the measured PSD of the relative motion (section 4), we can compute the PSD of the disturbance force. +Using the extracted transfer functions from the disturbance force to the relative motion of the hexapod with respect to the granite (section 3) and using the measured PSD of the relative motion (section 4), we can compute the PSD of the disturbance force.

    +

    +This is done below. +

    rz.psd_f  = rz.pxsp_r./abs(squeeze(freqresp(G('Vm', 'Frz'), rz.f, 'Hz'))).^2;
     tyz.psd_f = tyz.pxz_ty_r./abs(squeeze(freqresp(G('Vm', 'Fty'), tyz.f, 'Hz'))).^2;
     
    +

    +The obtained amplitude spectral densities of the disturbance forces are shown in Figure 8. +

    +

    dist_force_psd.png @@ -525,24 +574,31 @@ tyz.psd_f = tyz.pxz_ty_r./abs(squeeze(freqresp(G(<

    -Now, from the compute spectral density of the disturbance sources, we can compute the resulting relative motion of the Hexapod with respect to the granite using the model. -We should verify that this is coherent with the measurements. +From the obtained spectral density of the disturbance sources, we can compute the resulting relative motion of the Hexapod with respect to the granite using the model.

    +

    +This is equivalent as doing the inverse that was done in the previous section. +This is done in order to verify that this is coherent with the measurements. +

    + +

    +The power spectral density of the relative motion is computed below and the result is shown in Figure 9. +We can see that this is exactly the same as the Figure 6. +

    +
    +
    psd_gm_d = gm.psd_gm.*abs(squeeze(freqresp(G('Vm', 'Dw')/s, gm.f, 'Hz'))).^2;
    +psd_ty_d = tyz.psd_f.*abs(squeeze(freqresp(G('Vm', 'Fty')/s, tyz.f, 'Hz'))).^2;
    +psd_rz_d = rz.psd_f.*abs(squeeze(freqresp(G('Vm', 'Frz')/s, rz.f, 'Hz'))).^2;
    +
    +
    +

    psd_effect_dist_verif.png

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

    - - - -
    -

    cas_computed_relative_displacement.png -

    -

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

    -
    @@ -567,117 +623,10 @@ save('./mat/dist_psd.mat', -

    8 Error motion of the Sample without Control

    -
    -
    -
    initializeGround();
    -initializeGranite('Foffset', false);
    -initializeTy('Foffset', false);
    -initializeRy('Foffset', false);
    -initializeRz('Foffset', false);
    -initializeMicroHexapod('Foffset', false);
    -initializeAxisc('type', 'rigid');
    -initializeMirror('type', 'rigid');
    -
    -
    - -

    -The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg. -

    -
    -
    initializeNanoHexapod('type', 'rigid');
    -initializeSample('type', 'rigid', 'mass', 50);
    -
    -
    - -

    -We set the references and disturbances to zero. -

    -
    -
    initializeReferences();
    -initializeDisturbances();
    -
    -
    - -

    -We set the controller type to Open-Loop. -

    -
    -
    initializeController('type', 'open-loop');
    -
    -
    - -

    -And we put some gravity. -

    -
    -
    initializeSimscapeConfiguration('gravity', false);
    -
    -
    - -

    -We do not need to log any signal. -

    -
    -
    initializeLoggingConfiguration('log', 'all');
    -
    -
    - -
    -
    initializePosError('error', false);
    -
    -
    - -
    -
    load('mat/conf_simulink.mat');
    -set_param(conf_simulink, 'StopTime', '1');
    -
    -
    - -

    -We simulate the model. -

    -
    -
    sim('nass_model');
    -
    -
    - -
    -
    figure;
    -subplot(1, 2, 1);
    -hold on;
    -plot(simout.Em.Eg.Time, simout.Em.Eg.Data(:, 1), 'DisplayName', 'X');
    -plot(simout.Em.Eg.Time, simout.Em.Eg.Data(:, 2), 'DisplayName', 'Y');
    -plot(simout.Em.Eg.Time, simout.Em.Eg.Data(:, 3), 'DisplayName', 'Z');
    -hold off;
    -xlabel('Time [s]');
    -ylabel('Position error [m]');
    -legend();
    -
    -subplot(1, 2, 2);
    -hold on;
    -plot(simout.Em.Eg.Time, simout.Em.Eg.Data(:, 4));
    -plot(simout.Em.Eg.Time, simout.Em.Eg.Data(:, 5));
    -plot(simout.Em.Eg.Time, simout.Em.Eg.Data(:, 6));
    -hold off;
    -xlabel('Time [s]');
    -ylabel('Orientation error [rad]');
    -
    -
    - -
    -
    Eg = simout.Em.Eg;
    -save('./mat/motion_error_ol.mat', 'Eg');
    -
    -
    -
    -

    Author: Dehaeze Thomas

    -

    Created: 2020-03-13 ven. 17:39

    +

    Created: 2020-03-17 mar. 11:21

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zv7+P60^mq1xNb>> +The obtained sensitivity to disturbances are shown bellow: +- The transfer function from vertical ground motion $D_w$ to the vertical relative displacement from the micro-hexapod to the granite $D$ is shown in Figure [[fig:sensitivity_dist_gm]] +- The sensitive from vertical forces applied in the Translation stage is shown in Figure [[fig:sensitivity_dist_fty]] + #+begin_src matlab :exports none freqs = logspace(0, 3, 1000); @@ -349,8 +364,9 @@ The transfer functions from the disturbance forces to the relative velocity of t :CUSTOM_ID: Power-Spectral-Density-of-the-effect-of-the-disturbances :END: <> -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: -- Slip Ring Rotation + +The Power Spectral Densities of the relative velocity between the hexapod and the marble in $[(m/s)^2/Hz]$ are loaded for the following sources of disturbance: +- Slip Ring Rotation ($F_{r_z}$) - Scan of the translation stage (effect in the vertical direction and in the horizontal direction) Also, the Ground Motion is measured. @@ -369,7 +385,6 @@ Also, the Ground Motion is measured. tyx.f = tyx.f(2:end); gm.psd_gm = gm.psd_gm(2:end); % PSD of Ground Motion [m^2/Hz] - gm.psd_gv = gm.psd_gv(2:end); % PSD of Ground Velocity [(m/s)^2/Hz] rz.pxsp_r = rz.pxsp_r(2:end); % PSD of Relative Velocity [(m/s)^2/Hz] tyz.pxz_ty_r = tyz.pxz_ty_r(2:end); % PSD of Relative Velocity [(m/s)^2/Hz] tyx.pxe_ty_r = tyx.pxe_ty_r(2:end); % PSD of Relative Velocity [(m/s)^2/Hz] @@ -380,7 +395,7 @@ We now compute the relative velocity between the hexapod and the granite due to gm.psd_rv = gm.psd_gm.*abs(squeeze(freqresp(G('Vm', 'Dw'), gm.f, 'Hz'))).^2; #+end_src -The Power Spectral Density of the relative motion/velocity of the hexapod with respect to the granite are shown in figures [[fig:dist_effect_relative_velocity]] and [[fig:dist_effect_relative_motion]]. +The Power Spectral Density of the relative motion and velocity of the hexapod with respect to the granite are shown in figures [[fig:dist_effect_relative_velocity]] and [[fig:dist_effect_relative_motion]]. The Cumulative Amplitude Spectrum of the relative motion is shown in figure [[fig:dist_effect_relative_motion_cas]]. @@ -451,19 +466,27 @@ The Cumulative Amplitude Spectrum of the relative motion is shown in figure [[fi #+CAPTION: Cumulative Amplitude Spectrum of the relative motion due to different sources of perturbation ([[./figs/dist_effect_relative_motion_cas.png][png]], [[./figs/dist_effect_relative_motion_cas.pdf][pdf]]) [[file:figs/dist_effect_relative_motion_cas.png]] +#+begin_important + From Figure [[fig:dist_effect_relative_motion_cas]], we can see that the translation stage and the rotation stage have almost the same effect on the position error. + Also, the ground motion has a relatively negligible effect on the position error. +#+end_important + * Compute the Power Spectral Density of the disturbance force :PROPERTIES: :CUSTOM_ID: Compute-the-Power-Spectral-Density-of-the-disturbance-force :END: <> -Now, from the extracted transfer functions from the disturbance force to the relative motion of the hexapod with respect to the granite (section [[sec:sensitivity_disturbances]]) and from the measured PSD of the relative motion (section [[sec:psd_dist]]), we can compute the PSD of the disturbance force. +Using the extracted transfer functions from the disturbance force to the relative motion of the hexapod with respect to the granite (section [[sec:sensitivity_disturbances]]) and using the measured PSD of the relative motion (section [[sec:psd_dist]]), we can compute the PSD of the disturbance force. +This is done below. #+begin_src matlab rz.psd_f = rz.pxsp_r./abs(squeeze(freqresp(G('Vm', 'Frz'), rz.f, 'Hz'))).^2; tyz.psd_f = tyz.pxz_ty_r./abs(squeeze(freqresp(G('Vm', 'Fty'), tyz.f, 'Hz'))).^2; #+end_src +The obtained amplitude spectral densities of the disturbance forces are shown in Figure [[fig:dist_force_psd]]. + #+begin_src matlab :exports none figure; hold on; @@ -492,11 +515,14 @@ Now, from the extracted transfer functions from the disturbance force to the rel :END: <> -Now, from the compute spectral density of the disturbance sources, we can compute the resulting relative motion of the Hexapod with respect to the granite using the model. -We should verify that this is coherent with the measurements. +From the obtained spectral density of the disturbance sources, we can compute the resulting relative motion of the Hexapod with respect to the granite using the model. -#+begin_src matlab :exports none - % Power Spectral Density of the relative Displacement +This is equivalent as doing the inverse that was done in the previous section. +This is done in order to verify that this is coherent with the measurements. + +The power spectral density of the relative motion is computed below and the result is shown in Figure [[fig:psd_effect_dist_verif]]. +We can see that this is exactly the same as the Figure [[fig:dist_effect_relative_motion]]. +#+begin_src matlab psd_gm_d = gm.psd_gm.*abs(squeeze(freqresp(G('Vm', 'Dw')/s, gm.f, 'Hz'))).^2; psd_ty_d = tyz.psd_f.*abs(squeeze(freqresp(G('Vm', 'Fty')/s, tyz.f, 'Hz'))).^2; psd_rz_d = rz.psd_f.*abs(squeeze(freqresp(G('Vm', 'Frz')/s, rz.f, 'Hz'))).^2; @@ -508,7 +534,6 @@ We should verify that this is coherent with the measurements. plot(gm.f, sqrt(psd_gm_d), 'DisplayName', 'Ground Motion'); plot(tyz.f, sqrt(psd_ty_d), 'DisplayName', 'Ty'); plot(rz.f, sqrt(psd_rz_d), 'DisplayName', 'Rz'); - plot(rz.f, sqrt(psd_gm_d + psd_ty_d + psd_rz_d), 'k--', 'DisplayName', 'tot'); hold off; set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log'); xlabel('Frequency [Hz]'); ylabel('ASD of the relative motion $\left[\frac{m}{\sqrt{Hz}}\right]$') @@ -525,30 +550,6 @@ We should verify that this is coherent with the measurements. #+CAPTION: Computed Effect of the disturbances on the relative displacement hexapod/granite ([[./figs/psd_effect_dist_verif.png][png]], [[./figs/psd_effect_dist_verif.pdf][pdf]]) [[file:figs/psd_effect_dist_verif.png]] - -#+begin_src matlab :exports none - figure; - hold on; - plot(gm.f, flip(sqrt(-cumtrapz(flip(gm.f), flip(psd_gm_d)))), 'DisplayName', 'Ground Motion'); - 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'); - hold off; - set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log'); - xlabel('Frequency [Hz]'); ylabel('Cumulative Amplitude Spectrum [m]') - legend('location', 'northeast'); - xlim([2, 500]); ylim([1e-11, 1e-6]); -#+end_src - -#+HEADER: :tangle no :exports results :results none :noweb yes -#+begin_src matlab :var filepath="figs/cas_computed_relative_displacement.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") - <> -#+end_src - -#+NAME: fig:cas_computed_relative_displacement -#+CAPTION: CAS of the total Relative Displacement due to all considered sources of perturbation ([[./figs/cas_computed_relative_displacement.png][png]], [[./figs/cas_computed_relative_displacement.pdf][pdf]]) -[[file:figs/cas_computed_relative_displacement.png]] - * Save :PROPERTIES: :CUSTOM_ID: Save @@ -567,82 +568,3 @@ The PSD of the disturbance force are now saved for further analysis. save('./mat/dist_psd.mat', 'dist_f'); #+end_src -* Error motion of the Sample without Control -#+begin_src matlab - initializeGround(); - initializeGranite('Foffset', false); - initializeTy('Foffset', false); - initializeRy('Foffset', false); - initializeRz('Foffset', false); - initializeMicroHexapod('Foffset', false); - initializeAxisc('type', 'rigid'); - initializeMirror('type', 'rigid'); -#+end_src - -The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg. -#+begin_src matlab - initializeNanoHexapod('type', 'rigid'); - initializeSample('type', 'rigid', 'mass', 50); -#+end_src - -We set the references and disturbances to zero. -#+begin_src matlab - initializeReferences(); - initializeDisturbances(); -#+end_src - -We set the controller type to Open-Loop. -#+begin_src matlab - initializeController('type', 'open-loop'); -#+end_src - -And we put some gravity. -#+begin_src matlab - initializeSimscapeConfiguration('gravity', false); -#+end_src - -We do not need to log any signal. -#+begin_src matlab - initializeLoggingConfiguration('log', 'all'); -#+end_src - -#+begin_src matlab - initializePosError('error', false); -#+end_src - -#+begin_src matlab - load('mat/conf_simulink.mat'); - set_param(conf_simulink, 'StopTime', '1'); -#+end_src - -We simulate the model. -#+begin_src matlab - sim('nass_model'); -#+end_src - -#+begin_src matlab - figure; - subplot(1, 2, 1); - hold on; - plot(simout.Em.Eg.Time, simout.Em.Eg.Data(:, 1), 'DisplayName', 'X'); - plot(simout.Em.Eg.Time, simout.Em.Eg.Data(:, 2), 'DisplayName', 'Y'); - plot(simout.Em.Eg.Time, simout.Em.Eg.Data(:, 3), 'DisplayName', 'Z'); - hold off; - xlabel('Time [s]'); - ylabel('Position error [m]'); - legend(); - - subplot(1, 2, 2); - hold on; - plot(simout.Em.Eg.Time, simout.Em.Eg.Data(:, 4)); - plot(simout.Em.Eg.Time, simout.Em.Eg.Data(:, 5)); - plot(simout.Em.Eg.Time, simout.Em.Eg.Data(:, 6)); - hold off; - xlabel('Time [s]'); - ylabel('Orientation error [rad]'); -#+end_src - -#+begin_src matlab - Eg = simout.Em.Eg; - save('./mat/motion_error_ol.mat', 'Eg'); -#+end_src

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