From ae94d53186223b891afb67f616996db5e2b59391 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Wed, 11 Dec 2019 15:07:13 +0100 Subject: [PATCH] Add few forgotten files --- .gitignore | 2 + active_damping/mat/plants.mat | Bin 0 -> 9079685 bytes disturbances/matlab/modal_frf_coh.m | 343 ++++++++++++++++++++++++++++ metrology/matlab/modal_frf_coh.m | 88 +++++++ simscape/matlab/modal_frf_coh.m | 25 ++ 5 files changed, 458 insertions(+) create mode 100644 active_damping/mat/plants.mat create mode 100644 disturbances/matlab/modal_frf_coh.m create mode 100644 metrology/matlab/modal_frf_coh.m create mode 100644 simscape/matlab/modal_frf_coh.m diff --git a/.gitignore b/.gitignore index 1b79130..99d567f 100644 --- a/.gitignore +++ b/.gitignore @@ -1,6 +1,8 @@ auto/ *.tex +nohup.out + **/figs/*.pdf **/figs/*.svg **/figs/*.tex diff --git a/active_damping/mat/plants.mat b/active_damping/mat/plants.mat new file mode 100644 index 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+ +open 'simscape/sim_micro_station_disturbances.slx' + +% Identification +% <> + +% The transfer functions from the disturbance forces to the relative velocity of the hexapod with respect to the granite are computed using the Simscape Model representing the experimental setup with the code below. + + +%% Options for Linearized +options = linearizeOptions; +options.SampleTime = 0; + +%% Name of the Simulink File +mdl = 'sim_micro_station_disturbances'; + +%% Micro-Hexapod +% Input/Output definition +io(1) = linio([mdl, '/Dw'], 1, 'input'); % Ground Motion +io(2) = linio([mdl, '/Fty'], 1, 'input'); % Parasitic force Ty +io(3) = linio([mdl, '/Frz'], 1, 'input'); % Parasitic force Rz +io(4) = linio([mdl, '/Dgm'], 1, 'output'); % Absolute motion - Granite +io(5) = linio([mdl, '/Dhm'], 1, 'output'); % Absolute Motion - Hexapod +io(6) = linio([mdl, '/Vm'], 1, 'output'); % Relative Velocity hexapod/granite + +% Run the linearization +G = linearize(mdl, io, 0); + +% Input/Output names +G.InputName = {'Dw', 'Fty', 'Frz'}; +G.OutputName = {'Dgm', 'Dhm', 'Vm'}; + +% Sensitivity to Disturbances +% <> + + +freqs = logspace(0, 3, 1000); + +figure; +title('$D_w$ to $D$'); +hold on; +plot(freqs, abs(squeeze(freqresp(G('Vm', 'Dw')/s, freqs, 'Hz'))), 'k-'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]'); + + + +% #+NAME: fig:sensitivity_dist_gm +% #+CAPTION: Sensitivity to Ground Motion ([[./figs/sensitivity_dist_gm.png][png]], [[./figs/sensitivity_dist_gm.pdf][pdf]]) +% [[file:figs/sensitivity_dist_gm.png]] + + + +freqs = logspace(0, 3, 1000); + +figure; +title('$F_{ty}$ to $D$'); +hold on; +plot(freqs, abs(squeeze(freqresp(G('Vm', 'Fty')/s, freqs, 'Hz'))), 'k-'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]'); + + + +% #+NAME: fig:sensitivity_dist_fty +% #+CAPTION: Sensitivity to vertical forces applied by the Ty stage ([[./figs/sensitivity_dist_fty.png][png]], [[./figs/sensitivity_dist_fty.pdf][pdf]]) +% [[file:figs/sensitivity_dist_fty.png]] + + + +freqs = logspace(0, 3, 1000); + +figure; +title('$F_{rz}$ to $D$'); +hold on; +plot(freqs, abs(squeeze(freqresp(G('Vm', 'Frz')/s, freqs, 'Hz'))), 'k-'); +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]'); + +% 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: +% - Slip Ring Rotation +% - Scan of the translation stage (effect in the vertical direction and in the horizontal direction) + +% Also, the Ground Motion is measured. + + +gm = load('./disturbances/mat/psd_gm.mat', 'f', 'psd_gm', 'psd_gv'); +rz = load('./disturbances/mat/pxsp_r.mat', 'f', 'pxsp_r'); +tyz = load('./disturbances/mat/pxz_ty_r.mat', 'f', 'pxz_ty_r'); +tyx = load('./disturbances/mat/pxe_ty_r.mat', 'f', 'pxe_ty_r'); + +gm.f = gm.f(2:end); +rz.f = rz.f(2:end); +tyz.f = tyz.f(2:end); +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] + + + +% We now compute the relative velocity between the hexapod and the granite due to ground motion. + +gm.psd_rv = gm.psd_gm.*abs(squeeze(freqresp(G('Vm', 'Dw'), gm.f, 'Hz'))).^2; + + + +% 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 Cumulative Amplitude Spectrum of the relative motion is shown in figure [[fig:dist_effect_relative_motion_cas]]. + + +figure; +hold on; +plot(gm.f, sqrt(gm.psd_rv), 'DisplayName', 'Ground Motion'); +plot(tyz.f, sqrt(tyz.pxz_ty_r), 'DisplayName', 'Ty'); +plot(rz.f, sqrt(rz.pxsp_r), 'DisplayName', 'Rz'); +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', 'southwest'); +xlim([2, 500]); + + + +% #+NAME: fig:dist_effect_relative_velocity +% #+CAPTION: Amplitude Spectral Density of the relative velocity of the hexapod with respect to the granite due to different sources of perturbation ([[./figs/dist_effect_relative_velocity.png][png]], [[./figs/dist_effect_relative_velocity.pdf][pdf]]) +% [[file:figs/dist_effect_relative_velocity.png]] + + + +figure; +hold on; +plot(gm.f, sqrt(gm.psd_rv)./(2*pi*gm.f), 'DisplayName', 'Ground Motion'); +plot(tyz.f, sqrt(tyz.pxz_ty_r)./(2*pi*tyz.f), 'DisplayName', 'Ty'); +plot(rz.f, sqrt(rz.pxsp_r)./(2*pi*rz.f), 'DisplayName', 'Rz'); +hold off; +set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log'); +xlabel('Frequency [Hz]'); ylabel('ASD of the displacement $\left[\frac{m}{\sqrt{Hz}}\right]$') +legend('Location', 'southwest'); +xlim([2, 500]); + + + +% #+NAME: fig:dist_effect_relative_motion +% #+CAPTION: Amplitude Spectral Density of the relative displacement of the hexapod with respect to the granite due to different sources of perturbation ([[./figs/dist_effect_relative_motion.png][png]], [[./figs/dist_effect_relative_motion.pdf][pdf]]) +% [[file:figs/dist_effect_relative_motion.png]] + + +figure; +hold on; +plot(gm.f, flip(sqrt(-cumtrapz(flip(gm.f), flip(gm.psd_rv./((2*pi*gm.f).^2))))), 'DisplayName', 'Ground Motion'); +plot(tyz.f, flip(sqrt(-cumtrapz(flip(tyz.f), flip(tyz.pxz_ty_r./((2*pi*tyz.f).^2))))), 'DisplayName', 'Ty'); +plot(rz.f, flip(sqrt(-cumtrapz(flip(rz.f), flip(rz.pxsp_r./((2*pi*rz.f).^2))))), 'DisplayName', 'Rz'); +hold off; +set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log'); +xlabel('Frequency [Hz]'); ylabel('CAS of the relative displacement $[m]$') +legend('Location', 'southwest'); +xlim([2, 500]); ylim([1e-11, 1e-6]); + +% 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 [[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. + + +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; + +figure; +hold on; +set(gca,'ColorOrderIndex',2); +plot(tyz.f, sqrt(tyz.psd_f), 'DisplayName', 'F - Ty'); +plot(rz.f, sqrt(rz.psd_f), 'DisplayName', 'F - Rz'); +hold off; +set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log'); +xlabel('Frequency [Hz]'); ylabel('ASD of the disturbance force $\left[\frac{F}{\sqrt{Hz}}\right]$') +legend('Location', 'southwest'); +xlim([2, 500]); + +% Noise Budget +% <> + +% 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. + + +% Power Spectral Density of the relative Displacement +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; + +figure; +hold on; +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 $\left[\frac{m}{\sqrt{Hz}}\right]$') +legend('Location', 'southwest'); +xlim([2, 500]); + + + +% #+NAME: fig:psd_effect_dist_verif +% #+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]] + + + +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]); + +% Approximation +% We approximate the PSD of the disturbance with the following transfer functions. + +G_ty = 0.1*(s+634.3)*(s+283.7)/((s+2*pi)*(s+2*pi)); +G_rz = 0.5*(s+418.8)*(s+36.51)*(s^2 + 110.9*s + 3.375e04)/((s+0.7324)*(s+0.546)*(s^2 + 0.6462*s + 2.391e04)); +G_gm = 0.002*(s^2 + 3.169*s + 27.74)/(s*(s+32.73)*(s+8.829)*(s+7.983)^2); + + + +% We compute the effect of these approximate disturbances on $D$. + +% Power Spectral Density of the relative Displacement +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; + +figure; +ax1 = subplot(1, 2, 1); +hold on; +set(gca,'ColorOrderIndex',2); +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(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 $\left[\frac{F}{\sqrt{Hz}}\right]$') +legend('Location', 'southwest'); +xlim([2, 500]); + +ax2 = subplot(1, 2, 2); +hold on; +plot(gm.f, sqrt(psd_gm_d), 'DisplayName', 'D - Gm'); +set(gca,'ColorOrderIndex',1); +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 $\left[\frac{m}{\sqrt{Hz}}\right]$') +legend('Location', 'southwest'); +xlim([2, 500]); + + + +% #+NAME: fig:estimate_spectral_density_disturbances +% #+CAPTION: Estimated spectral density of the disturbances ([[./figs/estimate_spectral_density_disturbances.png][png]], [[./figs/estimate_spectral_density_disturbances.pdf][pdf]]) +% [[file:figs/estimate_spectral_density_disturbances.png]] + + +figure; +hold on; +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(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]') +legend('location', 'northeast'); +xlim([2, 500]); ylim([1e-11, 1e-6]); + +% Save +% The PSD of the disturbance force are now saved for further noise budgeting when control is applied (the mat file is accessible [[file:mat/dist_psd.mat][here]]). + + +dist_f = struct(); + +dist_f.f = gm.f; % Frequency Vector [Hz] + +dist_f.psd_gm = gm.psd_gm; % Power Spectral Density of the Ground Motion [m^2/Hz] +dist_f.psd_ty = tyz.psd_f; % Power Spectral Density of the force induced by the Ty stage in the Z direction [N^2/Hz] +dist_f.psd_rz = rz.psd_f; % Power Spectral Density of the force induced by the Rz stage in the Z direction [N^2/Hz] + +dist_f.G_gm = G_ty; +dist_f.G_ty = G_rz; +dist_f.G_rz = G_gm; + +save('./disturbances/mat/dist_psd.mat', 'dist_f'); + +% Display Obtained Disturbances + +initDisturbances(); +load('./mat/nass_disturbances.mat', 'Dwx', 'Dwy', 'Dwz', 'Fty_x', 'Fty_z', 'Frz_z', 'Fd', 'Ts', 't'); + +figure; +hold on; +plot(t, Dwx, 'DisplayName', 'Dw x'); +plot(t, Dwy, 'DisplayName', 'Dw y'); +plot(t, Dwz, 'DisplayName', 'Dw z'); +hold off; +xlabel('Time [s]'); ylabel('Amplitude [m]'); +legend('location', 'north east'); + +figure; +hold on; +plot(t, Fty_x, 'DisplayName', 'Ty x'); +plot(t, Fty_z, 'DisplayName', 'Ty z'); +plot(t, Frz_z, 'DisplayName', 'Rz z'); +hold off; +xlabel('Time [s]'); ylabel('Force [N]'); +legend('location', 'north east'); diff --git a/metrology/matlab/modal_frf_coh.m b/metrology/matlab/modal_frf_coh.m new file mode 100644 index 0000000..ebf57f9 --- /dev/null +++ b/metrology/matlab/modal_frf_coh.m @@ -0,0 +1,88 @@ +% computeReferencePose +% :PROPERTIES: +% :header-args:matlab+: :comments none :mkdirp yes +% :header-args:matlab+: :comments org :mkdirp yes +% :header-args:matlab+: :eval no :results none +% :END: +% <> + +% This Matlab function is accessible [[file:src/computeReferencePose.m][here]]. + + +function [WTr] = computeReferencePose(Dy, Ry, Rz, Dh, Dn) +% computeReferencePose - Compute the homogeneous transformation matrix corresponding to the wanted pose of the sample +% +% Syntax: [WTr] = computeReferencePose(Dy, Ry, Rz, Dh, Dn) +% +% Inputs: +% - Dy - Reference of the Translation Stage [m] +% - Ry - Reference of the Tilt Stage [rad] +% - Rz - Reference of the Spindle [rad] +% - Dh - Reference of the Micro Hexapod (Pitch, Roll, Yaw angles) [m, m, m, rad, rad, rad] +% - Dn - Reference of the Nano Hexapod [m, m, m, rad, rad, rad] +% +% Outputs: +% - WTr - + + %% Translation Stage + Rty = [1 0 0 0; + 0 1 0 Dy; + 0 0 1 0; + 0 0 0 1]; + + %% Tilt Stage - Pure rotating aligned with Ob + Rry = [ cos(Ry) 0 sin(Ry) 0; + 0 1 0 0; + -sin(Ry) 0 cos(Ry) 0; + 0 0 0 1]; + + %% Spindle - Rotation along the Z axis + Rrz = [cos(Rz) -sin(Rz) 0 0 ; + sin(Rz) cos(Rz) 0 0 ; + 0 0 1 0 ; + 0 0 0 1 ]; + + + %% Micro-Hexapod + Rhx = [1 0 0; + 0 cos(Dh(4)) -sin(Dh(4)); + 0 sin(Dh(4)) cos(Dh(4))]; + + Rhy = [ cos(Dh(5)) 0 sin(Dh(5)); + 0 1 0; + -sin(Dh(5)) 0 cos(Dh(5))]; + + Rhz = [cos(Dh(6)) -sin(Dh(6)) 0; + sin(Dh(6)) cos(Dh(6)) 0; + 0 0 1]; + + Rh = [1 0 0 Dh(1) ; + 0 1 0 Dh(2) ; + 0 0 1 Dh(3) ; + 0 0 0 1 ]; + + Rh(1:3, 1:3) = Rhz*Rhy*Rhx; + + %% Nano-Hexapod + Rnx = [1 0 0; + 0 cos(Dn(4)) -sin(Dn(4)); + 0 sin(Dn(4)) cos(Dn(4))]; + + Rny = [ cos(Dn(5)) 0 sin(Dn(5)); + 0 1 0; + -sin(Dn(5)) 0 cos(Dn(5))]; + + Rnz = [cos(Dn(6)) -sin(Dn(6)) 0; + sin(Dn(6)) cos(Dn(6)) 0; + 0 0 1]; + + Rn = [1 0 0 Dn(1) ; + 0 1 0 Dn(2) ; + 0 0 1 Dn(3) ; + 0 0 0 1 ]; + + Rn(1:3, 1:3) = Rnx*Rny*Rnz; + + %% Total Homogeneous transformation + WTr = Rty*Rry*Rrz*Rh*Rn; +end diff --git a/simscape/matlab/modal_frf_coh.m b/simscape/matlab/modal_frf_coh.m new file mode 100644 index 0000000..990c4a2 --- /dev/null +++ b/simscape/matlab/modal_frf_coh.m @@ -0,0 +1,25 @@ +%% Clear Workspace and Close figures +clear; close all; clc; + +%% Intialize Laplace variable +s = zpk('s'); + +cd('../'); + +% Simulink Project - Startup and Shutdown scripts +% <> + +% From the [[https://mathworks.com/products/simulink/projects.html][Simulink project]] mathworks page: +% #+begin_quote +% SimulinkĀ® and Simulink Projects provide a collaborative, scalable environment that enables teams to manage their files and data in one place. + +% With Simulink Projects, you can: +% - *Collaborate*: Enforce companywide standards such as company tools, libraries, and standard startup and shutdown scripts. Share your work with rich sharing options including MATLABĀ® toolboxes, email, and archives. +% - *Automate*: Set up your project environment correctly every time by automating steps such as loading the data, managing the path, and opening the models. +% - *Integrate with source control*: Enable easy integration with source control and configuration management tools. +% #+end_quote + +% The project can be opened using the =simulinkproject= function: + + +simulinkproject('./');

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