From 64c072f18794457601495192ab2078433c5cc273 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Wed, 6 Nov 2024 16:29:01 +0100 Subject: [PATCH] Add introduction --- figs/ustation_dist_source_ground_motion.pdf | Bin 44011 -> 38790 bytes figs/ustation_dist_source_ground_motion.png | Bin 48024 -> 47458 bytes figs/ustation_geophone_picture.jpg | Bin 0 -> 53377 bytes figs/ustation_ground_disturbance.pdf | Bin 31190 -> 60046 bytes figs/ustation_ground_disturbance.png | Bin 26460 -> 44686 bytes matlab/mat/nass_model_conf_log.mat | Bin 225 -> 223 bytes matlab/mat/nass_model_disturbances.mat | Bin 133616 -> 537 bytes matlab/mat/ustation_disturbance_psd.mat | Bin 56243 -> 36756 bytes .../mat/ustation_disturbance_sensitivity.mat | Bin 18740 -> 18740 bytes matlab/mat/ustation_ground_motion.mat | Bin 598731 -> 386386 bytes simscape-micro-station.org | 113 +++++++++++------- simscape-micro-station.pdf | Bin 8368269 -> 8447471 bytes simscape-micro-station.tex | 59 ++++++--- 13 files changed, 113 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glossary + +PoI | Point of interest + ** TODO [#C] Add picture of measured ground motion ** TODO [#C] Add screenshot of Simscape model ** WAIT [#B] I have no measurement of horizontal ground motion :@marc: @@ -874,7 +878,25 @@ xlim([2, 500]); * Introduction :ignore: -Introduction... +From the start of this work, it became increasingly clear that an accurate model of the micro-station was necessary. + +First, during the uniaxial study, it became apparent that the micro-station dynamics affects the nano-hexapod dynamics. +Then, using the 3-DoF rotating model, it was discovered that the rotation of the nano-hexapod induces gyroscopic effects that affects the system dynamics, and that it should therefore be modelled. +Finally, performing a modal analysis of the micro-station showed how complex the dynamics of the station is. +It also confirmed that each stage behaves as a rigid body in the frequency range of interest. +Therefore a multi-body model seems a good candidate to accurately represent the micro-station dynamics. + +In this report, the development of such multi-body model is presented. + +First, each stage of the micro-station is described. +The kinematics of the micro-station (i.e. how the motion of the stages are combined) is presented in Section ref:sec:ustation_kinematics. + +Then, the multi-body model is presented and tuned to match the measured dynamics of the micro-station (Section ref:sec:ustation_modeling). + +Disturbances affecting the positioning accuracy also need to be modelled properly. +To do so, the effect of these disturbances are first measured experimental and then injected in the multi-body model (Section ref:sec:ustation_disturbances). + +To validate the accuracy of the micro-station model, "real world" experiments are simulated and compared with measurements in Section ref:sec:ustation_experiments. # #+name: tab:ustation_section_matlab_code # #+caption: Report sections and corresponding Matlab files @@ -1928,65 +1950,70 @@ Therefore, from a control point of view, they are not important. **** Ground Motion -The ground motion is simply measured by using a sensitive 3-axis geophone placed on the ground. +The ground motion is measured by using a sensitive 3-axis geophone[fn:11] placed on the ground. The generated voltages are recorded with a high resolution DAC, and converted to displacement using the Geophone sensitivity transfer function. The obtained ground motion displacement is shown in Figure ref:fig:ustation_ground_disturbance. #+begin_src matlab %% Compute Floor Motion Spectral Density % Load floor motion data -% t: time in [s] -% V: measured voltage genrated by the geophone and amplified by a 60dB gain voltage amplifier [V] -load('ustation_ground_motion.mat', 't', 'V'); +% velocity in [m/s] is measured in X, Y and Z directions +load('ustation_ground_motion.mat', 'Ts', 'Fs', 'vel_x', 'vel_y', 'vel_z', 't'); -% Geophone Transfer Function -Tg = 88; % Sensitivity [V/(m/s)] -w0 = 2*2*pi; % Cut-off frequency [rad/s] -xi = 0.7; % Damping ratio +% Estimate ground displacement from measured velocity +% This is done by integrating the motion +gm_x = lsim(1/(s+0.1*2*pi), vel_x, t); +gm_y = lsim(1/(s+0.1*2*pi), vel_y, t); +gm_z = lsim(1/(s+0.1*2*pi), vel_z, t); -G_geo = Tg*s*s^2/(s^2 + 2*xi*w0*s + w0^2); % Geophone's transfer function [V/m] - -% Voltage amplifier transfer function -g0 = 10^(60/20); % [abs] - -% Compute measured voltage PSD -Ts = (t(2)-t(1)); % Sampling Time [s] Nfft = floor(2/Ts); win = hanning(Nfft); Noverlap = floor(Nfft/2); -[pxx_V, f_gm] = pwelch(V, win, Noverlap, Nfft, 1/Ts); % [V^2/Hz] +[pxx_gm_vx, f_gm] = pwelch(vel_x, win, Noverlap, Nfft, 1/Ts); +[pxx_gm_vy, ~] = pwelch(vel_y, win, Noverlap, Nfft, 1/Ts); +[pxx_gm_vz, ~] = pwelch(vel_z, win, Noverlap, Nfft, 1/Ts); -% Ground Motion ASD -pxx_gm_z = pxx_V./abs(squeeze(freqresp(G_geo*g0, f_gm, 'Hz'))).^2; % [m^2/Hz] -% Assumption here that horizontal ground motion is ~25% smaller -% than vertical one. -pxx_gm_x = (0.7)^2*pxx_gm_z; % [m^2/Hz] -pxx_gm_y = (0.8)^2*pxx_gm_z; % [m^2/Hz] +% Convert PSD in velocity to PSD in displacement +pxx_gm_x = pxx_gm_vx./((2*pi*f_gm).^2); +pxx_gm_y = pxx_gm_vy./((2*pi*f_gm).^2); +pxx_gm_z = pxx_gm_vz./((2*pi*f_gm).^2); #+end_src #+begin_src matlab :exports none :results none -% Estimate ground motion -w0_min = 0.1*2*pi; -gm_z = lsim(inv(g0*G_geo)*((s/w0_min)/(1+s/w0_min))^3, detrend(V, 0), t); - %% Measured ground motion figure; hold on; -plot(t(t>50)-50, 1e6*gm_z(t>50)) +plot(t, 1e6*gm_x, 'DisplayName', '$D_{xf}$') +plot(t, 1e6*gm_y, 'DisplayName', '$D_{yf}$') +plot(t, 1e6*gm_z, 'DisplayName', '$D_{zf}$') hold off; xlabel('Time [s]'); -ylabel('Vertical motion [$\mu$m]') +ylabel('Ground motion [$\mu$m]') +xlim([0, 5]); ylim([-2, 2]) +leg = legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1); +leg.ItemTokenSize(1) = 15; #+end_src -#+begin_src matlab :tangle no :exports results :results file replace -exportFig('figs/ustation_ground_disturbance.pdf', 'width', 'normal', 'height', 'short'); +#+begin_src matlab :tangle no :exports results :results file none +exportFig('figs/ustation_ground_disturbance.pdf', 'width', 'half', 'height', 450); #+end_src +#+attr_latex: :options [b]{0.54\linewidth} +#+begin_minipage #+name: fig:ustation_ground_disturbance #+caption: Measured ground motion -#+RESULTS: +#+attr_latex: :scale 1 :float nil [[file:figs/ustation_ground_disturbance.png]] +#+end_minipage +\hfill +#+attr_latex: :options [b]{0.44\linewidth} +#+begin_minipage +#+name: fig:ustation_geophone_picture +#+caption: (3D) L-4C geophone +#+attr_latex: :width 0.92\linewidth :float nil +[[file:figs/ustation_geophone_picture.jpg]] +#+end_minipage **** Ty Stage @@ -2381,7 +2408,7 @@ pxx_dy_fz = pxx_dy_dz./abs(squeeze(freqresp(Gd('Dz', 'Fdy_z'), f_dy, 'Hz'))).^2; % in the Simscape model % Ground motion -min_f = 1; max_f = 500; +min_f = 1; max_f = 100; gm_dist.f = f_gm(f_gm < max_f & f_gm > min_f); gm_dist.pxx_x = pxx_gm_x(f_gm < max_f & f_gm > min_f); gm_dist.pxx_y = pxx_gm_y(f_gm < max_f & f_gm > min_f); @@ -2573,7 +2600,6 @@ exportFig('figs/ustation_dist_source_ground_motion_time.pdf', 'width', 'third', :HEADER-ARGS:matlab+: :tangle matlab/ustation_4_experiments.m :END: <> - ** Introduction :ignore: In order to fully validate the micro-station multi-body model, two time domain simulations corresponding to typical use cases are performed. @@ -2797,6 +2823,9 @@ exportFig('figs/ustation_errors_model_dy_vertical.pdf', 'width', 'half', 'height [[file:figs/ustation_errors_model_dy_vertical.png]] * Conclusion +:PROPERTIES: +:UNNUMBERED: t +:END: <> In order to have good model: @@ -5350,14 +5379,14 @@ Otherwise, when the limbs' lengths derived yield complex numbers, then the posit #+end_src * Footnotes - -[fn:10]Laser source is manufactured by Agilent (5519b) +[fn:11]A 3-Axis L4C geophone manufactured Sercel was used. +[fn:10]Laser source is manufactured by Agilent (5519b). [fn:9]The special optics (straightness interferometer and reflector) are manufactured by Agilent (10774A). -[fn:8]C8 capacitive sensors and CPL290 capacitive driver electronics from Lion Precision +[fn:8]C8 capacitive sensors and CPL290 capacitive driver electronics from Lion Precision. [fn:7]The Spindle Error Analyzer is made by Lion Precision. [fn:6]The tools presented here are largely taken from [[cite:&taghirad13_paral]]. -[fn:5]Rotations are non commutative in 3D -[fn:4]Ball cage (N501) and guide bush (N550) from Mahr are used -[fn:3]Modified Zonda Hexapod by Symetrie -[fn:2]Made by LAB Motion Systems -[fn:1]HCR 35 A C1, from THK +[fn:5]Rotations are non commutative in 3D. +[fn:4]Ball cage (N501) and guide bush (N550) from Mahr are used. +[fn:3]Modified Zonda Hexapod by Symetrie. +[fn:2]Made by LAB Motion Systems. +[fn:1]HCR 35 A C1, from THK. diff --git a/simscape-micro-station.pdf b/simscape-micro-station.pdf index acd54cbd3a6aee6b81a41353db8ffff10f5c4891..f05bf3ede0529105c8c4d927bbf5a0ce34fa923d 100644 GIT binary patch delta 235014 zcmYgYbwCtd_m=MNP7wsDT~ZpUl}>4qmXeYXSh~ALQ0eXlMNmoU7LgV~I;2DVUElZP z`+k3%Wu6=7KKGfKvvcm9C2si|ZEqk1z2-44gyM!IM->rBAwlIruD(=rc_l*}zIRUX z!h~@2cX-=cev*+w+LOg`Mt+WA1SZd;=Hm~0OBlT5Qz#W>z6Qa5EU0~NXA^zf)6o|*3V5!f;wrh^Mtkj-h1#4Pu%4iDr-zz z`92m`Ys~k_x}M)%`E#kSR 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