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b/micro-station-compliance/index.html new file mode 100644 index 0000000..edf0d56 Binary files /dev/null and b/micro-station-compliance/index.html differ diff --git a/micro-station-compliance/index.org b/micro-station-compliance/index.org new file mode 100644 index 0000000..ccc09d3 --- /dev/null +++ b/micro-station-compliance/index.org @@ -0,0 +1,473 @@ +#+TITLE: Compliance Measurement of the Micro Station +:DRAWER: +#+STARTUP: overview + +#+LANGUAGE: en +#+EMAIL: dehaeze.thomas@gmail.com +#+AUTHOR: Dehaeze Thomas + +#+HTML_LINK_HOME: ../index.html +#+HTML_LINK_UP: ../index.html + +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: + +#+HTML_MATHJAX: align: center tagside: right font: TeX + +#+PROPERTY: header-args:matlab :session *MATLAB* +#+PROPERTY: header-args:matlab+ :comments org +#+PROPERTY: header-args:matlab+ :results none +#+PROPERTY: header-args:matlab+ :exports both +#+PROPERTY: header-args:matlab+ :eval no-export +#+PROPERTY: header-args:matlab+ :output-dir figs + +#+PROPERTY: header-args:shell :eval no-export +:END: + +* Setup +** Position of inertial sensors on top of the micro-hexapod +Orientation is relative to the frame determined by the X-ray +| *Num* | *Position* | *Orientation* | *Sensibility* | *Channels* | +|-------+------------+---------------+---------------+------------| +| 1 | [0, +A, 0] | [x, y, z] | 1V/g | 1-3 | +| 2 | [-B, 0, 0] | [x, y, z] | 1V/g | 4-6 | +| 3 | [0, -A, 0] | [x, y, z] | 0.1V/g | 7-9 | +| 4 | [+B, 0, 0] | [x, y, z] | 1V/g | 10-12 | + +Instrumented Hammer: +- Channel 13 +- Sensibility: 230 uV/N + +| Acc Number | Dir | Channel Number | +|------------+-----+----------------| +| 1 | x | 1 | +| 1 | y | 2 | +| 1 | z | 3 | +| 2 | x | 4 | +| 2 | y | 5 | +| 2 | z | 6 | +| 3 | x | 7 | +| 3 | y | 8 | +| 3 | z | 9 | +| 4 | x | 10 | +| 4 | y | 11 | +| 4 | z | 12 | +| Hammer | | 13 | + +From the acceleration measurement of the 4 accelerometers, we can compute the translations and rotations: +| | *Formula* | +|-------+--------------------------| +| $D_x$ | (1x + 2x + 3x + 4x)/4 | +| $D_y$ | (1y + 2y + 3y + 4y)/4 | +| $D_z$ | (1z + 2z + 3z + 4z)/4 | +| $R_x$ | (1z - 3z)/A | +| $R_y$ | (2z - 4z)/B | +| $R_z$ | (3x - 1x)/A, (4y - 2y)/B | + + +| | *Formula* | +|-------+-----------------------| +| $D_x$ | (1 + 4 + 7 + 10)/4 | +| $D_y$ | (2 + 5 + 8 + 11)/4 | +| $D_z$ | (3 + 6 + 9 + 12)/4 | +| $R_x$ | (1 - 9)/A | +| $R_y$ | (6 - 12)/B | +| $R_z$ | (7 - 1)/A, (11 - 5)/B | + +** Hammer blow position/orientation + +| *Num* | *Direction* | *Position* | +|-------+-------------+------------| +| 1 | -Y | [0, +A, 0] | +| 2 | -Z | [0, +A, 0] | +| 3 | X | [-B, 0, 0] | +| 4 | -Z | [-B, 0, 0] | +| 5 | Y | [0, -A, 0] | +| 6 | -Z | [0, -A, 0] | +| 7 | -X | [+B, 0, 0] | +| 8 | -Z | [+B, 0, 0] | +| 9 | -X | [0, -A, 0] | +| 10 | -X | [0, +A, 0] | + +From hammer blows to pure forces / torques: +| | *Formula* | Alternative | +|-------+--------------+-------------| +| $F_x$ | +3 | -7 | +| $F_y$ | -1 | +5 | +| $F_z$ | -(2 + 6)/2 | -(4 + 8)/2 | +| $M_x$ | A/2*(2 - 6) | | +| $M_y$ | B/2*(8 - 4) | | +| $M_z$ | A/2*(10 - 9) | | + +* Results +** Matlab Init :noexport:ignore: +#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) + <> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes + <> +#+end_src + +** Load Data +#+begin_src matlab + m1 = load('data/Measurement1.mat'); + m2 = load('data/Measurement2.mat'); + m3 = load('data/Measurement3.mat'); + m4 = load('data/Measurement4.mat'); + m5 = load('data/Measurement5.mat'); + m6 = load('data/Measurement6.mat'); + m7 = load('data/Measurement7.mat'); + m8 = load('data/Measurement8.mat'); + m9 = load('data/Measurement9.mat'); + m10 = load('data/Measurement10.mat'); +#+end_src + +** Compute Transfer Functions +#+begin_src matlab + freqs = m3.FFT1_H1_1_13_X_Val; + w = 2*pi*freqs'; + + A = 0.14; + B = 0.14; +#+end_src + +#+begin_src matlab + G = zeros(6,6,length(freqs)); + + % Fx + G(1,1,:) = (m3.FFT1_H1_1_13_Y_ReIm + m3.FFT1_H1_4_13_Y_ReIm + m3.FFT1_H1_7_13_Y_ReIm + m3.FFT1_H1_10_13_Y_ReIm)./4; + G(2,1,:) = (m3.FFT1_H1_2_13_Y_ReIm + m3.FFT1_H1_5_13_Y_ReIm + m3.FFT1_H1_8_13_Y_ReIm + m3.FFT1_H1_11_13_Y_ReIm)./4; + G(3,1,:) = (m3.FFT1_H1_3_13_Y_ReIm + m3.FFT1_H1_6_13_Y_ReIm + m3.FFT1_H1_9_13_Y_ReIm + m3.FFT1_H1_12_13_Y_ReIm)./4; + G(4,1,:) = (m3.FFT1_H1_1_13_Y_ReIm - m3.FFT1_H1_9_13_Y_ReIm )./A; + G(5,1,:) = (m3.FFT1_H1_6_13_Y_ReIm - m3.FFT1_H1_12_13_Y_ReIm)./B; + G(6,1,:) = (m3.FFT1_H1_7_13_Y_ReIm - m3.FFT1_H1_1_13_Y_ReIm )./A; + + % Fy + G(1,2,:) = -(m1.FFT1_H1_2_13_Y_ReIm + m1.FFT1_H1_5_13_Y_ReIm + m1.FFT1_H1_8_13_Y_ReIm + m1.FFT1_H1_11_13_Y_ReIm)./4; + G(2,2,:) = -(m1.FFT1_H1_2_13_Y_ReIm + m1.FFT1_H1_5_13_Y_ReIm + m1.FFT1_H1_8_13_Y_ReIm + m1.FFT1_H1_11_13_Y_ReIm)./4; + G(3,2,:) = -(m1.FFT1_H1_3_13_Y_ReIm + m1.FFT1_H1_6_13_Y_ReIm + m1.FFT1_H1_9_13_Y_ReIm + m1.FFT1_H1_12_13_Y_ReIm)./4; + G(4,2,:) = -(m1.FFT1_H1_1_13_Y_ReIm - m1.FFT1_H1_9_13_Y_ReIm )./A; + G(5,2,:) = -(m1.FFT1_H1_6_13_Y_ReIm - m1.FFT1_H1_12_13_Y_ReIm)./B; + G(6,2,:) = -(m1.FFT1_H1_7_13_Y_ReIm - m1.FFT1_H1_1_13_Y_ReIm )./A; + + + % Fz + G(1,3,:) = -1/2./(1./(m2.FFT1_H1_1_13_Y_ReIm + m2.FFT1_H1_4_13_Y_ReIm + m2.FFT1_H1_7_13_Y_ReIm + m2.FFT1_H1_10_13_Y_ReIm) + ... + 1./(m6.FFT1_H1_1_13_Y_ReIm + m6.FFT1_H1_4_13_Y_ReIm + m6.FFT1_H1_7_13_Y_ReIm + m6.FFT1_H1_10_13_Y_ReIm)); + G(2,3,:) = -1/2./(1./(m2.FFT1_H1_2_13_Y_ReIm + m2.FFT1_H1_5_13_Y_ReIm + m2.FFT1_H1_8_13_Y_ReIm + m2.FFT1_H1_11_13_Y_ReIm) + ... + 1./(m6.FFT1_H1_2_13_Y_ReIm + m6.FFT1_H1_5_13_Y_ReIm + m6.FFT1_H1_8_13_Y_ReIm + m6.FFT1_H1_11_13_Y_ReIm)); + G(3,3,:) = -1/2./(1./(m2.FFT1_H1_3_13_Y_ReIm + m2.FFT1_H1_6_13_Y_ReIm + m2.FFT1_H1_9_13_Y_ReIm + m2.FFT1_H1_12_13_Y_ReIm) + ... + 1./(m6.FFT1_H1_3_13_Y_ReIm + m6.FFT1_H1_6_13_Y_ReIm + m6.FFT1_H1_9_13_Y_ReIm + m6.FFT1_H1_12_13_Y_ReIm)); + G(4,3,:) = -2/A./(1./(m2.FFT1_H1_1_13_Y_ReIm - m2.FFT1_H1_9_13_Y_ReIm) + ... + 1./(m6.FFT1_H1_1_13_Y_ReIm - m6.FFT1_H1_9_13_Y_ReIm)); + G(5,3,:) = -2/B./(1./(m2.FFT1_H1_6_13_Y_ReIm - m2.FFT1_H1_12_13_Y_ReIm) + ... + 1./(m6.FFT1_H1_6_13_Y_ReIm - m6.FFT1_H1_12_13_Y_ReIm)); + G(6,3,:) = -2/A./(1./(m2.FFT1_H1_7_13_Y_ReIm - m2.FFT1_H1_1_13_Y_ReIm) + ... + 1./(m6.FFT1_H1_7_13_Y_ReIm - m6.FFT1_H1_1_13_Y_ReIm)); + + % Mx + G(1,4,:) = 1/A/2./(1./(m2.FFT1_H1_1_13_Y_ReIm + m2.FFT1_H1_4_13_Y_ReIm + m2.FFT1_H1_7_13_Y_ReIm + m2.FFT1_H1_10_13_Y_ReIm) - ... + 1./(m6.FFT1_H1_1_13_Y_ReIm + m6.FFT1_H1_4_13_Y_ReIm + m6.FFT1_H1_7_13_Y_ReIm + m6.FFT1_H1_10_13_Y_ReIm)); + G(2,4,:) = 1/A/2./(1./(m2.FFT1_H1_2_13_Y_ReIm + m2.FFT1_H1_5_13_Y_ReIm + m2.FFT1_H1_8_13_Y_ReIm + m2.FFT1_H1_11_13_Y_ReIm) - ... + 1./(m6.FFT1_H1_2_13_Y_ReIm + m6.FFT1_H1_5_13_Y_ReIm + m6.FFT1_H1_8_13_Y_ReIm + m6.FFT1_H1_11_13_Y_ReIm)); + G(3,4,:) = 1/A/2./(1./(m2.FFT1_H1_3_13_Y_ReIm + m2.FFT1_H1_6_13_Y_ReIm + m2.FFT1_H1_9_13_Y_ReIm + m2.FFT1_H1_12_13_Y_ReIm) - ... + 1./(m6.FFT1_H1_3_13_Y_ReIm + m6.FFT1_H1_6_13_Y_ReIm + m6.FFT1_H1_9_13_Y_ReIm + m6.FFT1_H1_12_13_Y_ReIm)); + G(4,4,:) = 1/A^2*2./(1./(m2.FFT1_H1_1_13_Y_ReIm - m2.FFT1_H1_9_13_Y_ReIm) - ... + 1./(m6.FFT1_H1_1_13_Y_ReIm - m6.FFT1_H1_9_13_Y_ReIm)); + G(5,4,:) = 2/A/B./(1./(m2.FFT1_H1_6_13_Y_ReIm - m2.FFT1_H1_12_13_Y_ReIm) - ... + 1./(m6.FFT1_H1_6_13_Y_ReIm - m6.FFT1_H1_12_13_Y_ReIm)); + G(6,4,:) = 1/A^2*2./(1./(m2.FFT1_H1_7_13_Y_ReIm - m2.FFT1_H1_1_13_Y_ReIm) - ... + 1./(m6.FFT1_H1_7_13_Y_ReIm - m6.FFT1_H1_1_13_Y_ReIm)); + + % My + G(1,5,:) = 1/B/2./(1./(m8.FFT1_H1_1_13_Y_ReIm + m8.FFT1_H1_4_13_Y_ReIm + m8.FFT1_H1_7_13_Y_ReIm + m8.FFT1_H1_10_13_Y_ReIm) - ... + 1./(m4.FFT1_H1_1_13_Y_ReIm + m4.FFT1_H1_4_13_Y_ReIm + m4.FFT1_H1_7_13_Y_ReIm + m4.FFT1_H1_10_13_Y_ReIm)); + G(2,5,:) = 1/B/2./(1./(m8.FFT1_H1_2_13_Y_ReIm + m8.FFT1_H1_5_13_Y_ReIm + m8.FFT1_H1_8_13_Y_ReIm + m8.FFT1_H1_11_13_Y_ReIm) - ... + 1./(m4.FFT1_H1_2_13_Y_ReIm + m4.FFT1_H1_5_13_Y_ReIm + m4.FFT1_H1_8_13_Y_ReIm + m4.FFT1_H1_11_13_Y_ReIm)); + G(3,5,:) = 1/B/2./(1./(m8.FFT1_H1_3_13_Y_ReIm + m8.FFT1_H1_6_13_Y_ReIm + m8.FFT1_H1_9_13_Y_ReIm + m8.FFT1_H1_12_13_Y_ReIm) - ... + 1./(m4.FFT1_H1_3_13_Y_ReIm + m4.FFT1_H1_6_13_Y_ReIm + m4.FFT1_H1_9_13_Y_ReIm + m4.FFT1_H1_12_13_Y_ReIm)); + G(4,5,:) = 2/B/A./(1./(m8.FFT1_H1_1_13_Y_ReIm - m8.FFT1_H1_9_13_Y_ReIm) - ... + 1./(m4.FFT1_H1_1_13_Y_ReIm - m4.FFT1_H1_9_13_Y_ReIm)); + G(5,5,:) = 1/B^2*2./(1./(m8.FFT1_H1_6_13_Y_ReIm - m8.FFT1_H1_12_13_Y_ReIm) - ... + 1./(m4.FFT1_H1_6_13_Y_ReIm - m4.FFT1_H1_12_13_Y_ReIm)); + G(6,5,:) = 2/B/A./(1./(m8.FFT1_H1_7_13_Y_ReIm - m8.FFT1_H1_1_13_Y_ReIm) - ... + 1./(m4.FFT1_H1_7_13_Y_ReIm - m4.FFT1_H1_1_13_Y_ReIm)); + + % Mz + G(1,6,:) = 1/A/2./(1./(m10.FFT1_H1_1_13_Y_ReIm + m10.FFT1_H1_4_13_Y_ReIm + m10.FFT1_H1_7_13_Y_ReIm + m10.FFT1_H1_10_13_Y_ReIm) - ... + 1./(m9.FFT1_H1_1_13_Y_ReIm + m9.FFT1_H1_4_13_Y_ReIm + m9.FFT1_H1_7_13_Y_ReIm + m9.FFT1_H1_10_13_Y_ReIm)); + G(2,6,:) = 1/A/2./(1./(m10.FFT1_H1_2_13_Y_ReIm + m10.FFT1_H1_5_13_Y_ReIm + m10.FFT1_H1_8_13_Y_ReIm + m10.FFT1_H1_11_13_Y_ReIm) - ... + 1./(m9.FFT1_H1_2_13_Y_ReIm + m9.FFT1_H1_5_13_Y_ReIm + m9.FFT1_H1_8_13_Y_ReIm + m9.FFT1_H1_11_13_Y_ReIm)); + G(3,6,:) = 1/A/2./(1./(m10.FFT1_H1_3_13_Y_ReIm + m10.FFT1_H1_6_13_Y_ReIm + m10.FFT1_H1_9_13_Y_ReIm + m10.FFT1_H1_12_13_Y_ReIm) - ... + 1./(m9.FFT1_H1_3_13_Y_ReIm + m9.FFT1_H1_6_13_Y_ReIm + m9.FFT1_H1_9_13_Y_ReIm + m9.FFT1_H1_12_13_Y_ReIm)); + G(4,6,:) = 1/A^2*2./(1./(m10.FFT1_H1_1_13_Y_ReIm - m10.FFT1_H1_9_13_Y_ReIm) - ... + 1./(m9.FFT1_H1_1_13_Y_ReIm - m9.FFT1_H1_9_13_Y_ReIm)); + G(5,6,:) = 2*A/B./(1./(m10.FFT1_H1_6_13_Y_ReIm - m10.FFT1_H1_12_13_Y_ReIm) - ... + 1./(m9.FFT1_H1_6_13_Y_ReIm - m9.FFT1_H1_12_13_Y_ReIm)); + G(6,6,:) = 1/A^2*2./(1./(m10.FFT1_H1_7_13_Y_ReIm - m10.FFT1_H1_1_13_Y_ReIm) - ... + 1./(m9.FFT1_H1_7_13_Y_ReIm - m9.FFT1_H1_1_13_Y_ReIm)); +#+end_src + +** Diagonal Dynamics +#+begin_src matlab + figure; + ax1 = subplot(2,1,1); + hold on; + plot(freqs, abs(squeeze(G(1,1,:))./(-w.^2)), '.') + plot(freqs, abs(squeeze(G(2,2,:))./(-w.^2)), '.') + plot(freqs, abs(squeeze(G(3,3,:))./(-w.^2)), '.') + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Magnitude [m/N]'); set(gca, 'XTickLabel',[]); + ylim([1e-9, 2e-6]); + + ax2 = subplot(2,1,2); + hold on; + plot(freqs, 180/pi*angle(squeeze(G(1,1,:))./(-w.^2)), '.', 'DisplayName', '$D_x/F_x$') + plot(freqs, 180/pi*angle(squeeze(G(2,2,:))./(-w.^2)), '.', 'DisplayName', '$D_y/F_y$') + plot(freqs, 180/pi*angle(squeeze(G(3,3,:))./(-w.^2)), '.', 'DisplayName', '$D_z/F_z$') + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + xlabel('Freqency [Hz]'); ylabel('Phase [deg]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([30, 300]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace + exportFig('figs/compliance_diagonal_translations.pdf', 'width', 'full', 'height', 'full'); +#+end_src + +#+name: fig:compliance_diagonal_translations +#+caption: Dynamics from Forces to Translations +#+RESULTS: +[[file:figs/compliance_diagonal_translations.png]] + +#+begin_src matlab + figure; + ax1 = subplot(2,1,1); + hold on; + plot(freqs, abs(squeeze(G(4,4,:))./(-w.^2)), '.') + plot(freqs, abs(squeeze(G(5,5,:))./(-w.^2)), '.') + plot(freqs, abs(squeeze(G(6,6,:))./(-w.^2)), '.') + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Magnitude [rad/Nm]'); set(gca, 'XTickLabel',[]); + ylim([1e-9, 2e-6]); + + ax2 = subplot(2,1,2); + hold on; + plot(freqs, 180/pi*angle(squeeze(G(4,4,:))./(-w.^2)), '.', 'DisplayName', '$R_x/M_x$') + plot(freqs, 180/pi*angle(squeeze(G(5,5,:))./(-w.^2)), '.', 'DisplayName', '$R_y/M_y$') + plot(freqs, 180/pi*angle(squeeze(G(6,6,:))./(-w.^2)), '.', 'DisplayName', '$R_z/M_z$') + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + xlabel('Freqency [Hz]'); ylabel('Phase [deg]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([30, 300]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace + exportFig('figs/compliance_diagonal_rotations.pdf', 'width', 'full', 'height', 'full'); +#+end_src + +#+name: fig:compliance_diagonal_rotations +#+caption: Dynamics from Torques to Rotations +#+RESULTS: +[[file:figs/compliance_diagonal_rotations.png]] + +| | Stiffness | Unit | +|-----------+-----------+----------| +| $K_x$ | 1e7 | [N/m] | +| $K_y$ | 1e7 | [N/m] | +| $K_z$ | 2e8 | [N/m] | +| $K_{R_x}$ | ? | [Nm/rad] | +| $K_{R_y}$ | 1.8e7 | [Nm/rad] | +| $K_{R_z}$ | 1e7 | [Nm/rad] | + +** Compare with Model +#+begin_src matlab + load('./mat/model.mat', 'Gm'); +#+end_src + +#+begin_src matlab + figure; + ax1 = subplot(2,1,1); + hold on; + plot(freqs, abs(squeeze(G(1,1,:))./(-w.^2)), '.') + plot(freqs, abs(squeeze(G(2,2,:))./(-w.^2)), '.') + plot(freqs, abs(squeeze(G(3,3,:))./(-w.^2)), '.') + set(gca,'ColorOrderIndex',1); + plot(freqs, abs(squeeze(freqresp(Gm(1,1,:), freqs, 'Hz'))), '-') + plot(freqs, abs(squeeze(freqresp(Gm(2,2,:), freqs, 'Hz'))), '-') + plot(freqs, abs(squeeze(freqresp(Gm(3,3,:), freqs, 'Hz'))), '-') + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Magnitude [m/N]'); set(gca, 'XTickLabel',[]); + ylim([1e-9, 2e-6]); + + ax2 = subplot(2,1,2); + hold on; + plot(freqs, 180/pi*angle(squeeze(G(1,1,:))./(-w.^2)), '.', 'DisplayName', '$D_x/F_x$') + plot(freqs, 180/pi*angle(squeeze(G(2,2,:))./(-w.^2)), '.', 'DisplayName', '$D_y/F_y$') + plot(freqs, 180/pi*angle(squeeze(G(3,3,:))./(-w.^2)), '.', 'DisplayName', '$D_z/F_z$') + set(gca,'ColorOrderIndex',1); + plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(1,1,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off') + plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(2,2,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off') + plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(3,3,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off') + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + xlabel('Freqency [Hz]'); ylabel('Phase [deg]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([30, 300]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace + exportFig('figs/compliance_diagonal_translations_comp_model.pdf', 'width', 'full', 'height', 'full'); +#+end_src + +#+name: fig:compliance_diagonal_translations_comp_model +#+caption: Dynamics from Forces to Translations +#+RESULTS: +[[file:figs/compliance_diagonal_translations_comp_model.png]] + +#+begin_src matlab + figure; + ax1 = subplot(2,1,1); + hold on; + plot(freqs, abs(squeeze(G(4,4,:))./(-w.^2)), '.') + plot(freqs, abs(squeeze(G(5,5,:))./(-w.^2)), '.') + plot(freqs, abs(squeeze(G(6,6,:))./(-w.^2)), '.') + set(gca,'ColorOrderIndex',1); + plot(freqs, abs(squeeze(freqresp(Gm(4,4,:), freqs, 'Hz'))), '-') + plot(freqs, abs(squeeze(freqresp(Gm(5,5,:), freqs, 'Hz'))), '-') + plot(freqs, abs(squeeze(freqresp(Gm(6,6,:), freqs, 'Hz'))), '-') + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Magnitude [rad/Nm]'); set(gca, 'XTickLabel',[]); + % ylim([1e-9, 2e-6]); + + ax2 = subplot(2,1,2); + hold on; + plot(freqs, 180/pi*angle(squeeze(G(4,4,:))./(-w.^2)), '.', 'DisplayName', '$R_x/M_x$') + plot(freqs, 180/pi*angle(squeeze(G(5,5,:))./(-w.^2)), '.', 'DisplayName', '$R_y/M_y$') + plot(freqs, 180/pi*angle(squeeze(G(6,6,:))./(-w.^2)), '.', 'DisplayName', '$R_z/M_z$') + set(gca,'ColorOrderIndex',1); + plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(4,4,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off') + plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(5,5,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off') + plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(6,6,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off') + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + xlabel('Freqency [Hz]'); ylabel('Phase [deg]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([30, 300]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace + exportFig('figs/compliance_diagonal_rotations_comp_model.pdf', 'width', 'full', 'height', 'full'); +#+end_src + +#+name: fig:compliance_diagonal_rotations_comp_model +#+caption: Dynamics from Torques to Rotations +#+RESULTS: +[[file:figs/compliance_diagonal_rotations_comp_model.png]] + +| | Stiffness | Unit | +|-----------+-----------+----------| +| $K_x$ | 1e7 | [N/m] | +| $K_y$ | 1e7 | [N/m] | +| $K_z$ | 2e8 | [N/m] | +| $K_{R_x}$ | 5e7 | [Nm/rad] | +| $K_{R_y}$ | 3e7 | [Nm/rad] | +| $K_{R_z}$ | 2e7 | [Nm/rad] | + +** Coupling Dynamics +#+begin_src matlab + figure; + ax1 = subplot(2,1,1); + hold on; + plot(freqs, abs(squeeze(G(1,1,:))./(-w.^2)), '.') + plot(freqs, abs(squeeze(G(2,1,:))./(-w.^2)), '.') + plot(freqs, abs(squeeze(G(3,1,:))./(-w.^2)), '.') + set(gca,'ColorOrderIndex',1); + plot(freqs, abs(squeeze(freqresp(Gm(1,1,:), freqs, 'Hz'))), '-') + plot(freqs, abs(squeeze(freqresp(Gm(2,1,:), freqs, 'Hz'))), '-') + plot(freqs, abs(squeeze(freqresp(Gm(3,1,:), freqs, 'Hz'))), '-') + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Magnitude [m/N]'); set(gca, 'XTickLabel',[]); + ylim([1e-9, 2e-6]); + + ax2 = subplot(2,1,2); + hold on; + plot(freqs, 180/pi*angle(squeeze(G(1,1,:))./(-w.^2)), '.', 'DisplayName', '$D_x/F_x$') + plot(freqs, 180/pi*angle(squeeze(G(2,1,:))./(-w.^2)), '.', 'DisplayName', '$D_y/F_x$') + plot(freqs, 180/pi*angle(squeeze(G(3,1,:))./(-w.^2)), '.', 'DisplayName', '$D_z/F_x$') + set(gca,'ColorOrderIndex',1); + plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(1,1,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off') + plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(2,1,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off') + plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(3,1,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off') + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + xlabel('Freqency [Hz]'); ylabel('Phase [deg]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([30, 300]); +#+end_src + +#+begin_src matlab + figure; + ax1 = subplot(2,1,1); + hold on; + plot(freqs, abs(squeeze(G(5,1,:))./(-w.^2)), '.') + plot(freqs, abs(squeeze(G(4,2,:))./(-w.^2)), '.') + set(gca,'ColorOrderIndex',1); + plot(freqs, abs(squeeze(freqresp(Gm(5,1,:), freqs, 'Hz'))), '-') + plot(freqs, abs(squeeze(freqresp(Gm(4,2,:), freqs, 'Hz'))), '-') + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Magnitude [m/N]'); set(gca, 'XTickLabel',[]); + ylim([1e-9, 2e-6]); + + ax2 = subplot(2,1,2); + hold on; + plot(freqs, 180/pi*angle(squeeze(G(5,1,:))./(-w.^2)), '.', 'DisplayName', '$R_y/F_x$') + plot(freqs, 180/pi*angle(squeeze(G(4,2,:))./(-w.^2)), '.', 'DisplayName', '$R_x/F_y$') + set(gca,'ColorOrderIndex',1); + plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(5,1,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off') + plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(4,2,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off') + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + xlabel('Freqency [Hz]'); ylabel('Phase [deg]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([30, 300]); +#+end_src + diff --git a/micro-station-compliance/mat/model.mat b/micro-station-compliance/mat/model.mat new file mode 100644 index 0000000..efe4d7b Binary files /dev/null and b/micro-station-compliance/mat/model.mat differ