Add micro-station compliance measurement/analysis

micro-station-compliance/data/id31_nass_11august2020.m

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+ID31 NASS - 11/08/2020
+
+ch1 to 3: acc 3D 1v/g
+ch4 to 6: acc 3D 1v/g
+ch7 to 9: acc 3D 100m/g
+ch10 to 12: acc 3D 1v/g
+Ch13: hammer 230uV/N
+
+
+
+%% 12/08/2020
+% change hammer tip to red
+% Bandwidth changed to 400Hz
+
+excitation capteur 1 Y
+Meas1
+
+excitation capteur 1 -Z
+Meas2
+
+excitation capteur 2 X
+Meas3
+
+excitation capteur 2 -Z
+Meas4
+
+excitation capteur 3 -Y
+Meas5
+
+
+excitation capteur 3 -Z
+Meas6
+
+excitation capteur 4 -X
+Meas7
+
+excitation capteur 4 -Z
+Meas8
+
+excitation capteur 3 -X on black block RZ 
+Meas9
+
+excitation capteur 1 -X on black block RZ 
+Meas10
+
+% ---------------------------
+%% vibrometre on TY 0.2mm/s/V
+excitation -Y
+Meas2

micro-station-compliance/index.org

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+#+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: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/>
+#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
+#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/zenburn.css"/>
+#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.min.js"></script>
+#+HTML_HEAD: <script type="text/javascript" src="../js/bootstrap.min.js"></script>
+#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.stickytableheaders.min.js"></script>
+#+HTML_HEAD: <script type="text/javascript" src="../js/readtheorg.js"></script>
+
+#+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)
+  <<matlab-dir>>
+#+end_src
+
+#+begin_src matlab :exports none :results silent :noweb yes
+  <<matlab-init>>
+#+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
+