2020-08-18 12:59:32 +02:00
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#+TITLE: Compliance Measurement of the Micro Station
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:DRAWER:
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#+STARTUP: overview
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#+LANGUAGE: en
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#+EMAIL: dehaeze.thomas@gmail.com
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#+AUTHOR: Dehaeze Thomas
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#+HTML_LINK_HOME: ../index.html
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2020-11-12 10:30:56 +01:00
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#+HTML_LINK_UP: ../index.html
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2020-08-18 12:59:32 +02:00
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2020-11-12 10:30:56 +01:00
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
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#+HTML_HEAD: <script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
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2020-08-18 12:59:32 +02:00
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#+HTML_MATHJAX: align: center tagside: right font: TeX
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#+PROPERTY: header-args:matlab :session *MATLAB*
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#+PROPERTY: header-args:matlab+ :comments org
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#+PROPERTY: header-args:matlab+ :results none
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#+PROPERTY: header-args:matlab+ :exports both
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#+PROPERTY: header-args:matlab+ :eval no-export
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#+PROPERTY: header-args:matlab+ :output-dir figs
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#+PROPERTY: header-args:shell :eval no-export
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:END:
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* Setup
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** Position of inertial sensors on top of the micro-hexapod
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Orientation is relative to the frame determined by the X-ray
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| *Num* | *Position* | *Orientation* | *Sensibility* | *Channels* |
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|-------+------------+---------------+---------------+------------|
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| 1 | [0, +A, 0] | [x, y, z] | 1V/g | 1-3 |
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| 2 | [-B, 0, 0] | [x, y, z] | 1V/g | 4-6 |
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| 3 | [0, -A, 0] | [x, y, z] | 0.1V/g | 7-9 |
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| 4 | [+B, 0, 0] | [x, y, z] | 1V/g | 10-12 |
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Instrumented Hammer:
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- Channel 13
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- Sensibility: 230 uV/N
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| Acc Number | Dir | Channel Number |
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|------------+-----+----------------|
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| 1 | x | 1 |
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| 1 | y | 2 |
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| 1 | z | 3 |
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| 2 | x | 4 |
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| 2 | y | 5 |
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| 2 | z | 6 |
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| 3 | x | 7 |
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| 3 | y | 8 |
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| 3 | z | 9 |
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| 4 | x | 10 |
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| 4 | y | 11 |
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| 4 | z | 12 |
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| Hammer | | 13 |
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From the acceleration measurement of the 4 accelerometers, we can compute the translations and rotations:
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| | *Formula* |
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|-------+--------------------------|
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| $D_x$ | (1x + 2x + 3x + 4x)/4 |
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| $D_y$ | (1y + 2y + 3y + 4y)/4 |
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| $D_z$ | (1z + 2z + 3z + 4z)/4 |
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| $R_x$ | (1z - 3z)/A |
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| $R_y$ | (2z - 4z)/B |
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| $R_z$ | (3x - 1x)/A, (4y - 2y)/B |
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| | *Formula* |
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|-------+-----------------------|
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| $D_x$ | (1 + 4 + 7 + 10)/4 |
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| $D_y$ | (2 + 5 + 8 + 11)/4 |
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| $D_z$ | (3 + 6 + 9 + 12)/4 |
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| $R_x$ | (1 - 9)/A |
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| $R_y$ | (6 - 12)/B |
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| $R_z$ | (7 - 1)/A, (11 - 5)/B |
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** Hammer blow position/orientation
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| *Num* | *Direction* | *Position* |
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|-------+-------------+------------|
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| 1 | -Y | [0, +A, 0] |
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| 2 | -Z | [0, +A, 0] |
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| 3 | X | [-B, 0, 0] |
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| 4 | -Z | [-B, 0, 0] |
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| 5 | Y | [0, -A, 0] |
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| 6 | -Z | [0, -A, 0] |
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| 7 | -X | [+B, 0, 0] |
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| 8 | -Z | [+B, 0, 0] |
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| 9 | -X | [0, -A, 0] |
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| 10 | -X | [0, +A, 0] |
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From hammer blows to pure forces / torques:
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| | *Formula* | Alternative |
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|-------+--------------+-------------|
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| $F_x$ | +3 | -7 |
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| $F_y$ | -1 | +5 |
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| $F_z$ | -(2 + 6)/2 | -(4 + 8)/2 |
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| $M_x$ | A/2*(2 - 6) | |
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| $M_y$ | B/2*(8 - 4) | |
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| $M_z$ | A/2*(10 - 9) | |
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* Results
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** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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** Load Data
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#+begin_src matlab
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m1 = load('data/Measurement1.mat');
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m2 = load('data/Measurement2.mat');
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m3 = load('data/Measurement3.mat');
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m4 = load('data/Measurement4.mat');
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m5 = load('data/Measurement5.mat');
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m6 = load('data/Measurement6.mat');
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m7 = load('data/Measurement7.mat');
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m8 = load('data/Measurement8.mat');
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m9 = load('data/Measurement9.mat');
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m10 = load('data/Measurement10.mat');
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#+end_src
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** Compute Transfer Functions
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#+begin_src matlab
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freqs = m3.FFT1_H1_1_13_X_Val;
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w = 2*pi*freqs';
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A = 0.14;
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B = 0.14;
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#+end_src
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#+begin_src matlab
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G = zeros(6,6,length(freqs));
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% Fx
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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;
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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;
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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;
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G(4,1,:) = (m3.FFT1_H1_1_13_Y_ReIm - m3.FFT1_H1_9_13_Y_ReIm )./A;
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G(5,1,:) = (m3.FFT1_H1_6_13_Y_ReIm - m3.FFT1_H1_12_13_Y_ReIm)./B;
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G(6,1,:) = (m3.FFT1_H1_7_13_Y_ReIm - m3.FFT1_H1_1_13_Y_ReIm )./A;
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% Fy
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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;
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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;
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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;
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G(4,2,:) = -(m1.FFT1_H1_1_13_Y_ReIm - m1.FFT1_H1_9_13_Y_ReIm )./A;
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G(5,2,:) = -(m1.FFT1_H1_6_13_Y_ReIm - m1.FFT1_H1_12_13_Y_ReIm)./B;
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G(6,2,:) = -(m1.FFT1_H1_7_13_Y_ReIm - m1.FFT1_H1_1_13_Y_ReIm )./A;
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% Fz
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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) + ...
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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));
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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) + ...
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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));
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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) + ...
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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));
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G(4,3,:) = -2/A./(1./(m2.FFT1_H1_1_13_Y_ReIm - m2.FFT1_H1_9_13_Y_ReIm) + ...
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1./(m6.FFT1_H1_1_13_Y_ReIm - m6.FFT1_H1_9_13_Y_ReIm));
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G(5,3,:) = -2/B./(1./(m2.FFT1_H1_6_13_Y_ReIm - m2.FFT1_H1_12_13_Y_ReIm) + ...
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1./(m6.FFT1_H1_6_13_Y_ReIm - m6.FFT1_H1_12_13_Y_ReIm));
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G(6,3,:) = -2/A./(1./(m2.FFT1_H1_7_13_Y_ReIm - m2.FFT1_H1_1_13_Y_ReIm) + ...
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1./(m6.FFT1_H1_7_13_Y_ReIm - m6.FFT1_H1_1_13_Y_ReIm));
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% Mx
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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) - ...
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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));
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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) - ...
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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));
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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) - ...
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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));
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G(4,4,:) = 1/A^2*2./(1./(m2.FFT1_H1_1_13_Y_ReIm - m2.FFT1_H1_9_13_Y_ReIm) - ...
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1./(m6.FFT1_H1_1_13_Y_ReIm - m6.FFT1_H1_9_13_Y_ReIm));
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G(5,4,:) = 2/A/B./(1./(m2.FFT1_H1_6_13_Y_ReIm - m2.FFT1_H1_12_13_Y_ReIm) - ...
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1./(m6.FFT1_H1_6_13_Y_ReIm - m6.FFT1_H1_12_13_Y_ReIm));
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G(6,4,:) = 1/A^2*2./(1./(m2.FFT1_H1_7_13_Y_ReIm - m2.FFT1_H1_1_13_Y_ReIm) - ...
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1./(m6.FFT1_H1_7_13_Y_ReIm - m6.FFT1_H1_1_13_Y_ReIm));
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% My
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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) - ...
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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));
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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) - ...
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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));
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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) - ...
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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));
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G(4,5,:) = 2/B/A./(1./(m8.FFT1_H1_1_13_Y_ReIm - m8.FFT1_H1_9_13_Y_ReIm) - ...
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1./(m4.FFT1_H1_1_13_Y_ReIm - m4.FFT1_H1_9_13_Y_ReIm));
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G(5,5,:) = 1/B^2*2./(1./(m8.FFT1_H1_6_13_Y_ReIm - m8.FFT1_H1_12_13_Y_ReIm) - ...
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1./(m4.FFT1_H1_6_13_Y_ReIm - m4.FFT1_H1_12_13_Y_ReIm));
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G(6,5,:) = 2/B/A./(1./(m8.FFT1_H1_7_13_Y_ReIm - m8.FFT1_H1_1_13_Y_ReIm) - ...
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1./(m4.FFT1_H1_7_13_Y_ReIm - m4.FFT1_H1_1_13_Y_ReIm));
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% Mz
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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',[]);
|
2020-11-03 09:34:55 +01:00
|
|
|
ylim([1e-7, 2e-4]);
|
2020-08-18 12:59:32 +02:00
|
|
|
|
|
|
|
|
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]]
|
|
|
|
|
|
2020-11-03 09:34:55 +01:00
|
|
|
** Equivalent Stiffness and Mass Estimation
|
|
|
|
|
|
|
|
|
|
#+begin_src matlab
|
|
|
|
|
K = [1e7, 1e7, 2e8, 5e7, 3e7, 2e7];
|
|
|
|
|
f_res = [125, 135, 390, 335, 335, 160];
|
|
|
|
|
#+end_src
|
|
|
|
|
|
|
|
|
|
#+begin_src matlab
|
|
|
|
|
M = [20, 20, 20, 11, 7, 20];
|
|
|
|
|
f_res_est = sqrt(K./M)./(2*pi);
|
|
|
|
|
#+end_src
|
|
|
|
|
|
|
|
|
|
Here is the inertia / stiffness to the granite that can represent the micro-station compliance dynamics:
|
|
|
|
|
#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
|
|
|
|
|
data2orgtable([K'], {'x', 'y', 'z', 'Rx', 'Ry', 'Rz'}, {'Stiffness', 'Inertia'}, ' %.1g ');
|
|
|
|
|
#+end_src
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
#+RESULTS:
|
|
|
|
|
| Stiffness | Inertia |
|
|
|
|
|
|-----------+-------------|
|
|
|
|
|
| x | 10000000.0 |
|
|
|
|
|
| y | 10000000.0 |
|
|
|
|
|
| z | 200000000.0 |
|
|
|
|
|
| Rx | 50000000.0 |
|
|
|
|
|
| Ry | 30000000.0 |
|
|
|
|
|
| Rz | 20000000.0 |
|
2020-08-18 12:59:32 +02:00
|
|
|
|
|
|
|
|
** 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;
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plot(freqs, 180/pi*angle(squeeze(G(1,1,:))./(-w.^2)), '.', 'DisplayName', '$D_x/F_x$')
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plot(freqs, 180/pi*angle(squeeze(G(2,1,:))./(-w.^2)), '.', 'DisplayName', '$D_y/F_x$')
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plot(freqs, 180/pi*angle(squeeze(G(3,1,:))./(-w.^2)), '.', 'DisplayName', '$D_z/F_x$')
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set(gca,'ColorOrderIndex',1);
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(1,1,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off')
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(2,1,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off')
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plot(freqs, 180/pi*angle(squeeze(freqresp(Gm(3,1,:), freqs, 'Hz'))), '-', 'HandleVisibility', 'off')
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|
hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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|
xlabel('Freqency [Hz]'); ylabel('Phase [deg]');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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legend('location', 'southwest');
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|
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linkaxes([ax1,ax2],'x');
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xlim([30, 300]);
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#+end_src
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#+begin_src matlab
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figure;
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ax1 = subplot(2,1,1);
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|
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|
|
hold on;
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plot(freqs, abs(squeeze(G(5,1,:))./(-w.^2)), '.')
|
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|
plot(freqs, abs(squeeze(G(4,2,:))./(-w.^2)), '.')
|
|
|
|
|
set(gca,'ColorOrderIndex',1);
|
|
|
|
|
plot(freqs, abs(squeeze(freqresp(Gm(5,1,:), freqs, 'Hz'))), '-')
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|
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|
|
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
|
|
|
|
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|
