Add compliance measurement
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@ -164,9 +164,8 @@ initializeController( 'type', 'open-loop');
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#+end_src
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** TODO [#B] Make good "init" for the Simscape model
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** TODO [#B] Just keep smallest number of variants for each stage
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** DONE [#B] Just keep smallest number of variants for each stage
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CLOSED: [2024-10-30 Wed 16:15]
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- [ ] none
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- [ ] rigid
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@ -178,10 +177,41 @@ initializeController( 'type', 'open-loop');
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SCHEDULED: <2024-10-30 Wed>
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- [ ] Find the compliance measurements
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- The one from modal analysis
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- [[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-measurements/2018-01-12 - Marc]] : Compliance measurement in X,Y,Z with geophone, marble not glued
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- [[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-measurements/2018-10-12 - Marc]]: same but in the hutch with glued marble
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- *08/2020*: [[file:~/Cloud/work-projects/ID31-NASS/matlab/nass-measurements/micro-station-compliance/index.org::+TITLE: Compliance Measurement of the Micro Station]]
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- [ ] See if it matches somehow the current model
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- [ ] If not, see if model parameters can be tuned to have better match
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For instance from values here: file:/home/thomas/Cloud/meetings/esrf-meetings/2018-04-24-Simscape-Model/2018-04-24-Simscape-Model.pdf
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** TODO [#B] Make good "init" for the Simscape model
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** TODO [#C] Could see the effect of each stage on the compliance
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- [ ] Put =rigid= mode one by one to see the effect
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** TODO [#C] Make a comparison of the measured vibrations of the micro-station with the vibrations of the simscape model of the micro-station
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Do we have a correlation? At least in the frequency domain?
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Procedure:
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- [ ] Take the time domain measurement of the vibrations due to spindle or translation stage
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- [ ] Take the estimated PSD of the estimated disturbance force
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- [ ] Simulate the Simscape model without the nano-hexapod (same conditions as when measuring the disturbances) and add only the considered disturbance
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- [ ] Save the position errors due to the disturbance
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- [ ] Compare with the measured vibrations
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** TODO [#C] Add two perturbations: =Frz_x= and =Frz_y=
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Maybe I can estimate them from the measurements that was made on the spindle?
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** TODO [#C] Determine which Degree-Of-Freedom to keep and which to constrain
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For instance, for now the granite can not rotate, but in reality, the modes may be linked to the granite's rotation.
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By constraining more DoF, the simulation will be faster and the obtain state space will have a lower order.
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** TODO [#B] Compute eigenvalues of the model to see if we have similar frequencies than the modal analysis?
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* Introduction :ignore:
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@ -894,7 +924,385 @@ end
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end
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#+end_src
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** Obtained Compliance of the Micro-Station
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** Measured micro-station compliance
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*** Introduction :ignore:
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The most important dynamical characteristic of the micro-station that should be well modeled is its compliance.
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This is what can impact the nano-hexapod dynamics.
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- [ ] Add schematic of the experiment with Micro-Hexapod top platform, location of accelerometers, of impacts, etc...
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- 4 3-axis accelerometers
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- 10 hammer impacts on the micro-hexapod top plaftorm
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- *Was the rotation compensation axis present?* (I don't think so)
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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* | *Formula (numbers)* |
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|-------+--------------------------+-----------------------|
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| $D_x$ | (1x + 2x + 3x + 4x)/4 | (1 + 4 + 7 + 10)/4 |
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| $D_y$ | (1y + 2y + 3y + 4y)/4 | (2 + 5 + 8 + 11)/4 |
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| $D_z$ | (1z + 2z + 3z + 4z)/4 | (3 + 6 + 9 + 12)/4 |
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| $R_x$ | (1z - 3z)/A | (1 - 9)/A |
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| $R_y$ | (2z - 4z)/B | (6 - 12)/B |
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| $R_z$ | (3x - 1x)/A, (4y - 2y)/B | (7 - 1)/A, (11 - 5)/B |
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dL = J X
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#+begin_src matlab
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d = 0.14;
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J = [1 0 0 0 0 -d;
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0 1 0 0 0 0;
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0 0 1 d 0 0;
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1 0 0 0 0 0;
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0 1 0 0 0 -d;
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0 0 1 0 d 0;
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1 0 0 0 0 d;
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0 1 0 0 0 0;
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0 0 1 -d 0 0;
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1 0 0 0 0 0;
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0 1 0 0 0 d;
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0 0 1 0 -d 0];
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J_inv = pinv(J);
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#+end_src
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| | Dx | Dy | Dz | Rx | Ry | Rz |
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|-----+----+----+----+----+----+----|
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| a1x | 1 | 0 | 0 | 0 | 0 | -d |
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| a1y | 0 | 1 | 0 | 0 | 0 | 0 |
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| a1z | 0 | 0 | 1 | d | 0 | 0 |
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| a2x | 1 | 0 | 0 | 0 | 0 | 0 |
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| a2y | 0 | 1 | 0 | 0 | 0 | -d |
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| a2z | 0 | 0 | 1 | 0 | d | 0 |
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| a3x | 1 | 0 | 0 | 0 | 0 | d |
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| a3y | 0 | 1 | 0 | 0 | 0 | 0 |
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| a3z | 0 | 0 | 1 | -d | 0 | 0 |
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| a4x | 1 | 0 | 0 | 0 | 0 | 0 |
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| a4y | 0 | 1 | 0 | 0 | 0 | d |
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| a4z | 0 | 0 | 1 | 0 | -d | 0 |
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#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
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data2orgtable(J_inv, {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'d1x', 'd1y', 'd1z', 'd2x', 'd2y', 'd2z', 'd3x', 'd3y', 'd3z', 'd4x', 'd4y', 'd4z'}, ' %.5f ');
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#+end_src
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#+RESULTS:
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| | d1x | d1y | d1z | d2x | d2y | d2z | d3x | d3y | d3z | d4x | d4y | d4z |
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|----+----------+------+---------+------+----------+---------+---------+------+----------+------+---------+----------|
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| Dx | 0.25 | 0.0 | 0.0 | 0.25 | 0.0 | 0.0 | 0.25 | 0.0 | 0.0 | 0.25 | 0.0 | 0.0 |
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| Dy | 0.0 | 0.25 | 0.0 | 0.0 | 0.25 | 0.0 | 0.0 | 0.25 | 0.0 | 0.0 | 0.25 | 0.0 |
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| Dz | 0.0 | 0.0 | 0.25 | 0.0 | 0.0 | 0.25 | 0.0 | 0.0 | 0.25 | 0.0 | 0.0 | 0.25 |
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| Rx | 0.0 | 0.0 | 3.57143 | 0.0 | 0.0 | -0.0 | 0.0 | 0.0 | -3.57143 | 0.0 | 0.0 | -0.0 |
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| Ry | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 3.57143 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | -3.57143 |
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| Rz | -1.78571 | 0.0 | -0.0 | 0.0 | -1.78571 | 0.0 | 1.78571 | 0.0 | -0.0 | 0.0 | 1.78571 | -0.0 |
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*** Hammer blow position/orientation
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| *Num* | *Direction* | *Position* | Accelerometer position | Jacobian number |
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|-------+-------------+------------+------------------------+-----------------|
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| 1 | -Y | [0, +A, 0] | 1 | -2 |
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| 2 | -Z | [0, +A, 0] | 1 | -3 |
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| 3 | X | [-B, 0, 0] | 2 | 4 |
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| 4 | -Z | [-B, 0, 0] | 2 | -6 |
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| 5 | Y | [0, -A, 0] | 3 | 8 |
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| 6 | -Z | [0, -A, 0] | 3 | -9 |
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| 7 | -X | [+B, 0, 0] | 4 | -10 |
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| 8 | -Z | [+B, 0, 0] | 4 | -12 |
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| 9 | -X | [0, -A, 0] | 3 | -7 |
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| 10 | -X | [0, +A, 0] | 1 | -1 |
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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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F = J' tau
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#+begin_src matlab
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Jf = [0 -1 0 0 0 0;
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0 0 -1 -d 0 0;
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1 0 0 0 0 0;
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0 0 -1 0 -d 0;
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0 1 0 0 0 0;
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0 0 -1 d 0 0;
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-1 0 0 0 0 0;
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0 0 -1 0 d 0;
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-1 0 0 0 0 -d;
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-1 0 0 0 0 d]';
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Jf_inv = pinv(Jf);
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#+end_src
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#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
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data2orgtable(Jf, {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'}, {'-F1y', '-F1z', '+F2x', '-F2z', '+F3y', '-F3z', '-F4x', '-F4z', '-F3x', '-F1x'}, ' %.2f ');
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#+end_src
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#+RESULTS:
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| | -F1y | -F1z | +F2x | -F2z | +F3y | -F3z | -F4x | -F4z | -F3x | -F1x |
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|----+------+-------+------+-------+------+------+------+------+-------+------|
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| Fx | 0.0 | 0.0 | 1.0 | 0.0 | 0.0 | 0.0 | -1.0 | 0.0 | -1.0 | -1.0 |
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| Fy | -1.0 | 0.0 | 0.0 | 0.0 | 1.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
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| Fz | 0.0 | -1.0 | 0.0 | -1.0 | 0.0 | -1.0 | 0.0 | -1.0 | 0.0 | 0.0 |
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| Mx | 0.0 | -0.14 | 0.0 | 0.0 | 0.0 | 0.14 | 0.0 | 0.0 | 0.0 | 0.0 |
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| My | 0.0 | 0.0 | 0.0 | -0.14 | 0.0 | 0.0 | 0.0 | 0.14 | 0.0 | 0.0 |
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| Mz | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | -0.14 | 0.14 |
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*** Compute FRF
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Raw measurements are in file:/home/thomas/Cloud/work-projects/ID31-NASS/matlab/nass-measurements/micro-station-compliance/data/record
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For each measurement (10):
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- Find the location of the 10 impacts based on "track13"
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- Then for the 12 accelerometer data, compute the FRF, and average them for the 10 impacts
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- Maybe have to take into account the sensitivity, etc...
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#+begin_src matlab
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raw_data_path = '/home/thomas/Cloud/work-projects/ID31-NASS/matlab/nass-measurements/micro-station-compliance/data/record/';
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data = [
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load(sprintf('%s/Measurement1.mat', raw_data_path)), ...
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load(sprintf('%s/Measurement2.mat', raw_data_path)), ...
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load(sprintf('%s/Measurement3.mat', raw_data_path)), ...
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load(sprintf('%s/Measurement4.mat', raw_data_path)), ...
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load(sprintf('%s/Measurement5.mat', raw_data_path)), ...
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load(sprintf('%s/Measurement6.mat', raw_data_path)), ...
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load(sprintf('%s/Measurement7.mat', raw_data_path)), ...
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load(sprintf('%s/Measurement8.mat', raw_data_path)), ...
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load(sprintf('%s/Measurement9.mat', raw_data_path)), ...
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load(sprintf('%s/Measurement10.mat', raw_data_path))];
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#+end_src
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#+begin_src matlab
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Ts = 1e-3; % Sampling Time [s]
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Nfft = floor(1/Ts); % Number of points for the FFT computation
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% win = hanning(Nfft); % Hanning window
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win = ones(Nfft, 1); % Rectangular window
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% Get the frequency vector
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[~, f] = tfestimate(data(1).Track13, data(1).Track1, win, [], Nfft, 1/Ts);
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#+end_src
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#+begin_src matlab
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pre_n = floor(0.1/Ts);
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post_n = Nfft - pre_n - 1;
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#+end_src
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#+begin_src matlab
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G_raw = zeros(12,10,length(f));
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for i = 1:10
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% Find the impacts
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[~, impacts_i] = find(diff(data(i).Track13 > 50)==1);
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% Only keep the first 10 impacts if there are more than 10 impacts
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if length(impacts_i)>10
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impacts_i(11:end) = [];
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end
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% Initialize the FRF for the current experiment
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G_impact = zeros(12,length(f));
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for impact_i = impacts_i
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i_start = impacts_i - pre_n;
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i_end = impacts_i + post_n;
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data_in = data(i).Track13(i_start:i_end); % [N]
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% Remove hammer DC offset
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data_in = data_in - mean(data_in(end-pre_n:end));
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% Combine all outputs [m/s^2]
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data_out = [data(i).Track1( i_start:i_end); ...
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data(i).Track2( i_start:i_end); ...
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data(i).Track3( i_start:i_end); ...
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data(i).Track4( i_start:i_end); ...
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data(i).Track5( i_start:i_end); ...
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data(i).Track6( i_start:i_end); ...
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data(i).Track7( i_start:i_end); ...
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data(i).Track8( i_start:i_end); ...
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data(i).Track9( i_start:i_end); ...
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data(i).Track10(i_start:i_end); ...
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data(i).Track11(i_start:i_end); ...
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data(i).Track12(i_start:i_end)];
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[frf, ~] = tfestimate(data_in, data_out', win, [], Nfft, 1/Ts);
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G_raw(:,i,:) = frf'./(-(2*pi*f').^2);
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end
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end
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#+end_src
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#+begin_src matlab
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%% Compute transfer function in cartesian frame
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G_compl_b = pagemtimes(J_inv, pagemtimes(G_raw, Jf_inv));
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#+end_src
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#+begin_src matlab
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colors = colororder;
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figure;
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hold on;
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% plot(freqs, abs(squeeze(G_compl(1,1,:))), 'color', colors(1,:), 'DisplayName', '$C_x/F_x$')
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% plot(freqs, abs(squeeze(G_compl(2,2,:))), 'color', colors(2,:), 'DisplayName', '$C_y/F_y$')
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% plot(freqs, abs(squeeze(G_compl(3,3,:))), 'color', colors(3,:), 'DisplayName', '$C_z/F_z$')
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plot(f, abs(squeeze(G_compl_b(1,1,:))), '-', 'color', colors(1,:), 'DisplayName', '$C_x/F_x$')
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plot(f, abs(squeeze(G_compl_b(2,2,:))), '-', 'color', colors(2,:), 'DisplayName', '$C_y/F_y$')
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plot(f, abs(squeeze(G_compl_b(3,3,:))), '-', 'color', colors(3,:), 'DisplayName', '$C_z/F_z$')
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Magnitude [m/N]');
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xlim([30, 300]); ylim([1e-9, 2e-6]);
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leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
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leg.ItemTokenSize(1) = 15;
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#+end_src
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*** Load Data
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#+begin_src matlab
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% Load data
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data = [load('data/Measurement1.mat'), ...
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load('data/Measurement2.mat'), ...
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load('data/Measurement3.mat'), ...
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load('data/Measurement4.mat'), ...
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load('data/Measurement5.mat'), ...
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load('data/Measurement6.mat'), ...
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load('data/Measurement7.mat'), ...
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load('data/Measurement8.mat'), ...
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load('data/Measurement9.mat'), ...
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load('data/Measurement10.mat')];
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#+end_src
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#+begin_src matlab
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% Frequency Vector
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freqs = m3.FFT1_H1_1_13_X_Val;
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w = 2*pi*freqs;
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% 12 outputs, 10 inputs
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G_raw = zeros(12, 10, length(freqs));
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for j = 1:10
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for i = 1:12
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G_raw(i,j,:) = data(j).(sprintf("FFT1_H1_%i_13_Y_ReIm", i))./(-w.^2);
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end
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end
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#+end_src
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#+begin_src matlab
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%% Compute transfer function in cartesian frame
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G_compl = pagemtimes(J_inv, pagemtimes(G_raw, Jf_inv));
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#+end_src
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#+begin_src matlab
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colors = colororder;
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figure;
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hold on;
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plot(freqs, abs(squeeze(G_compl(1,1,:))), 'color', colors(1,:), 'DisplayName', '$C_x/F_x$')
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plot(freqs, abs(squeeze(G_compl(2,2,:))), 'color', colors(2,:), 'DisplayName', '$C_y/F_y$')
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plot(freqs, abs(squeeze(G_compl(3,3,:))), 'color', colors(3,:), 'DisplayName', '$C_z/F_z$')
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plot(f, abs(squeeze(G_compl_b(1,1,:))), '.', 'color', colors(1,:), 'DisplayName', '$C_x/F_x$')
|
||||
plot(f, abs(squeeze(G_compl_b(2,2,:))), '.', 'color', colors(2,:), 'DisplayName', '$C_y/F_y$')
|
||||
plot(f, abs(squeeze(G_compl_b(3,3,:))), '.', 'color', colors(3,:), 'DisplayName', '$C_z/F_z$')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Magnitude [m/N]');
|
||||
xlim([30, 300]); ylim([1e-9, 2e-6]);
|
||||
leg = legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
colors = colororder;
|
||||
figure;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(G_compl(4,4,:))), 'color', colors(1,:), 'DisplayName', '$R_x/M_x$')
|
||||
plot(freqs, abs(squeeze(G_compl(5,5,:))), 'color', colors(2,:), 'DisplayName', '$R_y/M_y$')
|
||||
plot(freqs, abs(squeeze(G_compl(6,6,:))), 'color', colors(3,:), 'DisplayName', '$R_z/M_z$')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Magnitude [m/N]');
|
||||
xlim([30, 300]); ylim([5e-7, 5e-5]);
|
||||
leg = legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
|
||||
leg.ItemTokenSize(1) = 15;
|
||||
#+end_src
|
||||
|
||||
*** Diagonal Dynamics
|
||||
#+begin_src matlab
|
||||
figure;
|
||||
ax1 = subplot(2,1,1);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(G(1,1,:)), '-', 'DisplayName', '$D_x/F_x$')
|
||||
plot(freqs, abs(squeeze(G(2,2,:)), '-', 'DisplayName', '$D_y/F_y$')
|
||||
plot(freqs, abs(squeeze(G(3,3,:)), '-', 'DisplayName', '$D_z/F_z$')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Magnitude [m/N]');
|
||||
ylim([1e-9, 2e-6]);
|
||||
legend('location', 'southwest');
|
||||
xlim([30, 300]);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
figure;
|
||||
ax1 = subplot(2,1,1);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(G(4,4,:)), '-', 'DisplayName', '$R_x/M_x$')
|
||||
plot(freqs, abs(squeeze(G(5,5,:)), '-', 'DisplayName', '$R_y/M_y$')
|
||||
plot(freqs, abs(squeeze(G(6,6,:)), '-', 'DisplayName', '$R_z/M_z$')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Magnitude [rad/Nm]');
|
||||
ylim([1e-7, 2e-4]);
|
||||
legend('location', 'southwest');
|
||||
xlim([30, 300]);
|
||||
#+end_src
|
||||
|
||||
*** 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 |
|
||||
|
||||
** Compare with the Model
|
||||
#+begin_src matlab
|
||||
%% Initialize simulation with default parameters (flexible elements)
|
||||
initializeGround();
|
||||
@ -946,6 +1354,176 @@ legend('location', 'northwest');
|
||||
|
||||
- [ ] Comparison with the estimated (or measured) compliance
|
||||
|
||||
#+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
|
||||
|
||||
|
||||
|
||||
** Conclusion
|
||||
For such a complex system, we believe that the Simscape Model represents the dynamics of the system with enough fidelity.
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user