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Thomas Dehaeze
2020-03-03 15:53:02 +01:00
parent 467a04e239
commit 304ecf031b
14 changed files with 578 additions and 608 deletions
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8
org/control-study.org
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@@ -299,7 +299,7 @@ We then design a controller based on the transfer functions from $\bm{\mathcal{F
plot(freqs, abs(squeeze(freqresp(Gc_dvf('Rz', 'Mz'), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
ax2 = subplot(2, 1, 2);
hold on;
@@ -356,7 +356,7 @@ The controller is a pure integrator with a small lead near the crossover.
plot(freqs, abs(squeeze(freqresp(Kd_dvf(6,6)*Gc_dvf('Rz', 'Mz'), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
ylabel('Loop Gain'); set(gca, 'XTickLabel',[]);
ax2 = subplot(2, 1, 2);
hold on;
@@ -461,7 +461,7 @@ We identify the transmissibility and compliance of the system.
plot(freqs, abs(squeeze(freqresp(Gc_iff('Rz', 'Mz'), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
ax2 = subplot(2, 1, 2);
hold on;
@@ -518,7 +518,7 @@ The controller is a pure integrator with a small lead near the crossover.
plot(freqs, abs(squeeze(freqresp(Kd_iff(6,6)*Gc_iff('Rz', 'Mz'), freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
ylabel('Loop Gain'); set(gca, 'XTickLabel',[]);
ax2 = subplot(2, 1, 2);
hold on;

27
org/cubic-configuration.org
View File

@@ -488,6 +488,12 @@ However, the rotational stiffnesses are increasing with the cube's size but the
#+begin_important
We found that we can have a diagonal stiffness matrix using the cubic architecture when $\{A\}$ and $\{B\}$ are located above the top platform.
Depending on the cube's size, we obtain 3 different configurations.
| Cube's Size | Paper with the corresponding cubic architecture |
|-------------+--------------------------------------------------|
| Small | cite:furutani04_nanom_cuttin_machin_using_stewar |
| Medium | cite:yang19_dynam_model_decoup_contr_flexib |
| Large | |
#+end_important
* Cubic size analysis
@@ -738,6 +744,7 @@ We now identify the dynamics from forces applied in each strut $\bm{\tau}$ to th
Now, thanks to the Jacobian (Figure [[fig:local_to_cartesian_coordinates]]), we compute the transfer function from $\bm{\mathcal{F}}$ to $\bm{\mathcal{X}}$.
#+begin_src matlab
Gc = inv(stewart.kinematics.J)*G*inv(stewart.kinematics.J');
Gc = inv(stewart.kinematics.J)*G*stewart.kinematics.J;
Gc.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
Gc.OutputName = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'};
#+end_src
@@ -827,6 +834,26 @@ The obtain dynamics $\bm{G}_{c}(s) = \bm{J}^{-T} \bm{G}(s) \bm{J}^{-1}$ is shown
#+caption: Dynamics from $\bm{\mathcal{F}}$ to $\bm{\mathcal{X}}$ ([[./figs/stewart_cubic_decoupled_dynamics_cartesian.png][png]], [[./figs/stewart_cubic_decoupled_dynamics_cartesian.pdf][pdf]])
[[file:figs/stewart_cubic_decoupled_dynamics_cartesian.png]]
It is interesting to note here that the system shown in Figure [[fig:local_to_cartesian_coordinates_bis]] also yield a decoupled system (explained in section 1.3.3 in cite:li01_simul_fault_vibrat_isolat_point).
#+begin_src latex :file local_to_cartesian_coordinates_bis.pdf
\begin{tikzpicture}
\node[block] (Jt) at (0, 0) {$\bm{J}$};
\node[block, right= of Jt] (G) {$\bm{G}$};
\node[block, right= of G] (J) {$\bm{J}^{-1}$};
\draw[->] ($(Jt.west)+(-0.8, 0)$) -- (Jt.west);
\draw[->] (Jt.east) -- (G.west) node[above left]{$\bm{\tau}$};
\draw[->] (G.east) -- (J.west) node[above left]{$\delta\bm{\mathcal{L}}$};
\draw[->] (J.east) -- ++(0.8, 0) node[above left]{$\delta\bm{\mathcal{X}}$};
\end{tikzpicture}
#+end_src
#+name: fig:local_to_cartesian_coordinates_bis
#+caption: Alternative way to decouple the system
#+RESULTS:
[[file:figs/local_to_cartesian_coordinates_bis.png]]
#+begin_important
The dynamics is well decoupled at all frequencies.