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Update Content - 2024-12-17

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Thomas Dehaeze
2024-12-17 15:23:12 +01:00
parent ba5c203e48
commit f0d28899bf
6 changed files with 210 additions and 209 deletions
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5
content/zettels/air_bearing.md
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@@ -23,7 +23,7 @@ Advantages of air bearings compared to roller bearings:
## Air bearing stiffness {#air-bearing-stiffness}
Observing figure <fig:air_bearing_stiffness_gap>, we see that air bearings do not have a linear stiffness curve but rather an exponential one, producing higher and higher stiffness values as the film becomes thinner and the loading becomes higher.
Observing [1](#figure--fig:air-bearing-stiffness-gap), we see that air bearings do not have a linear stiffness curve but rather an exponential one, producing higher and higher stiffness values as the film becomes thinner and the loading becomes higher.
<a id="figure--fig:air-bearing-stiffness-gap"></a>
@@ -68,4 +68,5 @@ Due to the porous nature, even if some of the holes become clogged or damaged, t
## Bibliography {#bibliography}
<./biblio/references.bib>
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
</div>

6
content/zettels/feedforward_control.md
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@@ -38,7 +38,7 @@ F\_{ff} = m a + c v
<span class="org-target" id="org-target--sec-fourth-order-feedforward"></span>
The main advantage of "fourth order feedforward" is that it takes into account the flexibility in the system (one resonance between the actuation point and the measurement point, see Figure <fig:feedforward_double_mass_system>).
The main advantage of "fourth order feedforward" is that it takes into account the flexibility in the system (one resonance between the actuation point and the measurement point, see [2](#figure--fig:feedforward-double-mass-system)).
This can lead to better results than second order trajectory planning as demonstrated [here](https://www.20sim.com/control-engineering/snap-feedforward/).
<a id="figure--fig:feedforward-double-mass-system"></a>
@@ -76,7 +76,7 @@ q\_3 &= (m\_1 + m\_2)c + k\_1 k\_2 + (k\_1 + k\_2) k\_{12} \\\\
q\_4 &= (k\_1 + k\_2) c
\end{align}
This means that if a fourth-order trajectory for \\(x\_2\\) is used, the feedforward architecture shown in Figure <fig:feedforward_fourth_order_feedforward_architecture> can be used:
This means that if a fourth-order trajectory for \\(x\_2\\) is used, the feedforward architecture shown in [3](#figure--fig:feedforward-fourth-order-feedforward-architecture) can be used:
\begin{equation}
F\_{f2} = \frac{1}{k\_12 s + c} (q\_1 d + q\_2 j + q\_3 q + q\_4 v)
@@ -103,7 +103,7 @@ q\_4 &= c\_1 k
and \\(s\\) the snap, \\(j\\) the jerk, \\(a\\) the acceleration and \\(v\\) the velocity.
The same architecture shown in Figure <fig:feedforward_fourth_order_feedforward_architecture> can be used.
The same architecture shown in [3](#figure--fig:feedforward-fourth-order-feedforward-architecture) can be used.
In order to implement a fourth order trajectory, look at [this](https://www.mathworks.com/matlabcentral/fileexchange/16352-advanced-setpoints-for-motion-systems) nice implementation in Simulink of fourth-order trajectory planning (see also (<a href="#citeproc_bib_item_1">Lambrechts, Boerlage, and Steinbuch 2004</a>)).