tdehaeze/digital-brain
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Update Content - 2024-12-19

Browse Source
This commit is contained in:
Thomas Dehaeze
2024-12-19 13:21:36 +01:00
parent 200ab38842
commit 8abd7c44c6
3 changed files with 61 additions and 4 deletions
Download Patch File Download Diff File Expand all files Collapse all files

8
content/zettels/feedforward_control.md
View File

@@ -20,7 +20,7 @@ Depending on the physical system to be controlled, several feedforward controlle
Second order trajectory planning: the acceleration and velocity can be bound to wanted values.
Such trajectory is shown in [1](#figure--fig:feedforward-second-order-trajectory).
Such trajectory is shown in [Figure 1](#figure--fig:feedforward-second-order-trajectory).
<a id="figure--fig:feedforward-second-order-trajectory"></a>
@@ -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 [2](#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 [Figure 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 [3](#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 [Figure 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 [3](#figure--fig:feedforward-fourth-order-feedforward-architecture) can be used.
The same architecture shown in [Figure 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>)).