From 57672954e116fd2866188afc621a369aaff1db28 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Tue, 17 Dec 2024 11:37:04 +0100 Subject: [PATCH] Update Content - 2024-12-17 --- content/zettels/feedforward_control.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/content/zettels/feedforward_control.md b/content/zettels/feedforward_control.md index 34d569c..f1b4170 100644 --- a/content/zettels/feedforward_control.md +++ b/content/zettels/feedforward_control.md @@ -9,9 +9,9 @@ Tags Depending on the physical system to be controlled, several feedforward controllers can be used: -- [sec-fourth_order_feedforward](#sec-fourth_order_feedforward) -- [sec-model_based_feedforward](#sec-model_based_feedforward) - [sec-rigid-body-feedforward](#sec-rigid-body-feedforward) +- [sec-fourth-order-feedforward](#sec-fourth-order-feedforward) +- [sec-model-based-feedforward](#sec-model-based-feedforward) ## Rigid Body Feedforward {#rigid-body-feedforward} @@ -38,7 +38,7 @@ F\_{ff} = m a + c v -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](#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 [fig-feedforward-double-mass-system](#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/). @@ -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](#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 [fig-feedforward-fourth-order-feedforward-architecture](#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](#fig-feedforward_fourth_order_feedforward_architecture) can be used. +The same architecture shown in Figure [fig-feedforward-fourth-order-feedforward-architecture](#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 (Lambrechts, Boerlage, and Steinbuch 2004)).