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

Update Content - 2022-03-15

Browse Source
This commit is contained in:
Thomas Dehaeze
2022-03-15 16:40:48 +01:00
parent e6390908c4
commit 22fb3361a5
148 changed files with 3981 additions and 3197 deletions
Download Patch File Download Diff File Expand all files Collapse all files

14
content/zettels/singular_value_decomposition.md
View File

@@ -1,6 +1,6 @@
+++
title = "Singular Value Decomposition"
author = ["Thomas Dehaeze"]
author = ["Dehaeze Thomas"]
draft = false
+++
@@ -10,7 +10,7 @@ Tags
## SVD of a MIMO system {#svd-of-a-mimo-system}
This is taken from ([Skogestad and Postlethwaite 2007](#org8e4f47e)).
This is taken from (NO_ITEM_DATA:skogestad05_multiv_feedb_contr).
We are interested by the physical interpretation of the SVD when applied to the frequency response of a MIMO system \\(G(s)\\) with \\(m\\) inputs and \\(l\\) outputs.
@@ -43,7 +43,7 @@ Then is follows that:
## SVD to pseudo inverse rectangular matrices {#svd-to-pseudo-inverse-rectangular-matrices}
This is taken from ([Preumont 2018](#org6d4589f)).
This is taken from (<a href="#citeproc_bib_item_1">Preumont 2018</a>).
The **Singular Value Decomposition** (SVD) is a generalization of the eigenvalue decomposition of a rectangular matrix:
\\[ J = U \Sigma V^T = \sum\_{i=1}^r \sigma\_i u\_i v\_i^T \\]
@@ -63,9 +63,9 @@ When \\(c(J)\\) becomes large, the most straightforward way to handle the ill-co
This will have usually little impact of the fitting error while reducing considerably the actuator inputs \\(v\\).
## Bibliography {#bibliography}
<a id="org6d4589f"></a>Preumont, Andre. 2018. _Vibration Control of Active Structures - Fourth Edition_. Solid Mechanics and Its Applications. Springer International Publishing. <https://doi.org/10.1007/978-3-319-72296-2>.
<a id="org8e4f47e"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. _Multivariable Feedback Control: Analysis and Design_. John Wiley.
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>Preumont, Andre. 2018. <i>Vibration Control of Active Structures - Fourth Edition</i>. Solid Mechanics and Its Applications. Springer International Publishing. doi:<a href="https://doi.org/10.1007/978-3-319-72296-2">10.1007/978-3-319-72296-2</a>.</div>
<div class="csl-entry">NO_ITEM_DATA:skogestad05_multiv_feedb_contr</div>
</div>