Clamped Beam - Revision history

Saak at 08:57, 5 June 2025

2025-06-05T08:57:45Z

← Older revision		Revision as of 08:57, 5 June 2025
Line 93:		Line 93:
	assert np.all(A[:n2, n2:] == A[0, n2] * np.eye(n2))		assert np.all(A[:n2, n2:] == A[0, n2] * np.eye(n2))
	assert np.all(B[:n2] == 0)		assert np.all(B[:n2] == 0)
	assert np.all(C[:, :n2] == 0)		assert np.all(C[:, n2:] == 0)

	a = A[0, n2]		a = A[0, n2]
Line 128:		Line 128:
	\begin{align}		\begin{align}
	\ddot{x}(t) + E \dot{x}(t) + K x(t) &= B u(t) \\		\ddot{x}(t) + E \dot{x}(t) + K x(t) &= B u(t) \\
	y(t) &= C_p ~~\dot{~~x}(t)		y(t) &= C_p x(t)
	\end{align}		\end{align}
	</math>		</math>

Malhotra: infobox string

2023-11-30T09:28:21Z

infobox string

@@ Line 6: / Line 6: @@
 [[Category:second differential order]]
 [[Category:SISO]]
 ==Description: Clamped Beam Model==

Mlinaric: Fix Python

2023-09-01T23:48:52Z

Fix Python

← Older revision		Revision as of 23:48, 1 September 2023
Line 31:		Line 31:
	A = mat['A'].toarray()		A = mat['A'].toarray()
	B = mat['B']		B = mat['B']
	C = mat['C'].astype(np.~~float_~~)		C = mat['C'].astype(np.float64)
	</syntaxhighlight>		</syntaxhighlight>

Mlinaric: Edit SLICOT links

2023-08-30T12:50:55Z

Edit SLICOT links

← Older revision		Revision as of 12:50, 30 August 2023
Line 20:		Line 20:
	==Data==		==Data==

	The system matrices <math>A</math>, <math>B</math>, <math>C</math> are available from the [~~http~~://slicot.org/20-site/126-benchmark-examples-for-model-reduction SLICOT benchmarks] page: [~~http~~://slicot.org/objects/software/shared/bench-data/beam.zip beam.zip] and are stored as MATLAB [https://www.mathworks.com/help/matlab/import_export/mat-file-versions.html .mat] file.		The system matrices <math>A</math>, <math>B</math>, <math>C</math> are available from the [https://www.slicot.org/20-site/126-benchmark-examples-for-model-reduction SLICOT benchmarks] page: [https://www.slicot.org/objects/software/shared/bench-data/beam.zip beam.zip] and are stored as MATLAB [https://www.mathworks.com/help/matlab/import_export/mat-file-versions.html .mat] file.

	Here is [https://www.python.org Python] code for loading the matrices (<math>A</math> is stored as a sparse matrix that is mostly full and <math>C</math> is stored as an array of 8-bit unsigned integers):		Here is [https://www.python.org Python] code for loading the matrices (<math>A</math> is stored as a sparse matrix that is mostly full and <math>C</math> is stored as an array of 8-bit unsigned integers):

Mlinaric: Edit categories, add Python code, add second-order structure

2023-08-30T12:42:20Z

Edit categories, add Python code, add second-order structure

@@ Line 1: / Line 1: @@
 [[Category:benchmark]]
 [[Category:SLICOT]]
-[[Category:Sparse]]
+[[Category:linear]]
 [[Category:SISO]]
@@ Line 14: / Line 17: @@
 This benchmark is part of the '''SLICOT Benchmark Examples for Model Reduction'''<ref name="chahlaoui05"/>.
 ==Data==
@@ Line 20: / Line 22: @@
 The system matrices <math>A</math>, <math>B</math>, <math>C</math> are available from the [http://slicot.org/20-site/126-benchmark-examples-for-model-reduction SLICOT benchmarks] page: [http://slicot.org/objects/software/shared/bench-data/beam.zip beam.zip] and are stored as MATLAB [https://www.mathworks.com/help/matlab/import_export/mat-file-versions.html .mat] file.
 ==Dimensions==
 System structure:
 :<math>
-\begin{array}{rcl}
+\begin{align}
-\dot{x}(t) &=& Ax(t) + Bu(t) \\
+  \dot{x}(t) &= A x(t) + B u(t) \\
-y(t) &=& Cx(t)
+  y(t) &= C x(t)
-\end{array}
+\end{align}
 </math>
@@ Line 38: / Line 103: @@
 <math>C \in \mathbb{R}^{1 \times 348}</math>.
 ==Citation==

Lund: remove preliminary and stub warnings

2022-08-26T12:56:52Z

remove preliminary and stub warnings

← Older revision		Revision as of 12:56, 26 August 2022
Line 1:		Line 1:
	~~{{preliminary}} <!-- Do not remove -->~~

	[[Category:benchmark]]		[[Category:benchmark]]
	[[Category:SLICOT]]		[[Category:SLICOT]]
	[[Category:Sparse]]		[[Category:Sparse]]
	[[Category:SISO]]		[[Category:SISO]]

	~~'''This is a stub. Please expand.'''~~

	==Description: Clamped Beam Model==		==Description: Clamped Beam Model==

Himpe: init clamped beam

2018-08-16T08:21:55Z

init clamped beam

New page

{{preliminary}} 

[[Category:benchmark]]
[[Category:SLICOT]]
[[Category:Sparse]]
[[Category:SISO]]

'''This is a stub. Please expand.'''

==Description: Clamped Beam Model==

This benchmark models a [[wikipedia:Cantilever|cantilever beam]], which is a beam clamped on one end.
More details can be found in <ref name="antoulas01"/> and <ref name="chahlaoui02"/>, <ref name="chahlaoui05"/>.

For larger beam-type benchmarks see the [[Linear_1D_Beam|linear 1d beam]] and [[Electrostatic_Beam|electrostatic beam]] benchmarks.

==Origin==

This benchmark is part of the '''SLICOT Benchmark Examples for Model Reduction'''<ref name="chahlaoui05"/>.

==Data==

The system matrices <math>A</math>, <math>B</math>, <math>C</math> are available from the [http://slicot.org/20-site/126-benchmark-examples-for-model-reduction SLICOT benchmarks] page: [http://slicot.org/objects/software/shared/bench-data/beam.zip beam.zip] and are stored as MATLAB [https://www.mathworks.com/help/matlab/import_export/mat-file-versions.html .mat] file.

==Dimensions==

System structure:

:<math>
\begin{array}{rcl}
\dot{x}(t) &=& Ax(t) + Bu(t) \\
y(t) &=& Cx(t)
\end{array}
</math>

System dimensions:

<math>A \in \mathbb{R}^{348 \times 348}</math>,
<math>B \in \mathbb{R}^{348 \times 1}</math>,
<math>C \in \mathbb{R}^{1 \times 348}</math>.

==Citation==

To cite this benchmark, use the following references:

* For the benchmark itself and its data:
::Niconet e.V., '''SLICOT - Subroutine Library in Systems and Control Theory''', http://www.slicot.org

@MANUAL{slicot_beam,
title = {{SLICOT} - Subroutine Library in Systems and Control Theory},
organization = {Niconet e.V.}
address = <nowiki>{\url{http://www.slicot.org}}</nowiki>,
key = {SLICOT}
}

* For the background on the benchmark:

@ARTICLE{morAntSG01,
author = <nowiki>{A.C. Antoulas, D.C. Sorensen and S. Gugercin}</nowiki>,
title = {A survey of model reduction methods for large-scale systems},
journal = {Contemporary Mathematics},
volume = {280},
pages = {193--219},
year = {2001},
doi = {10.1090/conm/280}
}

==References==

<references>

<ref name="antoulas01"> A.C. Antoulas, D.C. Sorensen and S. Gugercin. [https://doi.org/10.1090/conm/280 A survey of model reduction methods for large-scale systems]. Contemporary Mathematics, 280: 193--219, 2001.</ref>

<ref name="chahlaoui02"> Y. Chahlaoui, P. Van Dooren, [http://eprints.maths.manchester.ac.uk/1040/1/ChahlaouiV02a.pdf A collection of Benchmark examples for model reduction of linear time invariant dynamical systems], Working Note 2002-2: 2002.</ref>

<ref name="chahlaoui05"> Y. Chahlaoui, P. Van Dooren, [https://doi.org/10.1007/3-540-27909-1_24 Benchmark Examples for Model Reduction of Linear Time-Invariant Dynamical Systems], Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol 45: 379--392, 2005.</ref>

</references>