Flexible Space Structures - Revision history

Schuetz2 at 05:31, 17 June 2025

2025-06-17T05:31:19Z

← Older revision		Revision as of 05:31, 17 June 2025
Line 94:		Line 94:
	title = {Flexible Space Structures},		title = {Flexible Space Structures},
	howpublished = {{MORwiki} -- Model Order Reduction Wiki},		howpublished = {{MORwiki} -- Model Order Reduction Wiki},
	url = <nowiki>{~~http~~://modelreduction.org/~~index.php~~/Flexible_Space_Structures}</nowiki>,		url = <nowiki>{https://modelreduction.org/morwiki/Flexible_Space_Structures}</nowiki>,
	year = 2018		year = 2018
	}		}

Lund: remove preliminary warning

2022-08-26T12:59:16Z

remove preliminary warning

← Older revision		Revision as of 12:59, 26 August 2022
Line 1:		Line 1:
	~~{{preliminary}} <!-- Do not remove -->~~

	[[Category:benchmark]]		[[Category:benchmark]]
	[[Category:linear]]		[[Category:linear]]

Himpe: added procedural cat

2018-08-22T12:22:38Z

added procedural cat

← Older revision		Revision as of 12:22, 22 August 2018
Line 4:		Line 4:
	[[Category:linear]]		[[Category:linear]]
	[[Category:second differential order]]		[[Category:second differential order]]
			[[Category:Procedural]]
	[[Category:SISO]]		[[Category:SISO]]

Werner: /* Citation */

2018-04-24T08:59:12Z

Citation

← Older revision		Revision as of 08:59, 24 April 2018
Line 92:		Line 92:

	@MISC{morwiki-flexspacstruc,		@MISC{morwiki-flexspacstruc,
	author = <nowiki>{{The MORwiki} Community}}</nowiki>,		author = <nowiki>{{The MORwiki Community}}</nowiki>,
	title = {Flexible Space Structures},		title = {Flexible Space Structures},
	howpublished = {{MORwiki} -- Model Order Reduction Wiki},		howpublished = {{MORwiki} -- Model Order Reduction Wiki},
Line 100:		Line 100:

	* For the background on the benchmark: [https://morwiki.mpi-magdeburg.mpg.de/BibTeX/#morGawW91 morGawW91] ([https://morwiki.mpi-magdeburg.mpg.de/BibTeX/html/mor_bib.html#morGawW91 BibTeX])		* For the background on the benchmark: [https://morwiki.mpi-magdeburg.mpg.de/BibTeX/#morGawW91 morGawW91] ([https://morwiki.mpi-magdeburg.mpg.de/BibTeX/html/mor_bib.html#morGawW91 BibTeX])


	==Reference==		==Reference==

Werner: Updated BibTeX entry.

2018-04-24T08:58:40Z

Updated BibTeX entry.

← Older revision		Revision as of 08:58, 24 April 2018
Line 89:		Line 89:

	* For the benchmark itself and its data:		* For the benchmark itself and its data:
	::The MORwiki Community. '''Flexible Space Structures'''. MORwiki - Model Order Reduction Wiki, 2018. http://modelreduction.org/index.php/Flexible_Space_Structures		::The MORwiki Community, '''Flexible Space Structures'''. MORwiki - Model Order Reduction Wiki, 2018. http://modelreduction.org/index.php/Flexible_Space_Structures

	@MISC{morwiki-flexspacstruc,		@MISC{morwiki-flexspacstruc,
	author = {The {MORwiki} Community},		author = <nowiki>{{The MORwiki} Community}}</nowiki>,
	title = {Flexible Space Structures},		title = {Flexible Space Structures},
	howpublished = {{MORwiki} -- Model Order Reduction Wiki},		howpublished = {{MORwiki} -- Model Order Reduction Wiki},
	url = {<nowiki>http://modelreduction.org/index.php/Flexible_Space_Structures</nowiki>},		url = <nowiki>{http://modelreduction.org/index.php/Flexible_Space_Structures}</nowiki>,
	year = {2018}		year = 2018
	}		}

	* For the background on the benchmark: [https://morwiki.mpi-magdeburg.mpg.de/BibTeX/#morGawW91 morGawW91] ([https://morwiki.mpi-magdeburg.mpg.de/BibTeX/html/mor_bib.html#morGawW91 BibTeX])		* For the background on the benchmark: [https://morwiki.mpi-magdeburg.mpg.de/BibTeX/#morGawW91 morGawW91] ([https://morwiki.mpi-magdeburg.mpg.de/BibTeX/html/mor_bib.html#morGawW91 BibTeX])

Himpe: Added Dimensions and Citaiton section, more references and some fixes.

2018-03-07T12:18:00Z

Added Dimensions and Citaiton section, more references and some fixes.

@@ Line 8: / Line 8: @@
 ==Description==
-The '''flexible space structure''' benchmark<ref>W. Gawronski and T. Williams, "<span class="plainlinks">[http://doi.org/10.2514/3.20606 Model Reduction for Flexible Space Structures]</span>", Journal of Guidance 14(1): 68--76, 1991</ref> is a procedural modal model which represents structural dynamics with a selectable number actuators and sensors. This model is used for truss structures in space environments i.e. the COFS-1 (Control of Flexible Structures) mast flight experiment.
+The '''flexible space structure''' benchmark <ref name="gawronski90"/>,<ref name="gawronski91"/>,<ref name="gawronski96"/> is a procedural modal model which represents structural dynamics with a selectable number actuators and sensors. This model is used for truss structures in space environments i.e. the COFS-1 (Control of Flexible Structures) mast flight experiment <ref name="horner86"/>,<ref name="horta86"/>.
-==Model==
+===Model===
 In modal form the '''flexible space structure''' model for <math>K</math> modes, <math>M</math> actuators and <math>Q</math> sensors is of second order and given by:
@@ Line 67: / Line 67: @@
 </source>
 </div>
 ==Reference==
-<references/>
+<references>
 ==Contact==
 ''[[User:Himpe|Christian Himpe]]''

Himpe: typo fix

2017-06-02T08:48:02Z

typo fix

← Older revision		Revision as of 08:48, 2 June 2017
Line 39:		Line 39:

	For this benchmark the system matrix is block diagonal and thus chosen to be sparse.		For this benchmark the system matrix is block diagonal and thus chosen to be sparse.
	The parameters <math>\xi</math> and math>\omega</math> are sampled from a uniform random distributions <math>\mathcal{U}_{[0,\frac{1}{1000}]}^K</math> and <math>\mathcal{U}_{[0,100]}^K</math> respectively.		The parameters <math>\xi</math> and <math>\omega</math> are sampled from a uniform random distributions <math>\mathcal{U}_{[0,\frac{1}{1000}]}^K</math> and <math>\mathcal{U}_{[0,100]}^K</math> respectively.
	The components of the input matrix <math>b_k</math> are sampled form a uniform random distribution <math>\mathcal{U}_{[0,1]}</math>,		The components of the input matrix <math>b_k</math> are sampled form a uniform random distribution <math>\mathcal{U}_{[0,1]}</math>,
	while the output matrix <math>C</math> is sampled from a uniform random distribution <math>\mathcal{U}_{[0,10]}</math> completely w.l.o.g, since if the components of <math>C_d</math> are random their scaling can be ignored.		while the output matrix <math>C</math> is sampled from a uniform random distribution <math>\mathcal{U}_{[0,10]}</math> completely w.l.o.g, since if the components of <math>C_d</math> are random their scaling can be ignored.

Himpe: /* Data */ Minor fixes

2017-05-12T08:12:19Z

Data: Minor fixes

← Older revision		Revision as of 08:12, 12 May 2017
Line 46:		Line 46:
	==Data==		==Data==

	The following Matlab code assembles the above described <math>A</math>, <math>B</math> and <math>C</math> matrix for a given number of modes <math>K</math>.		The following Matlab code assembles the above described <math>A</math>, <math>B</math> and <math>C</math> matrix for a given number of modes <math>K</math>, actuators (inputs) <math>M</math> and sensors (outputs) <math>Q</math>.

	<div class="thumbinner" style="width:540px;text-align:left;">		<div class="thumbinner" style="width:540px;text-align:left;">
Line 54:		Line 54:
	rand('seed',1009);		rand('seed',1009);
	xi = rand(1,K)*0.001; % Sample damping ratio		xi = rand(1,K)*0.001; % Sample damping ratio
	omega = rand(1,K)*100; % Sample natural frequencies		omega = rand(1,K)*100.0; % Sample natural frequencies

	A_k = cellfun(@(p) sparse([-2.0p(1)p(2),-p(2);p(2),0]), ...		A_k = cellfun(@(p) sparse([-2.0p(1)p(2),-p(2);p(2),0]), ...
Line 67:		Line 67:
	</source>		</source>
	</div>		</div>


	==Reference==		==Reference==

Himpe: Some fixes and more explanation.

2017-05-11T14:30:41Z

Some fixes and more explanation.

← Older revision		Revision as of 14:30, 11 May 2017
Line 8:		Line 8:
	==Description==		==Description==

	The '''flexible space structure''' benchmark<ref>W. Gawronski and T. Williams, "<span class="plainlinks">[http://doi.org/10.~~2541~~/3.20606 Model Reduction for Flexible Space Structures]</span>", Journal of Guidance 14(1): 68--76, 1991</ref> is a procedural modal model which represents structural dynamics with a selectable number actuators and sensors.		The '''flexible space structure''' benchmark<ref>W. Gawronski and T. Williams, "<span class="plainlinks">[http://doi.org/10.2514/3.20606 Model Reduction for Flexible Space Structures]</span>", Journal of Guidance 14(1): 68--76, 1991</ref> is a procedural modal model which represents structural dynamics with a selectable number actuators and sensors. This model is used for truss structures in space environments i.e. the COFS-1 (Control of Flexible Structures) mast flight experiment.

	==Model==		==Model==
Line 41:		Line 41:
	The parameters <math>\xi</math> and math>\omega</math> are sampled from a uniform random distributions <math>\mathcal{U}_{[0,\frac{1}{1000}]}^K</math> and <math>\mathcal{U}_{[0,100]}^K</math> respectively.		The parameters <math>\xi</math> and math>\omega</math> are sampled from a uniform random distributions <math>\mathcal{U}_{[0,\frac{1}{1000}]}^K</math> and <math>\mathcal{U}_{[0,100]}^K</math> respectively.
	The components of the input matrix <math>b_k</math> are sampled form a uniform random distribution <math>\mathcal{U}_{[0,1]}</math>,		The components of the input matrix <math>b_k</math> are sampled form a uniform random distribution <math>\mathcal{U}_{[0,1]}</math>,
	while the output matrix <math>C</math> is sampled from a uniform random distribution <math>\mathcal{U}^{}_[0,10]</math> completely w.l.o.g, since if the components of <math>C_d</math> are random their scaling can be ignored.		while the output matrix <math>C</math> is sampled from a uniform random distribution <math>\mathcal{U}_{[0,10]}</math> completely w.l.o.g, since if the components of <math>C_d</math> are random their scaling can be ignored.

Himpe: Fix tex errors

2017-05-11T10:01:42Z

Fix tex errors

← Older revision		Revision as of 10:01, 11 May 2017
Line 13:		Line 13:

	In modal form the '''flexible space structure''' model for <math>K</math> modes, <math>M</math> actuators and <math>Q</math> sensors is of second order and given by:		In modal form the '''flexible space structure''' model for <math>K</math> modes, <math>M</math> actuators and <math>Q</math> sensors is of second order and given by:
	:<math>
	\ddot{\nu}(t) &= (2 \xi \circ \omega) \circ \dot{\nu}(t) + (\omega \circ \omega) \circ \nu = Bu(t) \\		:<math>\ddot{\nu}(t) = (2 \xi \circ \omega) \circ \dot{\nu}(t) + (\omega \circ \omega) \circ \nu = Bu(t)</math>
	y(t) &= C_r\dot{\nu}(t) + C_d\nu(t)
	</math>		:<math>y(t) = C_r\dot{\nu}(t) + C_d\nu(t)</math>
	with the parameters <math>\xi \in \mathbb{R}_{>0}^K</math> (damping ratio), <math>\omega \in \mathbb{R}_{>0}^K</math> (natural frequency) and using the Hadamard product $\circ$.
	The first order representation follows for <math>x(t) = (\dot{nu}(t), \omega_1\nu_1, \dots, \omega_K\nu_K)</math> by:		with the parameters <math>\xi \in \mathbb{R}_{>0}^K</math> (damping ratio), <math>\omega \in \mathbb{R}_{>0}^K</math> (natural frequency) and using the Hadamard product <math>\circ</math>.
	:<math>		The first order representation follows for <math>x(t) = (\dot{\nu}(t), \omega_1\nu_1, \dots, \omega_K\nu_K)</math> by:
	\dot{x}(t) &= Ax(t) + Bu(t) \\
	y(t) &= Cx(t)		:<math>\dot{x}(t) = Ax(t) + Bu(t) </math>
	</math>
			:<math>y(t) = Cx(t)</math>

	with the matrices:		with the matrices:
	:<math>
	A := \begin{pmatrix} A_1 & & \\ & \ddots & \\ & & A_K \end{pmatrix}, \\		:<math>A := \begin{pmatrix} A_1 & & \\ & \ddots & \\ & & A_K \end{pmatrix}, \; B := \begin{pmatrix} B_1 \\ \vdots \\ B_K \end{pmatrix}, \; C := \begin{pmatrix} C_1 & \dots & C_K \end{pmatrix}, </math>
	B := \begin{pmatrix} B_1 \\ \vdots \\ B_K \end{pmatrix}, \\
	C := \begin{pmatrix} C_1 & \dots & C_K \end{pmatrix},
	</math>
	and their components:		and their components:
	:<math>
	A_k := \begin{pmatrix} -2\xi_k\omega_k & -\omega_k \\ \omega_k & 0 \end{pmatrix}, \\		:<math>A_k := \begin{pmatrix} -2\xi_k\omega_k & -\omega_k \\ \omega_k & 0 \end{pmatrix}, \; B_k := \begin{pmatrix} b_k \\ 0 \end{pmatrix}, \; C_k := \begin{pmatrix} c_{rk} & \frac{c_{dk}}{\omega_k} \end{pmatrix},</math>
	B_k := \begin{pmatrix} b_k \\ 0 \end{pmatrix}, \\
	C_k := \begin{pmatrix} c_{rk} & \frac{c_{dk}}{\omega_k} \end{pmatrix},
	</math>
	where <math>b_k \in \mathbb{R}^{1 \times M}</math> and <math>c_{rk}, c_{dk} \in \mathbb{R}^{Q \times 1}</math>.		where <math>b_k \in \mathbb{R}^{1 \times M}</math> and <math>c_{rk}, c_{dk} \in \mathbb{R}^{Q \times 1}</math>.

Line 41:		Line 39:

	For this benchmark the system matrix is block diagonal and thus chosen to be sparse.		For this benchmark the system matrix is block diagonal and thus chosen to be sparse.
	The parameters <math>\xi</math> and math>\omega</math> are sampled from a uniform random distributions <math>\mathcal{U}_[0,\frac{1}{1000}]}^K</math> and <math>\mathcal{U}_[0,100]}^K</math> respectively.		The parameters <math>\xi</math> and math>\omega</math> are sampled from a uniform random distributions <math>\mathcal{U}_{[0,\frac{1}{1000}]}^K</math> and <math>\mathcal{U}_{[0,100]}^K</math> respectively.
	The components of the input matrix <math>b_k</math> are sampled form a uniform random distribution <math>\mathcal{U}_{[0,1]}</math>,		The components of the input matrix <math>b_k</math> are sampled form a uniform random distribution <math>\mathcal{U}_{[0,1]}</math>,
	while the output matrix <math>C</math> is sampled from a uniform random distribution <math>\mathcal{U}^{}_[0,10]</math> completely w.l.o.g, since if the components of <math>C_d</math> are random their scaling can be ignored.		while the output matrix <math>C</math> is sampled from a uniform random distribution <math>\mathcal{U}^{}_[0,10]</math> completely w.l.o.g, since if the components of <math>C_d</math> are random their scaling can be ignored.