Artificial Fishtail - Revision history

Malhotra at 09:24, 30 November 2023

2023-11-30T09:24:57Z

@@ Line 6: / Line 6: @@
 [[Category:Sparse]]
 [[Category:MIMO]]
 <figure id="fig:plot1">

Mlinaric: Add MIMO category

2023-08-29T17:04:15Z

Add MIMO category

← Older revision		Revision as of 17:04, 29 August 2023
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	[[Category:Second differential order]]		[[Category:Second differential order]]
	[[Category:Sparse]]		[[Category:Sparse]]
			[[Category:MIMO]]

	<figure id="fig:plot1">		<figure id="fig:plot1">

Mlinaric: Fixes, N->n

2023-08-29T01:28:39Z

Fixes, N->n

← Older revision		Revision as of 01:28, 29 August 2023
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	==Description==		==Description==
	~~Todays~~ [[wikipedia:Autonomous_underwater_vehicle\|autonomous underwater vehicles]] (AUVs) are a source of noise pollution and inefficiency due to their screw propeller driven design.		Today's [[wikipedia:Autonomous_underwater_vehicle\|autonomous underwater vehicles]] (AUVs) are a source of noise pollution and inefficiency due to their screw propeller-driven design.
	The evolution of fish has, on the other hand, optimized their underwater efficiency and agility over millennia.		The evolution of fish has, on the other hand, optimized their underwater efficiency and agility over millennia.
	The adaption of fish-like drive systems for AUVs is therefore a promising choice.		The adaption of fish-like drive systems for AUVs is therefore a promising choice.
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	==Model Description==		==Model Description==
	This model describes the silicon body of an artificial fishtail supported by a central carbon beam.		This model describes the silicon body of an artificial fishtail supported by a central carbon beam.
	The rear part of the fish-body without the fins is modeled as as a 3D FEM model using linear elasticity.		The rear part of the fish body without the fins is modeled as a 3D FEM model using linear elasticity.
	In the current stage of modeling the tail is rigidly mounted in the front, the states in <math>x</math> represent the displacements of the finite element degrees of freedom.		In the current stage of modeling the tail is rigidly mounted in the front, the states in <math>x</math> represent the displacements of the finite element degrees of freedom.
	The fish-like locomotion is enabled by pumping air between two sets of pressure chambers in the left and right halves of the tail.		The fish-like locomotion is enabled by pumping air between two sets of pressure chambers in the left and right halves of the tail.
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	There are two variants of the model.		There are two variants of the model.
	The first has three outputs representing the displacements of the point of interest, the rear tip of the carbon beam, in the three spatial directions.		The first has three outputs representing the displacements of the point of interest, the rear tip of the carbon beam, in the three spatial directions.
	For the second variant six additional points <math>(z_1,z_2,z_3)</math> on the flank are added as outputs, yielding a total of 21 outputs.		For the second variant, six additional points <math>(z_1,z_2,z_3)</math> on the flank are added as outputs, yielding a total of 21 outputs.


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	Note that the POI (Point of Interest) is the last row in this table and in Cp_ext in the data files (see below).		Note that the POI (Point of Interest) is the last row in this table and in Cp_ext in the data files (see below).
	The additional outputs show two effects.		The additional outputs show two effects.
	On the one hand, for purely input output related reduction methods they avoid drastic deviations on the interior states,		On the one hand, for purely input-output-related reduction methods they avoid drastic deviations on the interior states.
	on the other hand they show a smoothing effect for the ~~models~~ transfer function.		On the other hand, they show a smoothing effect for the model's transfer function.

	==Origin==		==Origin==
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	==Data==		==Data==
	The model is based on ~~the~~ the finite element package [https://www.firedrakeproject.org Firedrake] and uses the material parameters:		The model is based on the finite element package [https://www.firedrakeproject.org Firedrake] and uses the material parameters:
	{\| class="wikitable" style="margin: auto;"		{\| class="wikitable" style="margin: auto;"
	\|+ style="caption-side:bottom;"\|		\|+ style="caption-side:bottom;"\|
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	\|		\|
	\|<math>\varrho_1</math>		\|<math>\varrho_1</math>
	\|<math>1.07\cdot 10^{−3}</math>		\|<math>1.07 \cdot 10^{-3}</math>
	\|<math>\frac{\text{kg}}{\text{m}^{3}}</math>		\|<math>\frac{\text{kg}}{\text{m}^{3}}</math>
	\|-style="background-color:#FFFFFF;"		\|-style="background-color:#FFFFFF;"
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	System dimensions:		System dimensions:

	<math>M ~~\in \mathbb{R}^{N \times N}</math>~~,		<math>M, E, K \in \mathbb{R}^{n \times n}</math>,
	~~<math>~~E ~~\in \mathbb{R}^{N \times N}</math>~~,		<math>B \in \mathbb{R}^{n \times m}</math>,
	~~<math>~~K \in \mathbb{R}^{N \times N}</math>,		<math>C \in \mathbb{R}^{p \times n}</math>,
	<math>B \in \mathbb{R}^{N \times M}</math>,		with <math>n = 779\,232</math> and <math>m = 1</math>.
	<math>C \in \mathbb{R}^{P \times N}</math>,
	with <math>N=779\,232</math> and <math>M=1</math>.

	The internal damping is modeled as Rayleigh damping <math>E=\alpha_r M + \beta_r K</math> using the coefficients from the table above.		The internal damping is modeled as Rayleigh damping <math>E = \alpha_r M + \beta_r K</math> using the coefficients from the table above.

	System variants:		System variants:

	* <math>P = 3</math>: <math>C=</math><tt>Cp</tt> in the <span class="plainlinks">[https://doi.org/10.5281/zenodo.2558728 data files]</span>,		* <math>p = 3</math>: <math>C=</math><tt>Cp</tt> in the <span class="plainlinks">[https://doi.org/10.5281/zenodo.2558728 data files]</span>,
	* <math>P = 21</math>: <math>C=</math><tt>Cp_ext</tt> in the <span class="plainlinks">[https://doi.org/10.5281/zenodo.2558728 data files]</span>.		* <math>p = 21</math>: <math>C=</math><tt>Cp_ext</tt> in the <span class="plainlinks">[https://doi.org/10.5281/zenodo.2558728 data files]</span>.

	== Remarks ==		== Remarks ==

Lund: added comment about size of data files

2022-08-31T12:30:58Z

added comment about size of data files

← Older revision		Revision as of 12:30, 31 August 2022
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	* The interesting operation frequencies are in the range between <math>0</math>Hz and <math>10</math>Hz.		* The interesting operation frequencies are in the range between <math>0</math>Hz and <math>10</math>Hz.
	* If required, the finite element mesh behind the model and a CSV file with the output locations are available [https://doi.org/10.5281/zenodo.2565173 separately].		* If required, the finite element mesh behind the model and a CSV file with the output locations are available [https://doi.org/10.5281/zenodo.2565173 separately].
			* Warning: the data files are quite large and may exceed the RAM of a typical machine if the user is also running MATLAB.

	==Citation==		==Citation==

Mitchell: typo

2022-03-14T13:13:41Z

typo

← Older revision		Revision as of 13:13, 14 March 2022
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	==Origin==		==Origin==
	The model was ~~setup~~ and computed at the [https://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/Artificial_Fishtail chair of automatic control] at CAU Kiel and first presented in <ref name="SieKM18" />.		The model was set up and computed at the [https://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/Artificial_Fishtail chair of automatic control] at CAU Kiel and first presented in <ref name="SieKM18" />.

	==Data==		==Data==

Mitchell: typo

2022-03-14T13:11:16Z

typo

← Older revision		Revision as of 13:11, 14 March 2022
Line 19:		Line 19:
	Todays [[wikipedia:Autonomous_underwater_vehicle\|autonomous underwater vehicles]] (AUVs) are a source of noise pollution and inefficiency due to their screw propeller driven design.		Todays [[wikipedia:Autonomous_underwater_vehicle\|autonomous underwater vehicles]] (AUVs) are a source of noise pollution and inefficiency due to their screw propeller driven design.
	The evolution of fish has, on the other hand, optimized their underwater efficiency and agility over millennia.		The evolution of fish has, on the other hand, optimized their underwater efficiency and agility over millennia.
	The adaption of fish-like drive systems for AUVs is therefore a ~~promissing~~ choice.		The adaption of fish-like drive systems for AUVs is therefore a promising choice.

	==Model Description==		==Model Description==

Werner at 09:27, 12 March 2020

2020-03-12T09:27:01Z

← Older revision		Revision as of 09:27, 12 March 2020
Line 10:		Line 10:
	</figure>		</figure>
	<figure id="fig:plot2">		<figure id="fig:plot2">
	[[File:fishtail_tf.png\|438px\|thumb\|right\|<caption>~~Bode Magnitude~~ Plot Fishtail Cp</caption>]]		[[File:fishtail_tf.png\|438px\|thumb\|right\|<caption>Sigma Plot Fishtail Cp</caption>]]
	</figure>		</figure>
	<figure id="fig:plot3">		<figure id="fig:plot3">
	[[File:fishtail_ext_tf.png\|438px\|thumb\|right\|<caption>~~Bode Magnitude~~ Plot Fishtail Cp_ext</caption>]]		[[File:fishtail_ext_tf.png\|438px\|thumb\|right\|<caption>Sigma Plot Fishtail Cp_ext</caption>]]
	</figure>		</figure>

Himpe: Small corrections and additions.

2019-03-04T14:18:07Z

Small corrections and additions.

← Older revision		Revision as of 14:18, 4 March 2019
Line 1:		Line 1:
	~~{{preliminary}} <!-- Do not remove -->~~
	[[Category:benchmark]]		[[Category:benchmark]]
	[[Category:ODE]]		[[Category:ODE]]
Line 18:		Line 17:

	==Description==		==Description==
	Todays autonomous underwater vehicles (AUVs) are ~~subject to~~ noise pollution and inefficiency due to their screw propeller driven design. The evolution of fish has, on the other hand, optimized their underwater efficiency and agility over millennia. The adaption of fish-like drive systems for AUVs is therefore ~~an obvious~~ choice.		Todays [[wikipedia:Autonomous_underwater_vehicle\|autonomous underwater vehicles]] (AUVs) are a source of noise pollution and inefficiency due to their screw propeller driven design.
			The evolution of fish has, on the other hand, optimized their underwater efficiency and agility over millennia.
			The adaption of fish-like drive systems for AUVs is therefore a promissing choice.

	==Model Description==		==Model Description==
	This model describes the silicon body of an artificial fishtail supported by a central carbon beam. The rear part of the fish-body without the fins is modeled as as a 3d FEM model using linear elasticity. In the current stage of modeling the tail is rigidly mounted in the front, the states in <math>x</math> represent the displacements of the finite element degrees of freedom. The fish-like locomotion is enabled by pumping air between two sets of pressure chambers in the left and right halves of the tail. The single input <math>u</math> of the system is thus the pumping pressure. The outputs are displacements of certain surface points. There are two variants of the model. The first has ~~only~~ three outputs representing the displacements of the point of interest, the rear tip of the carbon beam, in the three spatial directions. For the second variant 6 additional points on the flank are added as outputs.		This model describes the silicon body of an artificial fishtail supported by a central carbon beam.
			The rear part of the fish-body without the fins is modeled as as a 3D FEM model using linear elasticity.
			In the current stage of modeling the tail is rigidly mounted in the front, the states in <math>x</math> represent the displacements of the finite element degrees of freedom.
			The fish-like locomotion is enabled by pumping air between two sets of pressure chambers in the left and right halves of the tail.
			The single input <math>u</math> of the system is thus the pumping pressure.
			The outputs are displacements of certain surface points.
			There are two variants of the model.
			The first has three outputs representing the displacements of the point of interest, the rear tip of the carbon beam, in the three spatial directions.
			For the second variant six additional points <math>(z_1,z_2,z_3)</math> on the flank are added as outputs, yielding a total of 21 outputs.


Line 60:		Line 69:
	\|}		\|}

	Note that the POI is the last row in this table and in Cp_ext in the data files (see below). The additional outputs show two effects. On the one hand, for purely input output related reduction methods they avoid drastic deviations on the interior states. on the other hand they show a smoothing effect for the models transfer function.		Note that the POI (Point of Interest) is the last row in this table and in Cp_ext in the data files (see below).
			The additional outputs show two effects.
			On the one hand, for purely input output related reduction methods they avoid drastic deviations on the interior states,
			on the other hand they show a smoothing effect for the models transfer function.

	==Origin==		==Origin==
Line 66:		Line 78:

	==Data==		==Data==
	~~Based~~ on the the finite element package [https://www.firedrakeproject.org Firedrake] and ~~using~~ the material parameters		The model is based on the the finite element package [https://www.firedrakeproject.org Firedrake] and uses the material parameters:
	{\| class="wikitable" style="margin: auto;"		{\| class="wikitable" style="margin: auto;"
	\|+ style="caption-side:bottom;"\|		\|+ style="caption-side:bottom;"\|
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	title = {Matrices for an Artificial Fishtail},		title = {Matrices for an Artificial Fishtail},
	howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},		howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},
	~~month = feb,~~
	year = 2019,		year = 2019,
	doi = {10.5281/zenodo.2558728}		doi = {10.5281/zenodo.2558728}
Line 166:		Line 177:
	title = {Modeling and Motion Planning for an Artificial Fishtail},		title = {Modeling and Motion Planning for an Artificial Fishtail},
	journal = {IFAC-PapersOnLine},		journal = {IFAC-PapersOnLine},
	~~year = 2018,~~
	volume = 51,		volume = 51,
	number = 2,		number = 2,
			year = 2018,
	pages = {319--324},		pages = {319--324},
	doi = {10.1016/j.ifacol.2018.03.055},		doi = {10.1016/j.ifacol.2018.03.055},
Line 176:		Line 187:
	==References==		==References==
	<references>		<references>
	<ref name="SieKM18">D. Siebelts, A. Kater, T. Meurer, <span class="plainlinks">[https://doi.org/doi:10.1016/j.ifacol.2018.03.055 Modeling and ~~motion planning~~ for an ~~artificial fishtail~~]</span>, IFAC-PapersOnLine 51 (2) (2018~~) 319–324~~.</ref>		<ref name="SieKM18">D. Siebelts, A. Kater, T. Meurer, <span class="plainlinks">[https://doi.org/doi:10.1016/j.ifacol.2018.03.055 Modeling and Motion Planning for an Artificial Fishtail]</span>, IFAC-PapersOnLine (9th Vienna International Conference on Mathematical Modelling) 51(2): 319--324, 2018.</ref>
	</references>		</references>

Saak: /* Citation */

2019-02-15T07:46:14Z

Citation

← Older revision		Revision as of 07:46, 15 February 2019
Line 152:		Line 152:
	* For the benchmark itself and its data:		* For the benchmark itself and its data:
	@Misc{SieKM19,		@Misc{SieKM19,
	author = {Siebelts, D. and Kater, A. and Meurer, T.},		author = {Siebelts, D. and Kater, A. and Meurer, T. and Andrej, J.},
	title = {Matrices for an Artificial Fishtail},		title = {Matrices for an Artificial Fishtail},
	howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},		howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},

Saak: /* Remarks */

2019-02-15T06:51:53Z

Remarks

← Older revision		Revision as of 06:51, 15 February 2019
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	* Physically meaningful inputs are of dimension <math>u(t) = \mathcal{O}(10^3)</math>. As an example, a step signal with around <math>5\,000</math>Pa leads to a horizontal POI displacement of about <math>3</math>cm.		* Physically meaningful inputs are of dimension <math>u(t) = \mathcal{O}(10^3)</math>. As an example, a step signal with around <math>5\,000</math>Pa leads to a horizontal POI displacement of about <math>3</math>cm.
	* The interesting operation frequencies are in the range between <math>0</math>Hz and <math>10</math>Hz.		* The interesting operation frequencies are in the range between <math>0</math>Hz and <math>10</math>Hz.
			* If required, the finite element mesh behind the model and a CSV file with the output locations are available [https://doi.org/10.5281/zenodo.2565173 separately].

	==Citation==		==Citation==