Hydro-Electric Open Channel - Revision history

Mitchell: typos

2022-03-15T10:11:41Z

typos

← Older revision		Revision as of 10:11, 15 March 2022
Line 48:		Line 48:

	===Remark===		===Remark===
	As the original model is irrational and of infinite dimension, it exhibits an infinite number of singularities. Therefore, approximation over the complete frequency range is ~~un-achievable~~, at least with a rational function. That is why an approximation over a bounded frequency range is ~~prefferable~~. Indeed, strange ~~behaviours~~ may appear.		As the original model is irrational and of infinite dimension, it exhibits an infinite number of singularities. Therefore, approximation over the complete frequency range is unachievable, at least with a rational function. That is why an approximation over a bounded frequency range is preferable. Indeed, strange behaviors may appear.

	==Citation==		==Citation==

Mitchell: fixed a sentence

2022-03-15T10:10:12Z

fixed a sentence

← Older revision		Revision as of 10:10, 15 March 2022
Line 11:		Line 11:
	</math>		</math>

	The <math>\mathbf G_i</math> and <math>\mathbf G_o</math> ~~functions~~ are irrational ~~and read~~		The <math>\mathbf G_i</math> and <math>\mathbf G_o</math> are the following irrational functions:
	:<math>		:<math>
	\mathbf{G_i}(x,s)= \dfrac{\lambda_1(s)e^{\lambda_2(s)L+\lambda_1(s)x}-\lambda_2(s)e^{\lambda_1(s)L+\lambda_2(s)x}}{B_0s(e^{\lambda_1(s)L}-e^{\lambda_2(s)L})}		\mathbf{G_i}(x,s)= \dfrac{\lambda_1(s)e^{\lambda_2(s)L+\lambda_1(s)x}-\lambda_2(s)e^{\lambda_1(s)L+\lambda_2(s)x}}{B_0s(e^{\lambda_1(s)L}-e^{\lambda_2(s)L})}

Poussotvassal: /* Objective */

2021-03-17T06:31:20Z

Objective

← Older revision		Revision as of 06:31, 17 March 2021
Line 45:		Line 45:

	The model's main dynamics are a delayed one with an integral action.		The model's main dynamics are a delayed one with an integral action.
	Find a (linear) reduced order model stable but with one single singularity in 0 that approximates the irrational model over some frequency range (e.g. [0 0.01]rad/s)		Find a (linear) reduced order model stable but with one single singularity in 0 that approximates the irrational model over some frequency range (e.g. [0,0.01]rad/s)

	===Remark===		===Remark===

Poussotvassal: /* Objective */

2021-03-17T06:31:09Z

Objective

← Older revision		Revision as of 06:31, 17 March 2021
Line 45:		Line 45:

	The model's main dynamics are a delayed one with an integral action.		The model's main dynamics are a delayed one with an integral action.
	Find a (linear) reduced order model stable but with one single singularity in 0 that approximates the irrational model over some frequency range (e.g. [0,.01]rad/s)		Find a (linear) reduced order model stable but with one single singularity in 0 that approximates the irrational model over some frequency range (e.g. [0 0.01]rad/s)

	===Remark===		===Remark===

Poussotvassal: /* Objective */

2021-03-17T06:30:56Z

Objective

← Older revision		Revision as of 06:30, 17 March 2021
Line 45:		Line 45:

	The model's main dynamics are a delayed one with an integral action.		The model's main dynamics are a delayed one with an integral action.
	Find a (linear) reduced order model stable but with one single singularity in 0 that approximates the irrational model over some frequency range (e.g. [0,.01]rad/s		Find a (linear) reduced order model stable but with one single singularity in 0 that approximates the irrational model over some frequency range (e.g. [0,.01]rad/s)

	===Remark===		===Remark===

Poussotvassal: /* Data */

2021-03-17T06:30:47Z

Data

← Older revision		Revision as of 06:30, 17 March 2021
Line 45:		Line 45:

	The model's main dynamics are a delayed one with an integral action.		The model's main dynamics are a delayed one with an integral action.
	Find a (linear) reduced order model stable but with one single singularity in 0 that approximates the irrational model.		Find a (linear) reduced order model stable but with one single singularity in 0 that approximates the irrational model over some frequency range (e.g. [0,.01]rad/s

			===Remark===
			As the original model is irrational and of infinite dimension, it exhibits an infinite number of singularities. Therefore, approximation over the complete frequency range is un-achievable, at least with a rational function. That is why an approximation over a bounded frequency range is prefferable. Indeed, strange behaviours may appear.

	==Citation==		==Citation==

Poussotvassal: /* Description */

2021-03-17T06:19:29Z

Description

← Older revision		Revision as of 06:19, 17 March 2021
Line 38:		Line 38:
	* The <tt>dataONERA_Hydroelectric_withMOR.mat</tt> data file, with 2 ROMs obtained with the [https://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/MORE '''MOR toolbox'''] using the Loewner method		* The <tt>dataONERA_Hydroelectric_withMOR.mat</tt> data file, with 2 ROMs obtained with the [https://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/MORE '''MOR toolbox'''] using the Loewner method
	** Hr1 : linear rational ROM (state-space models in Matlab form).		** Hr1 : linear rational ROM (state-space models in Matlab form).
	** Hr2 : linear rational ROM with ~~varying dimensions, with~~ stability ~~post~~ enforcement and addition of the 0 singularity afterward (state-space models in Matlab form).		** Hr2 : linear rational ROM with post stability enforcement and addition of the 0 singularity afterward (state-space models in Matlab form).

	* The <tt>startONERA_Hydroelectric.m</tt> script file, used to load and plot the data for illustration.		* The <tt>startONERA_Hydroelectric.m</tt> script file, used to load and plot the data for illustration.

Himpe: Reviewed and revised.

2021-03-16T19:38:57Z

Reviewed and revised.

← Older revision		Revision as of 19:38, 16 March 2021
Line 1:		Line 1:
	~~{{preliminary}} <!-- Do not remove -->~~

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

Line 28:		Line 26:
	==Origin==		==Origin==

	Collaboration between [https://www.onera.fr ONERA] and [https://www.edf.fr/ EDF]. The data from the simplified hydro-electric open-channel model come from V. Dalmas and G. Robert while and the ~~treatment~~ performed jointly ~~with~~ P. Vuillemin, and C. Poussot-Vassal.		Collaboration between [https://www.onera.fr ONERA] and [https://www.edf.fr/ EDF]. The data from the simplified hydro-electric open-channel model come from V. Dalmas and G. Robert while and the post-processing was performed jointly by P. Vuillemin, and C. Poussot-Vassal.

	==Data==		==Data==
Line 36:		Line 34:
	The [[File:HydroelectricChannel.zip]] (67KB) repository contains three files:		The [[File:HydroelectricChannel.zip]] (67KB) repository contains three files:

	* The <tt>dataONERA_Hydroelectric.mat</tt> data file, with the data describing the irrational above ~~described~~		* The <tt>dataONERA_Hydroelectric.mat</tt> data file, with the data describing the irrational model described above

	* The <tt>dataONERA_Hydroelectric_withMOR.mat</tt> data file, with 2 ROMs obtained with the [https://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/MORE '''MOR toolbox'''] using the Loewner method		* The <tt>dataONERA_Hydroelectric_withMOR.mat</tt> data file, with 2 ROMs obtained with the [https://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/MORE '''MOR toolbox'''] using the Loewner method
Line 42:		Line 40:
	** Hr2 : linear rational ROM with varying dimensions, with stability post enforcement and addition of the 0 singularity afterward (state-space models in Matlab form).		** Hr2 : linear rational ROM with varying dimensions, with stability post enforcement and addition of the 0 singularity afterward (state-space models in Matlab form).

	* The <tt>startONERA_Hydroelectric.m</tt> script file, used to ~~loads~~ and ~~plots~~ the data for illustration.		* The <tt>startONERA_Hydroelectric.m</tt> script file, used to load and plot the data for illustration.

	===Objective===		===Objective===

	The model's main dynamics are a delayed one with an integral action.		The model's main dynamics are a delayed one with an integral action.
	Find a (linear) reduced order model stable but with one single singularity in 0 that ~~well reproduces~~ the irrational model.		Find a (linear) reduced order model stable but with one single singularity in 0 that approximates the irrational model.

	==Citation==		==Citation==

Himpe: /* Description */

2021-02-01T11:34:28Z

Description

← Older revision		Revision as of 11:34, 1 February 2021
Line 34:		Line 34:
	===Description===		===Description===

	The [[File:HydroelectricChannel.zip]] (~~67Ko~~) repository contains three files:		The [[File:HydroelectricChannel.zip]] (67KB) repository contains three files:

	* The <tt>dataONERA_Hydroelectric.mat</tt> data file, with the data describing the irrational above described		* The <tt>dataONERA_Hydroelectric.mat</tt> data file, with the data describing the irrational above described

Himpe: Minor fixes.

2021-02-01T11:34:04Z

Minor fixes.

← Older revision		Revision as of 11:34, 1 February 2021
Line 8:		Line 8:
	===Motivation===		===Motivation===

	The so-called Saint-Venant equations are largely used in the hydraulic domain to model the dynamics of an open channel flow. These equations consist of two nonlinear hyperbolic PDEs. In the considered benchmark, under mild simplifying assumptions detailed in <ref name= Dalmas2016>V. Dalmas, G. Robert, C. Poussot-Vassal, I. Pontes-Duff and C. Seren, "From infinite dimensional modelling to parametric reduced order approximation: Application to open-channel flow for hydroelectricity", in Proceedings of the European Control Conference (ECC), Aalborg, Denmark, July, 2016, pp. 1982-1987~~, DOI: https://doi.org/10~~.~~1109/ECC.2016.7810582~~</ref>, the St Venant PDE equations describing the height variation <math>h</math> of the river as a function of the inflow <math>q_i</math> and outflow <math>q_o</math> variations, at location <math>x</math> (<math>x\in[0\,\,L]</math>, <math>L\in\mathbb R_+</math>), obtained around some flow and height linearisation point, can be formulated as follows:		The so-called [[wikipedia:Shallow_water_equations\|Saint-Venant equations]] are largely used in the hydraulic domain to model the dynamics of an open channel flow. These equations consist of two nonlinear hyperbolic PDEs. In the considered benchmark, under mild simplifying assumptions detailed in <ref name= Dalmas2016>V. Dalmas, G. Robert, C. Poussot-Vassal, I. Pontes-Duff and C. Seren, "<span class="plainlinks">[https://doi.org/10.1109/ECC.2016.7810582 From infinite dimensional modelling to parametric reduced order approximation: Application to open-channel flow for hydroelectricity]</span>", in Proceedings of the European Control Conference (ECC), Aalborg, Denmark, July, 2016, pp. 1982-1987.</ref>, the St Venant PDE equations describing the height variation <math>h</math> of the river as a function of the inflow <math>q_i</math> and outflow <math>q_o</math> variations, at location <math>x</math> (<math>x\in[0\,\,L]</math>, <math>L\in\mathbb R_+</math>), obtained around some flow and height linearisation point, can be formulated as follows:
	:<math>		:<math>
	h(x,s) = \mathbf{G_i}(x,s)q_i(s) - \mathbf{G_o}(x,s)q_o(s) = \mathbf H(x,s) u(s).		h(x,s) = \mathbf{G_i}(x,s)q_i(s) - \mathbf{G_o}(x,s)q_o(s) = \mathbf H(x,s) u(s).
Line 26:		Line 26:
	The benchmark contains the above irrational model description together with the numerical data as used in the reference paper, given as Matlab handle functions.		The benchmark contains the above irrational model description together with the numerical data as used in the reference paper, given as Matlab handle functions.

	===Origin===		==Origin==

	Collaboration between [https://www.onera.fr ONERA] and [https://www.edf.fr/ EDF]. The data from the simplified hydro-electric open-channel model come from V. Dalmas and G. Robert while and the treatment performed jointly with P. Vuillemin, and C. Poussot-Vassal.		Collaboration between [https://www.onera.fr ONERA] and [https://www.edf.fr/ EDF]. The data from the simplified hydro-electric open-channel model come from V. Dalmas and G. Robert while and the treatment performed jointly with P. Vuillemin, and C. Poussot-Vassal.
Line 55:		Line 55:
	* For the benchmark itself and its data:		* For the benchmark itself and its data:
	::The MORwiki Community, '''Hydro-Electric Open Channel'''. MORwiki - Model Order Reduction Wiki, 2021. https://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/Hydro-Electric_Open_Channel		::The MORwiki Community, '''Hydro-Electric Open Channel'''. MORwiki - Model Order Reduction Wiki, 2021. https://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/Hydro-Electric_Open_Channel

			* For the background on the benchmark:

	@inproceedings{DalmasECC:2016,		@inproceedings{DalmasECC:2016,
	author = {V. Dalmas and G. Robert and C. Poussot-Vassal and I. {Pontes Duff} and C. Seren},		author = {V. Dalmas and G. Robert and C. Poussot-Vassal and I. {Pontes Duff} and C. Seren},
	title = {From infinite dimensional modelling to parametric reduced order approximation: Application to open-channel flow for hydroelectricity},		title = {From infinite dimensional modelling to parametric reduced order approximation: Application to open-channel flow for hydroelectricity},
	booktitle = {Proceedings of the 15th European Control Conference},		booktitle = {Proceedings of the 15th European Control Conference},
	~~address = {Aalborg, Denmark},~~
	~~month = {July},~~
	year = {2016},		year = {2016},
	pages = {1982-1987},		pages = {1982--1987},
			doi = {10.1109/ECC.2016.7810582}
	}		}