Methanol to Hydrocarbons problem - Revision history

FelixMueller at 08:32, 27 July 2016

2016-07-27T08:32:00Z

← Older revision		Revision as of 08:32, 27 July 2016
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	\|nz = 3		\|nz = 3
	\|np = 5		\|np = 5
			\|nc = 5
	}}<!-- Do not insert line break here or Dimensions Box moves up in the layout...		}}<!-- Do not insert line break here or Dimensions Box moves up in the layout...

FelixMueller: /* Mathematical formulation */

2016-07-04T09:55:37Z

Mathematical formulation

← Older revision		Revision as of 09:55, 4 July 2016
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	\displaystyle \min_{\theta} &\sum\limits_{j=1}^{16} &&\|\|y(\tau_j; \theta) - z_j\|\|^2 \\[1.5ex]		\displaystyle \min_{\theta} &\sum\limits_{j=1}^{16} &&\|\|y(\tau_j; \theta) - z_j\|\|^2 \\[1.5ex]
	\mbox{s.t.}		\mbox{s.t.}
	& \dot{y}_1 & = & -( 2 \theta_2 - \frac{\theta_1 y_2}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 + \theta_4) y_1, \\		& \dot{y}_1 & = & -( 2 \theta_2 - \frac{\theta_1 y_2}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 + \theta_4) y_1, \\[0.3cm]
	& \dot{y}_2 & = & \frac{\theta_1 y_1 (\theta_2 y_1 - y_2)}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 y_1, \\		& \dot{y}_2 & = & \frac{\theta_1 y_1 (\theta_2 y_1 - y_2)}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 y_1, \\[0.3cm]
	& \dot{y}_3 & = & \frac{\theta_1 y_1 (y_2 + \theta_5 y_1}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_4 y_1, \\		& \dot{y}_3 & = & \frac{\theta_1 y_1 (y_2 + \theta_5 y_1}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_4 y_1, \\[0.3cm]
	& \theta_i & \geq & 0.		& \theta_i & \geq & 0 \quad i = 1,...,5.
	\end{array}		\end{array}
	</math>		</math>

FelixMueller at 22:11, 27 June 2016

2016-06-27T22:11:43Z

← Older revision		Revision as of 22:11, 27 June 2016
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	[[Category:MIOCP]]		[[Category:MIOCP]]
	[[Category:ODE model]]		[[Category:ODE model]]
			[[Category:Chemical engineering]]

FelixMueller: /* Mathematical formulation */

2016-05-05T18:09:47Z

Mathematical formulation

← Older revision		Revision as of 18:09, 5 May 2016
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	& \dot{y}_2 & = & \frac{\theta_1 y_1 (\theta_2 y_1 - y_2)}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 y_1, \\		& \dot{y}_2 & = & \frac{\theta_1 y_1 (\theta_2 y_1 - y_2)}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 y_1, \\
	& \dot{y}_3 & = & \frac{\theta_1 y_1 (y_2 + \theta_5 y_1}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_4 y_1, \\		& \dot{y}_3 & = & \frac{\theta_1 y_1 (y_2 + \theta_5 y_1}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_4 y_1, \\
	& \theta_i & \geq & 0		& \theta_i & \geq & 0.
	\end{array}		\end{array}
	</math>		</math>

FelixMueller: /* Mathematical formulation */

2016-05-05T18:08:36Z

Mathematical formulation

← Older revision		Revision as of 18:08, 5 May 2016
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	& \dot{y}_1 & = & -( 2 \theta_2 - \frac{\theta_1 y_2}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 + \theta_4) y_1, \\		& \dot{y}_1 & = & -( 2 \theta_2 - \frac{\theta_1 y_2}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 + \theta_4) y_1, \\
	& \dot{y}_2 & = & \frac{\theta_1 y_1 (\theta_2 y_1 - y_2)}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 y_1, \\		& \dot{y}_2 & = & \frac{\theta_1 y_1 (\theta_2 y_1 - y_2)}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 y_1, \\
	& \dot{y}_2 & = & \frac{\theta_1 y_1 (y_2 + \theta_5 y_1}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_4 y_1, \\		& \dot{y}_3 & = & \frac{\theta_1 y_1 (y_2 + \theta_5 y_1}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_4 y_1, \\
	& \theta_i & \geq & 0		& \theta_i & \geq & 0
	\end{array}		\end{array}

FelixMueller at 18:08, 5 May 2016

2016-05-05T18:08:26Z

← Older revision		Revision as of 18:08, 5 May 2016
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	\mbox{s.t.}		\mbox{s.t.}
	& \dot{y}_1 & = & -( 2 \theta_2 - \frac{\theta_1 y_2}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 + \theta_4) y_1, \\		& \dot{y}_1 & = & -( 2 \theta_2 - \frac{\theta_1 y_2}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 + \theta_4) y_1, \\
	& \dot{y}_2 & = & \theta_1 y_1^2 - \theta_2 y_2. \\		& \dot{y}_2 & = & \frac{\theta_1 y_1 (\theta_2 y_1 - y_2)}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 y_1, \\
			& \dot{y}_2 & = & \frac{\theta_1 y_1 (y_2 + \theta_5 y_1}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_4 y_1, \\
			& \theta_i & \geq & 0
	\end{array}		\end{array}
	</math>		</math>
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	== Parameters ==		== Parameters ==
	The values <math> z_j </math> are measurements for the concentration for <math> y </math> at time points <math> \tau_1, ..., \tau_{21} </math> and initial conditions are known.		The values <math> z_j </math> are measurements for the concentration for <math> y </math> at time points <math> \tau_1, ..., \tau_{16} </math> and initial conditions are known.

	== Source Code ==		== Source Code ==
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	Model descriptions are available in		Model descriptions are available in

	* [[:Category:AMPL/TACO \| AMPL/TACO code]] at [[~~Catalytic cracking~~ problem (TACO)]]		* [[:Category:AMPL/TACO \| AMPL/TACO code]] at [[Methanol to Hydrocarbons problem (TACO)]]

FelixMueller: /* Mathematical formulation */

2016-05-05T18:05:17Z

Mathematical formulation

← Older revision		Revision as of 18:05, 5 May 2016
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	\displaystyle \min_{\theta} &\sum\limits_{j=1}^{16} &&\|\|y(\tau_j; \theta) - z_j\|\|^2 \\[1.5ex]		\displaystyle \min_{\theta} &\sum\limits_{j=1}^{16} &&\|\|y(\tau_j; \theta) - z_j\|\|^2 \\[1.5ex]
	\mbox{s.t.}		\mbox{s.t.}
	& \dot{y}_1 & = & -~~\bigleft~~( 2 \theta_2 - \frac{\theta_1 y_2}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 + \theta_4 ~~\bigright~~) y_1, \\		& \dot{y}_1 & = & -( 2 \theta_2 - \frac{\theta_1 y_2}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 + \theta_4) y_1, \\
	& \dot{y}_2 & = & \theta_1 y_1^2 - \theta_2 y_2. \\		& \dot{y}_2 & = & \theta_1 y_1^2 - \theta_2 y_2. \\
	\end{array}		\end{array}

FelixMueller: Created page with "{{Dimensions |nz = 3 |np = 5 }}The Methanol to Hydrocarbons problem tries to d..."

2016-05-05T18:05:06Z

Created page with "{{Dimensions |nz = 3 |np = 5 }}The Methanol to Hydrocarbons problem tries to d..."

New page

{{Dimensions
|nz = 3
|np = 5
}}The Methanol to Hydrocarbons problem tries to determine "reaction coefficients for the conversion of methanol into various hydrocarbons." (Cite and problem taken from the [http://www.mcs.anl.gov/~more/cops/ COPS library])

== Mathematical formulation ==

The problem is given by

<p>
<math>
\begin{array}{llcl}
\displaystyle \min_{\theta} &\sum\limits_{j=1}^{16} &&||y(\tau_j; \theta) - z_j||^2 \\[1.5ex]
\mbox{s.t.}
& \dot{y}_1 & = & -\bigleft( 2 \theta_2 - \frac{\theta_1 y_2}{(\theta_2 + \theta_5) y_1 + y_2} + \theta_3 + \theta_4 \bigright) y_1, \\
& \dot{y}_2 & = & \theta_1 y_1^2 - \theta_2 y_2. \\
\end{array}
</math>
</p>

== Parameters ==
The values <math> z_j </math> are measurements for the concentration for <math> y </math> at time points <math> \tau_1, ..., \tau_{21} </math> and initial conditions are known.

== Source Code ==

Model descriptions are available in

* [[:Category:AMPL/TACO | AMPL/TACO code]] at [[Catalytic cracking problem (TACO)]]


[[Category:MIOCP]]
[[Category:ODE model]]