Difference between revisions of "Methanol to Hydrocarbons problem"
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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> | ||
Revision as of 10:55, 4 July 2016
| Methanol to Hydrocarbons problem | |
|---|---|
| Algebraic states: | 3 |
| Continuous control values: | 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 COPS library)
Mathematical formulation
The problem is given by
![\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 & = & -( 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, \\[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, \\[0.3cm]
& \theta_i & \geq & 0 \quad i = 1,...,5.
\end{array}](https://mintoc.de/images/math/f/c/4/fc4a9478c894191036370aa1c2d64751.png)
Parameters
The values 
are measurements for the concentration for 
at time points 
and initial conditions are known.
Source Code
Model descriptions are available in
