Difference between revisions of "Catalytic cracking problem"
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{{Dimensions | {{Dimensions | ||
| − | | | + | |nz = 2 |
| − | + | ||
|np = 3 | |np = 3 | ||
| + | |nc = 3 | ||
}}<!-- 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... | ||
| − | --> | + | -->The Catalytic cracking problem tries to determine "reaction coefficients for the catalytic cracking of gas oil into gas and other byproducts." (Cite and problem taken from the [http://www.mcs.anl.gov/~more/cops/ COPS library]) |
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\begin{array}{llcl} | \begin{array}{llcl} | ||
\displaystyle \min_{\theta} &\sum\limits_{j=1}^{21} &&||y(\tau_j; \theta) - z_j||^2 \\[1.5ex] | \displaystyle \min_{\theta} &\sum\limits_{j=1}^{21} &&||y(\tau_j; \theta) - z_j||^2 \\[1.5ex] | ||
| − | \mbox{s.t.} & \dot{y}_1 & = & -(\theta_1 + \theta_3) y_1^2, \\ | + | \mbox{s.t.} |
| − | & \dot{y}_2 & = & \theta_1 y_1^2 - \theta_2 y_2 | + | & \dot{y}_1 & = & -(\theta_1 + \theta_3) y_1^2, \\ |
| + | & \dot{y}_2 & = & \theta_1 y_1^2 - \theta_2 y_2, \\ | ||
| + | & \theta_i & \geq & 0 \quad i = 1,...,3. | ||
\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, ..., \ | + | 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 == | == Source Code == | ||
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Model descriptions are available in | Model descriptions are available in | ||
| − | * [[:Category:AMPL/TACO | AMPL/TACO code]] at [[ | + | * [[:Category:AMPL/TACO | AMPL/TACO code]] at [[Catalytic cracking problem (TACO)]] |
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[[Category:MIOCP]] | [[Category:MIOCP]] | ||
[[Category:ODE model]] | [[Category:ODE model]] | ||
| + | [[Category:DAE model]] | ||
| + | [[Category:Chemical engineering]] | ||
Latest revision as of 20:21, 29 September 2016
| Catalytic cracking problem | |
|---|---|
| Algebraic states: | 2 |
| Continuous control values: | 3 |
| Path constraints: | 3 |
The Catalytic cracking problem tries to determine "reaction coefficients for the catalytic cracking of gas oil into gas and other byproducts." (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}^{21} &&||y(\tau_j; \theta) - z_j||^2 \\[1.5ex]
\mbox{s.t.}
& \dot{y}_1 & = & -(\theta_1 + \theta_3) y_1^2, \\
& \dot{y}_2 & = & \theta_1 y_1^2 - \theta_2 y_2, \\
& \theta_i & \geq & 0 \quad i = 1,...,3.
\end{array}](https://mintoc.de/images/math/e/5/9/e5991f4430c34fdc73b65828df913923.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
