Difference between revisions of "Catalytic cracking problem"

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(Created page with "{{Dimensions |nd = 1 |nx = 2 |nw = 1 |nre = 2 }}<!-- Do not insert line break here or Dimensions Box moves up in the layout... -->This problem trie...")
 
 
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{{Dimensions
 
{{Dimensions
|nd       = 1
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|nz       = 2
|nx       = 2
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|np       = 3
|nw       = 1
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|nc       = 3
|nre      = 2
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}}<!-- 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...
  
-->This 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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-->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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<math>
 
<math>
 
\begin{array}{llcl}
 
\begin{array}{llcl}
  \displaystyle \min_{\theta} &\sum\limits_{j=1}^{21} \norm{y(\tau_j; \theta) - z_j}^2  \\[1.5ex]
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  \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, \\
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  \mbox{s.t.}  
  & \dot{y}_2 & = & \theta_1 y_1^2 - \theta_2 y_2. \\
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& \dot{y}_1 & = &  -(\theta_1 + \theta_3) y_1^2, \\
 +
  & \dot{y}_2 & = & \theta_1 y_1^2 - \theta_2 y_2, \\
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& \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, ..., \tau_21 </math>.
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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 [[Catalyst cracking problem (TACO)]]
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* [[: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]]
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[[Category:DAE model]]
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[[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}

Parameters

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

Source Code

Model descriptions are available in