Difference between revisions of "Isomerization of Alpha-Pinene problem"

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(Created page with "{{Dimensions |nz = 5 |np = 5 }}<!-- Do not insert line break here or Dimensions Box moves up in the layout... -->The Isomerization of Alpha-Pinene problem tries...")
 
 
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|nz        = 5
 
|nz        = 5
 
|np        = 5
 
|np        = 5
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|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...
  
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-->The Isomerization of Alpha-Pinene problem tries to determine "reaction coe�cients in the thermal isometrization of <math> \alpha </math>-Pinene." (Cite and problem taken from the [http://www.mcs.anl.gov/~more/cops/ COPS library])
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-->The Isomerization of Alpha-Pinene problem tries to determine "reaction coefficients in the thermal isometrization of <math> \alpha </math>-Pinene." (Cite and problem taken from the [http://www.mcs.anl.gov/~more/cops/ COPS library])
  
  
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  \displaystyle \min_{\theta} &\sum\limits_{j=1}^{8} &&||y(\tau_j; \theta) - z_j||^2  \\[1.5ex]
 
  \displaystyle \min_{\theta} &\sum\limits_{j=1}^{8} &&||y(\tau_j; \theta) - z_j||^2  \\[1.5ex]
 
  \mbox{s.t.}  
 
  \mbox{s.t.}  
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  & \dot{y}_1 & = &  -(\theta_1 + \theta_3) y_1^2, \\
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  & \dot{y}_1 & = &  -(\theta_1 + \theta_2) y_1, \\
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  & \dot{y}_2 & = & \theta_1 y_1^2 - \theta_2 y_2. \\
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  & \dot{y}_2 & = & \theta_1 y_1, \\
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  & \dot{y}_3 & = & \theta_1 y_1^2 - \theta_2 y_2. \\
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  & \dot{y}_3 & = & \theta_2 y_1 - (\theta_3 + \theta_4) y_3 + \theta_5 y_5, \\
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  & \dot{y}_4 & = & \theta_1 y_1^2 - \theta_2 y_2. \\
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  & \dot{y}_4 & = & \theta_3 y_3, \\
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  & \dot{y}_5 & = & \theta_1 y_1^2 - \theta_2 y_2. \\
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  & \dot{y}_5 & = & \theta_4 y_3 - \theta_5 y_5, \\
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  & \theta_i & \geq & 0 \quad i = 1,...,5.
 
\end{array}  
 
\end{array}  
 
</math>
 
</math>
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Model descriptions are available in
 
Model descriptions are available in
  
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* [[:Category:AMPL/TACO | AMPL/TACO code]] at [[Catalytic cracking problem (TACO)]]
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* [[:Category:AMPL/TACO | AMPL/TACO code]] at [[Isomerization of Alpha-Pinene 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 21:22, 29 September 2016

Isomerization of Alpha-Pinene problem
Algebraic states: 5
Continuous control values: 5
Path constraints: 5

The Isomerization of Alpha-Pinene problem tries to determine "reaction coefficients in the thermal isometrization of \alpha -Pinene." (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}^{8} &&||y(\tau_j; \theta) - z_j||^2 \\[1.5ex] \mbox{s.t.} & \dot{y}_1 & = & -(\theta_1 + \theta_2) y_1, \\ & \dot{y}_2 & = & \theta_1 y_1, \\ & \dot{y}_3 & = & \theta_2 y_1 - (\theta_3 + \theta_4) y_3 + \theta_5 y_5, \\ & \dot{y}_4 & = & \theta_3 y_3, \\ & \dot{y}_5 & = & \theta_4 y_3 - \theta_5 y_5, \\ & \theta_i & \geq & 0 \quad i = 1,...,5. \end{array}

Parameters

The values z_j are measurements for the concentration for y at time points \tau_1, ..., \tau_8 and initial conditions are known.

Source Code

Model descriptions are available in

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