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

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  & \dot{y}_4 & = & \theta_3 y_3,  \\
 
  & \dot{y}_4 & = & \theta_3 y_3,  \\
 
  & \dot{y}_5 & = & \theta_4 y_3 - \theta_5 y_5, \\
 
  & \dot{y}_5 & = & \theta_4 y_3 - \theta_5 y_5, \\
  & \theta_i & \geq & 0.
+
  & \theta_i & \geq & 0 \quad i = 1,...,5.
 
\end{array}  
 
\end{array}  
 
</math>
 
</math>
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[[Category:ODE model]]
 
[[Category:ODE model]]
 
[[Category:DAE model]]
 
[[Category:DAE model]]
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[[Category:Chemical engineering]]

Latest revision as of 20:22, 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