Isomerization of Alpha-Pinene problem: Difference between revisions

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

Latest revision as of 19:22, 29 September 2016

The Isomerization of Alpha-Pinene problem tries to determine "reaction coefficients in the thermal isometrization of $α$ -Pinene." (Cite and problem taken from the COPS library)

Mathematical formulation

The problem is given by

$\begin{array}{llcl} \min_{θ} & \sum_{j = 1}^{8} & | | y (τ_{j}; θ) - z_{j} | |^{2} \\ s.t. & {\dot{y}}_{1} & = & - (θ_{1} + θ_{2}) y_{1}, \\ {\dot{y}}_{2} & = & θ_{1} y_{1}, \\ {\dot{y}}_{3} & = & θ_{2} y_{1} - (θ_{3} + θ_{4}) y_{3} + θ_{5} y_{5}, \\ {\dot{y}}_{4} & = & θ_{3} y_{3}, \\ {\dot{y}}_{5} & = & θ_{4} y_{3} - θ_{5} y_{5}, \\ θ_{i} & \geq & 0 i = 1, . . ., 5 . \end{array}$

Parameters

The values $z_{j}$ are measurements for the concentration for $y$ at time points $τ_{1}, . . ., τ_{8}$ and initial conditions are known.

Source Code

Model descriptions are available in

AMPL/TACO code at Isomerization of Alpha-Pinene problem (TACO)

@@ Line 2: / Line 2: @@
 |nz        = 5
 |np        = 5
+|nc        = 5
 }}<!-- Do not insert line break here or Dimensions Box moves up in the layout...
--->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])
+-->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])
@@ Line 17: / Line 18: @@
   \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_3) y_1^2, \\
+  & \dot{y}_1 & = &  -(\theta_1 + \theta_2) y_1, \\
-  & \dot{y}_2 & = & \theta_1 y_1^2 - \theta_2 y_2.  \\
+  & \dot{y}_2 & = & \theta_1 y_1,  \\
-  & \dot{y}_3 & = & \theta_1 y_1^2 - \theta_2 y_2.  \\
+  & \dot{y}_3 & = & \theta_2 y_1 - (\theta_3 + \theta_4) y_3 + \theta_5 y_5,  \\
-  & \dot{y}_4 & = & \theta_1 y_1^2 - \theta_2 y_2.  \\
+  & \dot{y}_4 & = & \theta_3 y_3,  \\
-  & \dot{y}_5 & = & \theta_1 y_1^2 - \theta_2 y_2.  \\
+  & \dot{y}_5 & = & \theta_4 y_3 - \theta_5 y_5, \\
+  & \theta_i & \geq & 0 \quad i = 1,...,5.
 \end{array}
 </math>
@@ Line 33: / Line 35: @@
 Model descriptions are available in
-* [[:Category:AMPL/TACO | AMPL/TACO code]] at [[Catalytic cracking problem (TACO)]]
+* [[:Category:AMPL/TACO | AMPL/TACO code]] at [[Isomerization of Alpha-Pinene problem (TACO)]]
@@ Line 39: / Line 41: @@
 [[Category:MIOCP]]
 [[Category:ODE model]]
+[[Category:DAE model]]
+[[Category:Chemical engineering]]