# Difference between revisions of "Catalytic cracking problem"

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{{Dimensions | {{Dimensions | ||

− | | | + | |nz = 2 |

− | | | + | |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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<math> | <math> | ||

\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

## Parameters

The values are measurements for the concentration for at time points and initial conditions are known.

## Source Code

Model descriptions are available in