Difference between revisions of "Oil Shale Pyrolysis"
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& \displaystyle k_i &= a_i e^{-u\frac{b_i}{R}},\quad \forall i\in \{1,\dots,5\} \\ [1.5ex] | & \displaystyle k_i &= a_i e^{-u\frac{b_i}{R}},\quad \forall i\in \{1,\dots,5\} \\ [1.5ex] | ||
& \displaystyle t &\in \left[t_0,t_N\right] \\ | & \displaystyle t &\in \left[t_0,t_N\right] \\ | ||
| − | & \displaystyle u(t) &\in \left[ | + | & \displaystyle u(t) &\in \left[698.15/748.15,1\right]\\ |
& \displaystyle x(t_0) &= (1,0)^T\\ | & \displaystyle x(t_0) &= (1,0)^T\\ | ||
\end{array} | \end{array} | ||
Revision as of 17:07, 22 February 2016
| Oil Shale Pyrolysis | |
|---|---|
| State dimension: | 1 |
| Differential states: | 2 |
| Continuous control functions: | 1 |
| Discrete control functions: | 0 |
| Interior point equalities: | 2 |
The following problem is an example from the global optimal control literature and was introduced in [Wen1977]The entry doesn't exist yet..
Mathematical formulation
![\begin{array}{lll}
\displaystyle \min_{u} & \displaystyle &-x_1(t_N)^2 \\[1.5ex]
\mbox{s.t.} & \displaystyle \dot{x}_0 &= -k_0x_0-(k_2+k_3+k_4)x_0x_1\\
& \displaystyle \dot{x}_1 &= k_0x_0-k_1x_1 + k_2x_0x_1\\
& \displaystyle k_i &= a_i e^{-u\frac{b_i}{R}},\quad \forall i\in \{1,\dots,5\} \\ [1.5ex]
& \displaystyle t &\in \left[t_0,t_N\right] \\
& \displaystyle u(t) &\in \left[698.15/748.15,1\right]\\
& \displaystyle x(t_0) &= (1,0)^T\\
\end{array}](https://mintoc.de/images/math/4/6/d/46ddc2d2f9d24f0b215038e800d12467.png)
where this is the normalized form with
, with
![u_{temp} \in \left[698.15,748.15\right]](https://mintoc.de/images/math/9/8/a/98ac80bcd09490e8b25c526ea84b2ce9.png)
Parameters
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[\frac{698.15}{748.15},1] |
Measurement grid
Reference solution
Coming soon.
Source Code
Model descriptions are not yet available.
References
| [Wen1977] | The entry doesn't exist yet. |
