Difference between revisions of "Oil Shale Pyrolysis"

Oil Shale Pyrolysis
State dimension:	1
Differential states:	2
Continuous control functions:	1
Discrete control functions:	0
Interior point equalities:	2

Revision as of 17:06, 22 February 2016

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

$\begin{array}{lll} \displaystyle \min_{u} & \displaystyle &-x_1(t_N)^2 \\[1.5ex] \mbox{s.t.} & \displaystyle \dot{x}_0 &= -k_0x_0-(k_2+k_3+k_4)x_0x_1\\ & \displaystyle \dot{x}_1 &= k_0x_0-k_1x_1 + k_2x_0x_1\\ & \displaystyle k_i &= a_i e^{-u\frac{b_i}{R}},\quad \forall i\in \{1,\dots,5\} \\ [1.5ex] & \displaystyle t &\in \left[t_0,t_N\right] \\ & \displaystyle u(t) &\in \left[\frac{698.15}{748.15},1\right]\\ & \displaystyle x(t_0) &= (1,0)^T\\ \end{array}$

where this is the normalized form with

$u(t)= \frac{1}{u_{temp}}$ , with

$u_{temp} \in \left[698.15,748.15\right]$

Parameters

State variables
Symbol	Initial value ( $t_0$ )
$x_0(t)$	$1$
$x_1(t)$	$0$

Parameters
Symbol	Value
$a_1$	$8.86$
$a_2$	$24.25$
$a_3$	$23.67$
$a_4$	$18.75$
$a_5$	$20.7$
$b_1$	$20.3$
$b_2$	$37.4$
$b_3$	$33.8$
$b_4$	$28.2$
$b_5$	$31.0$

Control variable
Symbol	Interval
$u(t)$	[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.

Difference between revisions of "Oil Shale Pyrolysis"

Revision as of 17:06, 22 February 2016

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Mathematical formulation

Parameters

Reference solution

Source Code

References

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@@ Line 19: / Line 19: @@
   &  \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 u(t) &\in \left[\frac{698.15}{748.15},1\right]\\
   &  \displaystyle x(t_0) &= (1,0)^T\\
 \end{array}