Tubular Reactor: Difference between revisions
RobertLampel (talk | contribs) Created page with "{{Dimensions |nd = 1 |nx = 2 |nw = 1 }} The '''Tubular Reactor problem''' is a two-dimensional ODE model. It aims to maximize the value of the second differential state at the end of the time interval. The optimal integer control functions exhibits a singular arc. == Mathematical formulation == <p> <math> \begin{array}{lll} \displaystyle \min_{w} && -x_2(1) dt \\ \text{subject to} \..." |
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<math> | <math> | ||
\begin{array}{lll} | \begin{array}{lll} | ||
\displaystyle \min_{w} && -x_2(1) | \displaystyle \min_{w} && -x_2(1) \\ | ||
\text{subject to} \\ | \text{subject to} \\ | ||
\quad \dot{x_1}(t) & = & -(w(t) + \frac{1}{2} \cdot w(t)^2) \cdot x_1(t),\\ | \quad \dot{x_1}(t) & = & -(w(t) + \frac{1}{2} \cdot w(t)^2) \cdot x_1(t),\\ | ||
| Line 27: | Line 27: | ||
Here is one local solution to the above control problem. | Here is one local solution to the above control problem. | ||
<gallery caption="Reference solution plots" widths=" | <gallery caption="Reference solution plots" widths="500px" heights="300px" perrow="1"> | ||
Image: | Image:Tubular_Reactor.png| States and discretized control for a local optimum. | ||
</gallery> | </gallery> | ||
== Miscellaneous and Further Reading == | == Miscellaneous and Further Reading == | ||
This formulation and a detailed description can be found in [[#apmonitor|[1]]]. | |||
== References == | == References == | ||
<span id=" | <span id="apmonitor">[1]</span> https://apmonitor.com/do/index.php/Main/DynamicOptimizationBenchmarks <br> | ||
[[Category:MIOCP]] | [[Category:MIOCP]] | ||
[[Category: | [[Category:Sensitivity-seeking arcs]] | ||
Latest revision as of 13:46, 28 November 2025
| Tubular Reactor | |
|---|---|
| State dimension: | 1 |
| Differential states: | 2 |
| Discrete control functions: | 1 |
The Tubular Reactor problem is a two-dimensional ODE model. It aims to maximize the value of the second differential state at the end of the time interval.
The optimal integer control functions exhibits a singular arc.
Mathematical formulation
Reference Solutions
Here is one local solution to the above control problem.
- Reference solution plots
-
States and discretized control for a local optimum.
Miscellaneous and Further Reading
This formulation and a detailed description can be found in [1].
References
[1] https://apmonitor.com/do/index.php/Main/DynamicOptimizationBenchmarks