Difference between revisions of "Batch reactor"
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This solution was computed using JuMP with a collocation method and 300 discretization points. The differential equations were solved using the explicit Euler Method. The source code can be found at [[Batch reactor (JuMP)]]. | This solution was computed using JuMP with a collocation method and 300 discretization points. The differential equations were solved using the explicit Euler Method. The source code can be found at [[Batch reactor (JuMP)]]. | ||
− | The optimal objective value of the problem is <math> x_2(t_f) = | + | The optimal objective value of the problem is <math> x_2(t_f) = 0.611715 </math>. |
<gallery caption="Reference solution plots" widths="180px" heights="140px" perrow="2"> | <gallery caption="Reference solution plots" widths="180px" heights="140px" perrow="2"> | ||
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Model descriptions are available in | Model descriptions are available in | ||
+ | * [[:Category:Gekko | GEKKO Python code]] at [[Batch reactor (GEKKO)]] | ||
* [[:Category: Julia/JuMP | JuMP code]] at [[Batch reactor (JuMP)]] | * [[:Category: Julia/JuMP | JuMP code]] at [[Batch reactor (JuMP)]] | ||
Revision as of 14:41, 11 April 2019
Batch reactor | |
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State dimension: | 1 |
Differential states: | 2 |
Continuous control functions: | 1 |
Path constraints: | 2 |
Interior point equalities: | 2 |
This batch reactor problem describes the consecutive reaction of some substance A via substance B into a desired product C.
The system is interacted with via the control function which stands for the temperature. The goal is to produce as much of substance B (which can then be converted into product C) as possible within the time limit.
Mathematical formulation
The optimal control problem is given by
and represent the concentrations of A and B at timepoint respectively. The control function represents the temperature.
Parameters
The starting time and end time are given by .
Reference Solutions
This solution was computed using JuMP with a collocation method and 300 discretization points. The differential equations were solved using the explicit Euler Method. The source code can be found at Batch reactor (JuMP).
The optimal objective value of the problem is .
Source Code
Model descriptions are available in
References
The problem can be found in the Tomlab PROPT guide or in the Dynopt guide.