DOTcvpSB: a Matlab Toolbox for Dynamic Optimization in Systems ...

CHAPTER 10Other benchmarks10.1 SIMPLE BATCH REACTORDOTcvp: cdop_SimpleBatchReactorA, B.mThe simple batch reactor given in [11] was considered with the following chemical reactionA → B → C (10.1)The parameters of the reactor are: e 1 = 18000 cal mol −1 ,e 2 = 30000 cal mol −1 ,k 10 = 0.535x10 11 min −1 ,k 20 = 0.461x10 18 min −1 , r = 2 cal mol −1 K −1 , β 1 = 0.53 mol l −1 , β 2 = 0.43 mol l −1 , α = e2e 1, c = k20k, and10αfinal timet F = 8.0 min.The objective of the optimization is to maximize an amount of the product B at the final timesubject tomaxJ 0 = x 2 (t F ) (10.2)u i,t iẋ 1 = −ux 1 (10.3)ẋ 2 = ux 1 −cu α x 2 (10.4)with the process: x(0) = [β 1 ;β 2 ] and decision: u(0) = [0.5] initial variables. The decision variables have definedlower and upper bounds as follows: u ∈ [0.1;2.0]. The additional equality constraint was defined. This constraintholds the total time of simulation at the fixed valueN∑t i = t F (10.5)i=11 ______________2 Final results [single-optimization; the scenario with the free time and with the piecewise constant control trajectory]:3 ............. Problem name: SimpleBatchReactorA4 ...... NLP or MINLP solver: FMINCON5 . Number of time intervals: 66 ... IVP relative tolerance: 1.000000e-0127 ... IVP absolute tolerance: 1.000000e-0128 . Sens. absolute tolerance: 1.000000e-0129 ............ NLP tolerance: 1.000000e-01010 ....... Final state values: 1.704654e-001 6.794171e-00111 ...... 1th optimal control: ...12 ..... Final size of the dt: 7.469692e-001 1.247365e+000 1.420018e+000 1.495831e+000 1.534227e+000 1.555590e+00013 ..... Final time [sum(dt)]: 8.000000e+00014 ______________15 ............ Final CPUtime: ... seconds16 . Cost function [max(J_0)]: 0.679417061718 ______________19 Final results [single-optimization; the scenario with the fixed time and with the piecewise constant control trajectory]:20 ............. Problem name: SimpleBatchReactorB