PROPT Batch Reactor Problem
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This page is part of the PROPT Manual. See PROPT Manual. |
Example 6: DYNOPT User's Guide version 4.1.0
Batch reactor with reactions: A -> B -> C.
M. Cizniar, M. Fikar, M. A. Latifi, MATLAB Dynamic Optimisation Code DYNOPT. User's Guide, Technical Report, KIRP FCHPT STU Bratislava, Slovak Republic, 2006.
Problem description
Find T over t in [0; 1 ] to maximize
subject to:
where
% Copyright (c) 2007-2008 by Tomlab Optimization Inc.
Problem setup
toms t
p = tomPhase('p', t, 0, 1, 30);
setPhase(p);
tomStates x1 x2
tomControls T
% Initial guess
% Note: The guess for t_f must appear in the list before expression involving t.
x0 = {icollocate({x1 == 1; x2 == 0})
collocate(T==398-t*100)};
% Box constraints
cbox = {298 <= collocate(T) <= 398};
% Boundary constraints
cbnd = initial({x1 == 1; x2 == 0});
% Various constants and expressions
k1 = 4000*exp(-2500./T);
k2 = 620000*exp(-5000./T);
% ODEs and path constraints
ceq = collocate({dot(x1) == -k1.*x1.^2
dot(x2) == k1.*x1.^2-k2.*x2});
% Objective
objective = -final(x2);
Solve the problem
options = struct;
options.name = 'Batch Reactor';
solution = ezsolve(objective, {cbox, cbnd, ceq}, x0, options);
% Extract optimal states and controls from solution
t = subs(collocate(t),solution);
x1 = subs(collocate(x1),solution);
x2 = subs(collocate(x2),solution);
T = subs(collocate(T),solution);
Problem type appears to be: lpcon Time for symbolic processing: 0.16316 seconds Starting numeric solver ===== * * * =================================================================== * * * TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31 ===================================================================================== Problem: --- 1: Batch Reactor f_k -0.610799380695554950 sum(|constr|) 0.000006007956394549 f(x_k) + sum(|constr|) -0.610793372739160350 f(x_0) 0.000000000000000000 Solver: snopt. EXIT=0. INFORM=1. SNOPT 7.2-5 NLP code Optimality conditions satisfied FuncEv 1 ConstrEv 26 ConJacEv 26 Iter 23 MinorIter 84 CPU time: 0.031200 sec. Elapsed time: 0.048000 sec.
Plot result
subplot(2,1,1)
plot(t,x1,'*-',t,x2,'*-');
legend('x1','x2');
title('Batch Reactor state variables');
subplot(2,1,2)
plot(t,T,'+-');
legend('T');
title('Batch Reactor control');