PROPT Parallel Reactions in Tubular Reactor: Difference between revisions
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Latest revision as of 05:32, 14 February 2012
This page is part of the PROPT Manual. See PROPT Manual. |
Problem 4: DYNOPT User's Guide version 4.1.0
Batch reactor with reactions: A -> B and A -> 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 u
% Initial guess
x0 = {icollocate({x1 == 1; x2 == 0})
collocate(u == 5*t)};
% Box constraints
cbox = {0 <= collocate(u) <= 5};
% Boundary constraints
cbnd = initial({x1 == 1; x2 == 0});
% ODEs and path constraints
ceq = collocate({
dot(x1) == -(u+0.5*u.^2).*x1
dot(x2) == u.*x1});
% Objective
objective = -final(x2);
Solve the problem
options = struct;
options.name = 'Parallel Reactions';
solution = ezsolve(objective, {cbox, cbnd, ceq}, x0, options);
t = subs(collocate(t),solution);
x1 = subs(collocate(x1),solution);
x2 = subs(collocate(x2),solution);
u = subs(collocate(u),solution);
Problem type appears to be: lpcon Time for symbolic processing: 0.087774 seconds Starting numeric solver ===== * * * =================================================================== * * * TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31 ===================================================================================== Problem: --- 1: Parallel Reactions f_k -0.573540787113988930 sum(|constr|) 0.000000228705850230 f(x_k) + sum(|constr|) -0.573540558408138670 f(x_0) 0.000000000000000000 Solver: snopt. EXIT=0. INFORM=1. SNOPT 7.2-5 NLP code Optimality conditions satisfied FuncEv 1 ConstrEv 35 ConJacEv 35 Iter 34 MinorIter 118 CPU time: 0.046800 sec. Elapsed time: 0.042000 sec.
Plot result
subplot(2,1,1)
plot(t,x1,'*-',t,x2,'*-');
legend('x1','x2');
title('Parallel Reactions state variables');
subplot(2,1,2)
plot(t,u,'+-');
legend('u');
title('Parallel Reactions control');