PROPT Parametric Sensitivity Control - Revision history

Per: /* Solve the problem */

2012-02-14T09:33:42Z

Solve the problem

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	[[File:optimalParametricSensitivity_01.png]]		[[File:optimalParametricSensitivity_01.png]]

			[[Category:PROPT Examples]]

Mbot at 13:07, 8 November 2011

2011-11-08T13:07:12Z

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	Problem type appears to be: lpcon		Problem type appears to be: lpcon
	Time for symbolic processing: 0.~~22951~~ seconds		Time for symbolic processing: 0.20428 seconds
	Starting numeric solver		Starting numeric solver
	===== * * * =================================================================== * * *		===== * * * =================================================================== * * *
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	FuncEv 1 ConstrEv 192 ConJacEv 192 Iter 89 MinorIter 2466		FuncEv 1 ConstrEv 192 ConJacEv 192 Iter 89 MinorIter 2466
	CPU time: 0.~~234002~~ sec. Elapsed time: 0.~~306000~~ sec.		CPU time: 0.280802 sec. Elapsed time: 0.279000 sec.

	</pre>		</pre>

	[[File:optimalParametricSensitivity_01.png]]		[[File:optimalParametricSensitivity_01.png]]

Mbot at 18:25, 2 November 2011

2011-11-02T18:25:17Z

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	{{Part Of Manual\|title=the PROPT Manual\|link=[[PROPT \|PROPT Manual]]}}		{{Part Of Manual\|title=the PROPT Manual\|link=[[PROPT\|PROPT Manual]]}}

	Optimal Parametric Sensitivity control of a fed-batch reactor		Optimal Parametric Sensitivity control of a fed-batch reactor
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			[[File:optimalParametricSensitivity_01.png]]

Mbot: Created page with "{{Part Of Manual|title=the PROPT Manual|link=PROPT Manual}} Optimal Parametric Sensitivity control of a fed-batch reactor ==Problem description== From the paper: ..."

2011-11-02T15:30:15Z

Created page with "{{Part Of Manual|title=the PROPT Manual|link=PROPT Manual}} Optimal Parametric Sensitivity control of a fed-batch reactor ==Problem description== From the paper: ..."

New page

{{Part Of Manual|title=the PROPT Manual|link=[[PROPT |PROPT Manual]]}}

Optimal Parametric Sensitivity control of a fed-batch reactor

==Problem description==

From the paper: J.D. Stigter, K.J. Keesman, 2004, "Optimal Parametric Sensitivity control of a fed-batch reactor", Automatica, 40, 4, pp. 1459-1464.

Programmer: Gerard Van Willigenburg (Wageningen University)

<source lang="matlab">
% Copyright (c) 2009-2009 by Tomlab Optimization Inc.
</source>

==Problem setup==

<source lang="matlab">
toms t

t_f = 250; % Fixed final time
p = tomPhase('p', t, 0, t_f, 25);
setPhase(p)

tomStates x1 x2 x3 x4
tomControls u

% Initial state amd maximum control
xi = [0; 0; 0; 0];
umax = 20;
x = [x1; x2; x3; x4];

% Initial guess
x0 = {icollocate(x == xi)
collocate(u == umax)};

% Box constraints
cbox = {collocate({0 <= u <= umax; 0 <= x1 <= 100})};

% Boundary constraints
cbnd = initial(x == xi);

% Bio kinectic parameters
mu_m = 2.62e-4; Y = 0.64; K_S = 1.0;
X = 4e3; muXY = mu_m*X/Y;

% Sensitivity parameters
q = [1 3e-2]/250;

% Odes: state and state sensitivity dynamics
Kx1 = K_S+x1; Kx12 = Kx1*Kx1;

ceq = collocate({
dot(x1) == -muXY*x1/Kx1 + u
dot(x2) == muXY*(x1-K_S*x2)/Kx12
dot(x3) == -muXY*K_S*x3/Kx12-x1/Kx1
dot(x4) == q(1)*x2*x2+q(2)*x3*x3});

% Objective
objective = -final(x4);
</source>

==Solve the problem==

<source lang="matlab">
options = struct;
options.name = 'Optimal Parametric Sensitivity';
solution = ezsolve(objective, {cbox, cbnd, ceq}, x0, options);

% Plot intermediate results
subplot(2,1,1);
ezplot([x1; x2; x3]); legend('x1','x2','x3');
title('Optimal Parametric Sensitivity controls states');

subplot(2,1,2);
ezplot(u); legend('u');
title('Optimal Parametric Sensitivity controls'); drawnow;
</source>

<pre>
Problem type appears to be: lpcon
Time for symbolic processing: 0.22951 seconds
Starting numeric solver
===== * * * =================================================================== * * *
TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31
=====================================================================================
Problem: --- 1: Optimal Parametric Sensitivity f_k -205.617761338544000000
sum(|constr|) 0.000000048671862886
f(x_k) + sum(|constr|) -205.617761289872130000
f(x_0) 0.000000000000000000

Solver: snopt. EXIT=0. INFORM=1.
SNOPT 7.2-5 NLP code
Optimality conditions satisfied

FuncEv 1 ConstrEv 192 ConJacEv 192 Iter 89 MinorIter 2466
CPU time: 0.234002 sec. Elapsed time: 0.306000 sec.

</pre>