PROPT Max Radius Orbit Transfer - Revision history

Per: /* Solve the problem */

2012-02-14T09:36:58Z

Solve the problem

← Older revision		Revision as of 04:36, 14 February 2012
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	[[File:maximumOrbitTransfer_01.png]]		[[File:maximumOrbitTransfer_01.png]]

			[[Category:PROPT Examples]]

Mbot at 13:06, 8 November 2011

2011-11-08T13:06:28Z

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	<pre>		<pre>
	Problem type appears to be: lpcon		Problem type appears to be: lpcon
	Time for symbolic processing: 0.~~20447~~ seconds		Time for symbolic processing: 0.17673 seconds
	Starting numeric solver		Starting numeric solver
	===== * * * =================================================================== * * *		===== * * * =================================================================== * * *
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	FuncEv 1 ConstrEv 75 ConJacEv 75 Iter 43 MinorIter 94		FuncEv 1 ConstrEv 75 ConJacEv 75 Iter 43 MinorIter 94
	CPU time: 0.078001 sec. Elapsed time: 0.~~078000~~ sec.		CPU time: 0.078001 sec. Elapsed time: 0.066000 sec.

	</pre>		</pre>
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	<pre>		<pre>
	Problem type appears to be: lpcon		Problem type appears to be: lpcon
	Time for symbolic processing: 0.~~19188~~ seconds		Time for symbolic processing: 0.17837 seconds
	Starting numeric solver		Starting numeric solver
	===== * * * =================================================================== * * *		===== * * * =================================================================== * * *
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	FuncEv 1 ConstrEv 15 ConJacEv 15 Iter 13 MinorIter 158		FuncEv 1 ConstrEv 15 ConJacEv 15 Iter 13 MinorIter 158
	CPU time: 0.~~062400~~ sec. Elapsed time: 0.~~061000~~ sec.		CPU time: 0.046800 sec. Elapsed time: 0.057000 sec.

	</pre>		</pre>

Mbot at 18:24, 2 November 2011

2011-11-02T18:24:29Z

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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]]}}

	==Problem description==		==Problem description==
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	title('Spacecraft controls');		title('Spacecraft controls');
	</source>		</source>

			[[File:maximumOrbitTransfer_01.png]]

Mbot: Created page with "{{Part Of Manual|title=the PROPT Manual|link=PROPT Manual}} ==Problem description== Maximum radius orbit transfer of a spacecraft. Applied Optimal Control, Bryson..."

2011-11-02T15:29:54Z

Created page with "{{Part Of Manual|title=the PROPT Manual|link=PROPT Manual}} ==Problem description== Maximum radius orbit transfer of a spacecraft. Applied Optimal Control, Bryson..."

New page

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

==Problem description==

Maximum radius orbit transfer of a spacecraft.

Applied Optimal Control, Bryson & Ho, 1975. Example on pages 66-69.

Programmers: Gerard Van Willigenburg (Wageningen University) Willem De Koning (retired from Delft University of Technology)

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

==Problem setup==

<source lang="matlab">
% Array with consecutive number of collocation points
narr = [20 40];

toms t;
t_f = 1; % Fixed final time

for n=narr
</source>

<source lang="matlab">
p = tomPhase('p', t, 0, t_f, n);
setPhase(p)

tomStates x1 x2 x3
tomControls u1

% Parameters
r0 = 1; mmu = 11; th = 1.55;
m0 = 1; rm0 = -0.25;

% Initial state
xi=[r0; 0; sqrt(mmu/r0)];

% Initial guess
if n==narr(1)
x0 = {icollocate({x1 == xi(1); x2 == xi(2); x3 == xi(3)})
collocate({u1 == 0})};
else
x0 = {icollocate({x1 == xopt1; x2 == xopt2; x3 == xopt3})
collocate({u1 == uopt1})};
end

% Boundary constraints
cbnd = {initial({x1 == xi(1); x2 == xi(2); x3 == xi(3)})
final({x3 == sqrt(mmu/x1); x2 == 0})};

% ODEs and path constraints
dx1 = x2;
dx2 = x3.*x3./x1-mmu./(x1.*x1)+th*sin(u1)./(m0+rm0*t);
dx3 = -x2.*x3./x1+th*cos(u1)./(m0+rm0*t);

ceq = collocate({
dot(x1) == dx1
dot(x2) == dx2
dot(x3) == dx3});

% Objective
objective = -final(x1);
</source>

==Solve the problem==

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

xopt1 = subs(x1,solution);
xopt2 = subs(x2,solution);
xopt3 = subs(x3,solution);
uopt1 = subs(u1,solution);
</source>

<pre>
Problem type appears to be: lpcon
Time for symbolic processing: 0.20447 seconds
Starting numeric solver
===== * * * =================================================================== * * *
TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31
=====================================================================================
Problem: --- 1: Spacecraft f_k -1.526286382793850200
sum(|constr|) 0.000000153661967715
f(x_k) + sum(|constr|) -1.526286229131882400
f(x_0) -0.999999999999998220

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

FuncEv 1 ConstrEv 75 ConJacEv 75 Iter 43 MinorIter 94
CPU time: 0.078001 sec. Elapsed time: 0.078000 sec.

</pre>

<pre>
Problem type appears to be: lpcon
Time for symbolic processing: 0.19188 seconds
Starting numeric solver
===== * * * =================================================================== * * *
TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31
=====================================================================================
Problem: --- 1: Spacecraft f_k -1.526020732841174300
sum(|constr|) 0.000002928423841178
f(x_k) + sum(|constr|) -1.526017804417333100
f(x_0) -1.526286382793840000

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

FuncEv 1 ConstrEv 15 ConJacEv 15 Iter 13 MinorIter 158
CPU time: 0.062400 sec. Elapsed time: 0.061000 sec.

</pre>

<source lang="matlab">
end

% Get final solution
t = subs(collocate(t),solution);
x1 = subs(collocate(x1),solution);
x2 = subs(collocate(x2),solution);
x3 = subs(collocate(x3),solution);
u1 = subs(collocate(u1),solution);

%Bound u1 to [0,2pi]
u1 = rem(u1,2*pi); u1 = (u1<0)*2*pi+u1;

% Plot final solution
subplot(2,1,1)
plot(t,x1,'*-',t,x2,'*-',t,x3,'*-');
legend('x1','x2','x3');
title('Spacecraft states');

subplot(2,1,2)
plot(t,u1,'+-');
legend('u1');
title('Spacecraft controls');
</source>