PROPT Coloumb Friction 1: Difference between revisions
From TomWiki
Jump to navigationJump to search
(Created page with "{{Part Of Manual|title=the PROPT Manual|link=PROPT Manual}} Minimum-Time Control of Systems With Coloumb Friction: Near Global Optima Via Mixed Integer Linear Progr...") |
No edit summary |
||
Line 1: | Line 1: | ||
{{Part Of Manual|title=the PROPT | {{Part Of Manual|title=the PROPT Manual|link=[[PROPT|PROPT Manual]]}} | ||
Minimum-Time Control of Systems With Coloumb Friction: Near Global Optima Via Mixed Integer Linear Programming, Brian J. Driessen, Structural Dynamics Department, Sandia National Labs. | Minimum-Time Control of Systems With Coloumb Friction: Near Global Optima Via Mixed Integer Linear Programming, Brian J. Driessen, Structural Dynamics Department, Sandia National Labs. | ||
Line 102: | Line 102: | ||
title('Coloumb Friction 1 control'); | title('Coloumb Friction 1 control'); | ||
</source> | </source> | ||
[[File:coloumbFriction1_01.png]] |
Revision as of 14:22, 2 November 2011
This page is part of the PROPT Manual. See PROPT Manual. |
Minimum-Time Control of Systems With Coloumb Friction: Near Global Optima Via Mixed Integer Linear Programming, Brian J. Driessen, Structural Dynamics Department, Sandia National Labs.
4. Numerical Examples
Problem Formulation
Find u over t in [0; t_F ] to minimize
subject to:
% Copyright (c) 2007-2008 by Tomlab Optimization Inc.
Problem setup
toms t
toms t_f
p = tomPhase('p', t, 0, t_f, 60);
setPhase(p);
tomStates q qdot
tomControls u
% Initial guess
x0 = {t_f == 1, icollocate(q == -t)};
% Box constraints
cbox = {-2 <= collocate(u) <= 2
0.001 <= t_f};
% Boundary constraints
cbnd = {initial({q == 0; qdot == 1}), final({q == -1, qdot == 0})};
% ODEs and path constraints
ceq = collocate({
dot(q) == qdot
dot(qdot) == u-sign(qdot)});
objective = t_f;
Solve the problem
options = struct;
options.name = 'Coloumb Friction 1';
constr = {cbox, cbnd, ceq};
solution = ezsolve(objective, constr, x0, options);
t = subs(collocate(p,t),solution);
q = subs(collocate(p,q),solution);
qdot = subs(collocate(p,qdot),solution);
u = subs(collocate(p,u),solution);
Problem type appears to be: lpcon Time for symbolic processing: 0.11257 seconds Starting numeric solver ===== * * * =================================================================== * * * TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31 ===================================================================================== Problem: --- 1: Coloumb Friction 1 f_k 2.070229757012032900 sum(|constr|) 0.000000001042092519 f(x_k) + sum(|constr|) 2.070229758054125600 f(x_0) 1.000000000000000000 Solver: snopt. EXIT=0. INFORM=1. SNOPT 7.2-5 NLP code Optimality conditions satisfied FuncEv 1 ConstrEv 130 ConJacEv 130 Iter 23 MinorIter 676 CPU time: 0.187201 sec. Elapsed time: 0.199000 sec.
Plot result
subplot(2,1,1)
plot(t,q,'*-',t,qdot,'*-');
legend('q','qdot');
title('Coloumb Friction 1 state variables');
subplot(2,1,2)
plot(t,u,'+-');
legend('u');
title('Coloumb Friction 1 control');