Cushioned Oscillation (PROPT) - Revision history

FelixMueller at 17:49, 31 January 2016

2016-01-31T17:49:48Z

← Older revision		Revision as of 17:49, 31 January 2016
Line 1:		Line 1:
	Below you can find the MATLAB file that was used in [[Category: TomDyn/PROPT \| TomDyn/PROPT]] to create the reference solution and its plot for the [[Cushioned Oscillation]] problem.		Below you can find the MATLAB file that was used in [[:Category: TomDyn/PROPT \| TomDyn/PROPT]] to create the reference solution and its plot for the [[Cushioned Oscillation]] problem.

	<source lang="matlab">		<source lang="matlab">

FelixMueller at 17:49, 31 January 2016

2016-01-31T17:49:38Z

← Older revision		Revision as of 17:49, 31 January 2016
Line 1:		Line 1:
	Below you can find the MATLAB file that was used in [[:Category: ~~Tomdyn~~/PROPT]] to create the reference solution and its plot for the [[Cushioned Oscillation]] problem.		Below you can find the MATLAB file that was used in [[Category: TomDyn/PROPT \| TomDyn/PROPT]] to create the reference solution and its plot for the [[Cushioned Oscillation]] problem.

	<source lang="matlab">		<source lang="matlab">

FelixMueller at 17:49, 31 January 2016

2016-01-31T17:49:12Z

← Older revision		Revision as of 17:49, 31 January 2016
Line 1:		Line 1:
	Below you can find the MATLAB file that was used in [[Category: Tomdyn/PROPT]] to create the reference solution and its plot for the [[Cushioned Oscillation]] problem.		Below you can find the MATLAB file that was used in [[:Category: Tomdyn/PROPT]] to create the reference solution and its plot for the [[Cushioned Oscillation]] problem.

	<source lang="matlab">		<source lang="matlab">

FelixMueller at 17:48, 31 January 2016

2016-01-31T17:48:56Z

← Older revision		Revision as of 17:48, 31 January 2016
Line 1:		Line 1:
	Below you can find the MATLAB file that was used to create the reference solution and its plot.		Below you can find the MATLAB file that was used in [[Category: Tomdyn/PROPT]] to create the reference solution and its plot for the [[Cushioned Oscillation]] problem.

	<source lang="matlab">		<source lang="matlab">

MaxWolff at 13:59, 19 January 2016

2016-01-19T13:59:32Z

← Older revision		Revision as of 13:59, 19 January 2016
Line 38:		Line 38:
	collocate({u == 0		collocate({u == 0
	})		})
	icollocate({x1 == xi(1)		icollocate({x == xi(1)
	x2 == xi(2)		v == xi(2)
	})};		})};

Line 74:		Line 74:

	tfopt = subs(t_f,solution);		tfopt = subs(t_f,solution);
	xopt = subs(x1,solution);		xopt = subs(x,solution);
	vopt = subs(v,solution);		vopt = subs(v,solution);
	uopt = subs(u,solution);		uopt = subs(u,solution);

MaxWolff at 10:27, 18 January 2016

2016-01-18T10:27:54Z

← Older revision		Revision as of 10:27, 18 January 2016
Line 25:		Line 25:
	%Setup		%Setup

	toms t t_f %~~independant~~ variables		toms t t_f %independent variables
	p = tomPhase('p', t, t_0, t_f, n);		p = tomPhase('p', t, t_0, t_f, n);
	setPhase(p);		setPhase(p);

MaxWolff at 10:06, 18 January 2016

2016-01-18T10:06:36Z

← Older revision		Revision as of 10:06, 18 January 2016
Line 16:		Line 16:
	v_0 = 5; %starting velocity in m/s		v_0 = 5; %starting velocity in m/s
	umm = 5; %control constraint		umm = 5; %control constraint
	m = 10; %mass in kg		m = 5; %mass in kg
	c = 10; %spring stiffness in N/m		c = 10; %spring stiffness in N/m

MaxWolff at 00:07, 13 January 2016

2016-01-13T00:07:22Z

← Older revision		Revision as of 00:07, 13 January 2016
Line 103:		Line 103:

	</source>		</source>


			[[Category:TomDyn/PROPT]]

MaxWolff: Created page with "Below you can find the MATLAB file that was used to create the reference solution and its plot. %% Cushioned Oscillation % (c) Maximilian von Wolff %..."

2016-01-13T00:06:52Z

Created page with "Below you can find the MATLAB file that was used to create the reference solution and its plot. <source lang="matlab"> %% Cushioned Oscillation % (c) Maximilian von Wolff %..."

New page

Below you can find the MATLAB file that was used to create the reference solution and its plot.

<source lang="matlab">

%% Cushioned Oscillation
% (c) Maximilian von Wolff
%
%% Problem Setup
%
%
%
%Problem Parameters
t_0 = 0;

x_0 = 2; %starting position
v_0 = 5; %starting velocity in m/s
umm = 5; %control constraint
m = 10; %mass in kg
c = 10; %spring stiffness in N/m

n=80; %Number of collocation points

%Setup

toms t t_f %independant variables
p = tomPhase('p', t, t_0, t_f, n);
setPhase(p);
tomStates x v
tomControls u

%initial states
xi = [x_0; v_0];

%initial guess
x0 = {t_f == 10
collocate({u == 0
})
icollocate({x1 == xi(1)
x2 == xi(2)
})};

%Box constraints
cbox = {-umm <= collocate(u) <= umm
};

%Boundary constraints
cbnd = {initial({ x == xi(1);
v == xi(2);
})
final({ x == 0;
v == 0;
})};

% ODE's

dx = v;
dv = 1./m.*(u-c*x);

ceq = collocate({
dot(x) == dx
dot(v) == dv
});

objective = t_f;

%% Solve the problem
options = struct;
options.name = 'cushioned oscillation';
solution = ezsolve(objective, {cbox, cbnd, ceq}, x0, options);

tfopt = subs(t_f,solution);
xopt = subs(x1,solution);
vopt = subs(v,solution);
uopt = subs(u,solution);

%Plotting solution

figure(1)
subplot(3,1,1);
ezplot(x); legend('x');
xlabel('time');
ylabel('position in m');
title('Position');

subplot(3,1,2);
ezplot(v); legend('v');
xlabel('time');
ylabel('velocity in m/s');
title('Velocity');

subplot(3,1,3);
ezplot(u); legend('u');
xlabel('time');
title('Control');

disp('Final Time');
disp(solution.t_f)

</source>