rocket.gms : Goddard rocket COPS 2.0 #10
Maximize the final altitude of a vertically launched rocket, using the
thrust as a control and given the initial mass, the fuel mass, and the
drag characteristics of the rocket.
This model is from the COPS benchmarking suite.
See http://www-unix.mcs.anl.gov/~more/cops/.
The number of discretization points can be specified using the command
line parameter. COPS performance tests have been reported for nh = 50,
100, 200, 400
References:
- Dolan, E D, and More, J J, Benchmarking Optimization Software with COPS. Tech. rep., Mathematics and Computer Science Division, 2000.
- Bryson, A E, Dynamic Optimization. Addison Wesley, 1999.
Large Model of Type: NLP
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$Title Goddard rocket COPS 2.0 #10 (ROCKET,SEQ=238)
$ontext
Maximize the final altitude of a vertically launched rocket, using the
thrust as a control and given the initial mass, the fuel mass, and the
drag characteristics of the rocket.
This model is from the COPS benchmarking suite.
See http://www-unix.mcs.anl.gov/~more/cops/.
The number of discretization points can be specified using the command
line parameter. COPS performance tests have been reported for nh = 50,
100, 200, 400
Dolan, E D, and More, J J, Benchmarking Optimization
Software with COPS. Tech. rep., Mathematics and Computer
Science Division, 2000.
Bryson, A E, Dynamic Optimization. Addison Wesley, 1999.
$offtext
$if set n $set nh %n%
$if not set nh $set nh 50
set h intervals / h0 * h%nh%/
scalars
h_0 Initial height / 1 /
v_0 Initial velocity / 0 /
m_0 Initial mass / 1 /
g_0 Gravity at the surface / 1 /
nh Number of intervals in mesh / %nh% /
t_c Thrust constant /3.5/
v_c / 620 /
h_c / 500 /
m_c / 0.6 /
D_c
m_f final mass
c ;
variable final_velocity
positive
variables step step size
v(h) velocity
ht(h) height
g(h) gravity
m(h) mass
t(h) thrust
d(h) drag
equations df(h) Drag function
gf(h) Gravity function
obj
h_eqn(h), v_eqn(h), m_eqn(h);
obj.. final_velocity =e= ht('h%nh%');
df(h).. d(h) =e= D_c*sqr(v(h))*exp(-h_c*(ht(h)-h_0)/h_0);
gf(h).. g(h) =e= g_0*sqr(h_0/ht(h));
h_eqn(h-1).. ht(h) =e= ht(h-1) + .5*step*(v(h) + v(h-1));
m_eqn(h-1).. m(h) =e= m(h-1) - .5*step*(T(h) + T(h-1))/c;
v_eqn(h-1).. v(h) =e= v(h-1)
+ .5*step*((T(h) - D(h) - m(h) *g(h)) /m(h)
+(T(h-1) - D(h-1) - m(h-1)*g(h-1))/m(h-1));
c = 0.5*sqrt(g_0*h_0);
m_f = m_c*m_0;
D_c = 0.5*v_c*(m_0/g_0);
ht.lo(h) = h_0;
t.lo(h) = 0.0;
t.up(h) = T_c*(m_0*g_0);
m.lo(h) = m_f;
m.up(h) = m_0;
ht.fx('h0') = h_0;
v.fx('h0') = v_0;
m.fx('h0') = m_0;
m.fx('h%nh%') = m_f;
ht.l(h) = 1;
v.l(h) = ((ord(h)-1)/nh)*(1 - ((ord(h)-1)/nh));
m.l(h) = (m_f - m_0)*((ord(h)-1)/nh) + m_0;
t.l(h) = t.up(h)/2;
step.l = 1/nh;
* Initial values for intermediate variables
d.l(h) = D_c*sqr(v.l(h))*exp(-h_c*(ht.l(h)-h_0)/h_0);
g.l(h) = g_0*sqr(h_0/ht.l(h));
model rocket /all/;
$if set workspace rocket.workspace = %workspace%;
solve rocket using nlp maximizing final_velocity;
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