Difference between revisions of "Goddart's rocket problem (TACO)"

# ----------------------------------------------------------------
# Rocket problem of Goddart using AMPL and TACO
# (c) Christian Kirches, Sven Leyffer
#
# Source: COPS 3.1 collocation formulation - March 2004
# ----------------------------------------------------------------
include OptimalControl.mod;
 
var t;
 
var tf := 1.0, >= 0.01, <= 1;
 
param v0 := 0.0;
param m0 := 1.0;
param g0 := 1.0;
param h0 := 1.0;
param hc := 500.0;
param vc := 620.0;
param mc := 0.6;
param Tmax := 3.5*g0*m0;
param c := 0.5*sqrt(g0*h0);
param mf := mc*m0;
 
var h >= h0, := 1;
let h.interp_to := h0;
var v >= v0;
let v.interp_to := v0;
var m <= m0;
let m.interp_to := mf;
 
var T >= 0, <= Tmax, := Tmax/2;
let T.type := "u0";
 
param Dc := 0.5*vc*m0/g0;
var D = Dc*v^2*exp(-hc*(h-h0)/h0);
var g = g0*(h0/h)^2;
 
maximize FinalHeight: eval(h,tf);
let FinalHeight.scale := 0.01;
subject to
 
dh: diff(h,t) = v;
dv: diff(v,t) = (T - D)/m - g;
dm: diff(m,t) = -T/c;
 
ih: eval(h,0) = h0;
iv: eval(v,0) = v0;
im: eval(m,0) = m0;
fm: eval(m,tf) = mf;
 
option solver ...;
 
solve;