## Apps.RocketLaunch History

June 21, 2020, at 05:09 AM by 136.36.211.159 -
Deleted lines 125-142:
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Changed lines 29-30 from:
!!!! Solution
to:
!!!! APM MATLAB and APM Python Solution

!!!! Python GEKKO Solution

The GEKKO package is available through the package manager '''pip''' in Python.

python -m pip install gekko

GEKKO Python is designed for large-scale optimization and accesses solvers of constrained, unconstrained, continuous, and discrete problems.

%width=550px%Attach:rocket_launch.png

(:source lang=python:)
import numpy as np
import matplotlib.pyplot as plt
from gekko import GEKKO

# create GEKKO model
m = GEKKO()

# scale 0-1 time with tf
m.time = np.linspace(0,1,101)

# options
m.options.NODES = 6
m.options.SOLVER = 3
m.options.IMODE = 6
m.options.MAX_ITER = 500
m.options.MV_TYPE = 0
m.options.DIAGLEVEL = 0

# final time
tf = m.FV(value=1.0,lb=0.1,ub=100)
tf.STATUS = 1

# force
u = m.MV(value=0,lb=-1.1,ub=1.1)
u.STATUS = 1
u.DCOST = 1e-5

# variables
s = m.Var(value=0)
v = m.Var(value=0,lb=0,ub=1.7)
mass = m.Var(value=1,lb=0.2)

# differential equations scaled by tf
m.Equation(s.dt()==tf*v)
m.Equation(mass*v.dt()==tf*(u-0.2*v**2))
m.Equation(mass.dt()==tf*(-0.01*u**2))

# specify endpoint conditions
m.fix(s, pos=len(m.time)-1,val=10.0)
m.fix(v, pos=len(m.time)-1,val=0.0)

# minimize final time
m.Obj(tf)

# Optimize launch
m.solve()

print('Optimal Solution (final time): ' + str(tf.value))

# scaled time
ts = m.time * tf.value

# plot results
plt.figure(1)
plt.subplot(4,1,1)
plt.plot(ts,s.value,'r-',linewidth=2)
plt.ylabel('Position')
plt.legend(['s (Position)'])

plt.subplot(4,1,2)
plt.plot(ts,v.value,'b-',linewidth=2)
plt.ylabel('Velocity')
plt.legend(['v (Velocity)'])

plt.subplot(4,1,3)
plt.plot(ts,mass.value,'k-',linewidth=2)
plt.ylabel('Mass')
plt.legend(['m (Mass)'])

plt.subplot(4,1,4)
plt.plot(ts,u.value,'g-',linewidth=2)
plt.ylabel('Force')
plt.legend(['u (Force)'])

plt.xlabel('Time')
plt.show()
(:sourceend:)
August 26, 2016, at 05:14 PM by 10.5.113.104 -
August 26, 2016, at 05:13 PM by 10.5.113.104 -

!!!! Problem Statement

minimize tf

subject to
ds/dt = v
dv/dt = (u-0.2*v^2)/m
dm/dt = -0.01 * u^2

path constraints
0.0 <= v(t) <= 1.7
-1.1 <= u(t) <= 1.1

initial boundary conditions
s(0) = 0
v(0) = 0
m(0) = 1

final boundary conditions
s(tf) = 10.0
v(tf) = 0.0

!!!! Solution
August 26, 2016, at 04:51 PM by 10.5.113.104 -
Changed lines 13-30 from:
to:
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<script type="text/javascript">
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(function() {
var dsq = document.createElement('script'); dsq.type = 'text/javascript'; dsq.async = true;
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August 26, 2016, at 04:49 PM by 10.5.113.104 -